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k 



VOCATIONAL 
MATHEMATICS 



FOR GIRLS 



BY 

WILLIAM H. DOOLEY 

AUTHOR OP ** VOCATIONAL MATHEMATICS*' 
"TBXTILB8," ETC. 



t J , o 



» 






D. C. HEATH & CO., PUBLISHERS 
BOSTON NEW YORK CHICAGO 



\ ^ ^^^ '^ 



Copyright, 1917, 
By D. C. Hkath & Co. 

IB7 



u O WW bwccc 

w 



PREFACE 

The author has had, during the last ten years, considerable 
experience in organizing and conducting intermediate and sec- 
ondary technical schools for boys and girls. During this time 
he has noticed the inability of the average teacher in mathe- 
matics to give pupils pmctical applications of the subject. 
Many teachers are not familiar with the commercial and rule 
of thumb methods of solving mathematical problems of every- 
day life. Too often a girl graduates from the course in mathe- 
matics without being able to "commercialize" or apply her 
mathematical knowledge in such a way as to meet the needs 
of trade, commerce, and home life. 

It is to overcome this difficulty that the author has prepared 
this book on vocational mathematics for girls. He does not 
believe in omitting the regular secondary school course in 
mathematics, but offers vocational mathematics as an introduc- 
tion to the regular course. 

The problems have been used by the author during the past 
few years with girls of high school age. . The method of teach- 
ing has consisted in arousing an interest in mathematics by 
showing its value in daily life. Important facts^ based upon 
actual experience and observation, are recalled to the pupil's 
mind before she attempts to solve the problems. 

A discussion of each division of the subject usually precedes 
the problems. This information is provided for the regular 
teacher in mathematics who may not be familiar with the 
subject or the terms used. The book contains samples of 

• • • 

111 

4!283o 



IV PREFACE 

problems from all occupations that women are likely to enter, 
from the textile mill to the home. 

The author has received valuable suggestions from his for- 
mer teachers and from the following: Miss Lilian Baylies 
Green, Editor Ladies'^ Home Journal, Philadelphia, Pa. ; Miss 
Bessie Kingman, Brockton High School, Brockton, Mass. ; Mrs. 
Ellen B. McGowan, Teachers College, New York City ; Miss 
Susan Watson, Instructor at Peter Bent Brigham Hospital, 
Boston; Mr. Frank F. Murdock, Principal Normal School, 
North Adams, Mass. ; Mr. Frank Rollins, Principal Bushwick 
High School, Brooklyn ; Mr. George M. Lattimer, Mechanics 
Institute, Rochester, N. Y. ; Mr. J. J. Eaton, Director of In- 
dustrial Arts, Yonkers, N. Y. ; Dr. Mabel Belt, Baltimore, Md. ; 
Mr. Curtis J. Lewis, Philadelphia, Pa. ; Mrs. F. H. Consalus, 
Washington Irving High School, New York City ; Miss Griselda 
Ellis, Girls' Industrial School, Newark, N. J. ; Mr. J. C. Dono- 
hue. Technical High School, Syracuse, N. Y. ; Mr. W. E. Weafer, 
Hutchinson-Central High School, Buffalo, N. Y. ; The Bur- 
roughs Adding Machine Company ; The Women's Educational 
and Industrial Union ; the Department of Agriculture, Wash- 
ington, D. C. ; and Reports of Conference of New York State 
Vocational Teachers. 

This preface would not be complete without reference to 
the author's wife, Mrs. Ellen V. Dooley, who has offered many 
valuable suggestions and corrected both the manuscript and 
the proof. 

The author will be pleased to receive any suggestions or 
corrections from any teacher. 



CONTENTS 

PART I— REVIEW OF ARITHMETIC 

OHAPTKR PAGK 

I. Essentials of Arithmetic .... . . 1 

Fundamental Processes; Fractions; Decimals; Com- 
pound Numbers ; Percentage ; Ratio and Proportion ; 
Involution ; Evolution. 

11. Mensuration . . . . * . , . . . .64 

Circles ; Triangles ; Quadrilaterals ; Polygons ; Ellipses ; 
Pyramid ; Cone ; Sphere ; Similar Figures. 

in. Interpretation of Results 80 

Reading of Blue Print ; Plans of a Home ; Drawing to 
Scale ; Estimating Distances and Weight ; Methods of 
Solving Examples. 

PART II — PROBLEMS IN HOMEMAKING 

IV. The Distribution of Income 89 

Incomes of American Families ; Division of Income ; 
Expense Account Book. 

V. Food ^100 

Different Kinds of Food ; Kitchen Weights and Meas- 
ures ; Cost of Meals ; Recipes ; Economical Marketing. 

VI. Problems on the Construction of a House . . 128 

Advantages of Different Types of Houses; Building 
Materials; Taxes; United States Revenue. 

VII. Cost of Furnishing a House 146 

Different Kinds of Furniture ; Hall ; Floor Coverings ; 
Linen ; Living Room ; Bedroom ; Dining Room ; Value 
of Coal ; How to Read Gas Meters ; How to Read Elec- 
tric Meters ; Heating. 

V 



vi CONTENTS 

CHAPTXB PAOB 

VIII. Thrift and Investment 178 

Different Institutions of Savings ; Bonds ; Stocks ; Ex- 
change; Insurance. 

PART III — DRESSMAKING AND MILLINERY 

IX. Problems in Dressmaking 198 

Fractions of a Yard; Tucks; Hem; Rufles; Cost of 
Finished Garments ; Millinery Problems. 

X. Clothing 217 

Parts of Cloth ; Materials of Yam ; Kinds ; Weight. 

PART IV— THE OFFICE AND THE STORE 

XL Arithmetic for Office Assistants .... 233 

Rapid Calculations ; Invoices ; Profit and Loss ; Time 
Sheets and Pay Rolls. 

XII. Arithmetic for Salesgirls and Cashiers . . 260 
Saleslips ; Extensions ; Making Change. 

XIIL Civil Service 268 

PART V — ARITHMETIC FOR NURSES 

XIV. Arithmetic for Nurses 276 

Apothecary ^s Weights and Measures ; Household Meas- 
ures; Approximate Equivalents of Metric and English 
Weights and Measures ; Doses ; Strength of Solutions ; 
Prescription Reading. 

PART VI — PROBLEMS ON THE FARM 
XV. Problems on the Farm 304 

Appendix 317 

Metric System ; Graphs ; Formulas ; Useful Mechanical 
Information. 

Index 365 






VOCATIONAL MATHEMATICS 

FOR GIRLS 

PART I — REVIEW OF ARITHMETIC 

CHAPTER I 

Notation and Numeration 

A unit is one thing ; as, one book, one pencil, one inch. 
A number is made up of units and teUs how many units are 
taken. 

An integer is a whole number. 

A single figure expresses a certain number of units and is said to be in 
the units coiumn. For example, 6 or 8 is a single figure in the units 
column ; 63 is a number of two figures and has the figure 3 in the units 
column and the figure 6 in the tens column, for the second figure 
represents a certain number of tens. Each column has its own name, 
as shown below. 



•o 



63 . o S ^ 

i I . § - 

alls 



? 


• 
a 




s 


1 


p 

2 


m 
a 


1 


•c 


wo 


o 


•o 


c 


• 

a 
S 


2 


s 



a 



1 3 8, 69 5, 40 7, 125 

Reading Numbers. — For convenience in reading and writing 
numbers they are separated into groups of three figures each 
by commas, beginning at the right : 

138,695,407,125. 
The first group is 125 units. 
The second group is 407 thousands. 
The third group is 695 millions. 
The fourth group is 138 billions. 

1 



••: ••• 



• • • 






• •, 



• • • • • 



2 A:icgC5AjRt6Ni/!tIw/M^^ FOR GIRLS 

The preceding number is read one hundred thirty-eight 
billion, six hundred ninety-five million, four hundred seven 
thousand, one hundred twenty-five ; or 138 billion, 695 million, 
407 thousand, 125. 

Roman Numerals 

A knowledge of Roman numerals is very important. Dates 
in buildings and amounts on prescriptions are usually expressed 
in Roman numerals. They are also used for numbering 
chapters and dials. The following capital letters, seven in 
all, are used to express Roman numerals : 



I 


II 


V 


X 


L 


C 


D 


M 


One 


Two 


Five 


Ten 


Fifty 


100 


600 


1000 



All other numbers are expressed by combining the letters 
according to the following principles ; 

1. When a letter is repeated, the value is repeated. Thus, 
II represents 2 ; XXX, 30. 

2. When a letter of less value is placed after one of greater 
value, the lesser is added to the greater. Thus, VII, 7 — two 
added to five. 

3. When a letter of less value is placed before one of greater 
value, the lesser is taken from the greater. Thus, IX, 9 — ten 
less one. 

Read the following Roman numeral? according to the above 
rules: 



1. 


Ill 


9. 


XIX 


17. 


LXVI 


2. 


XXX 


10. 


LXXVII 


18. 


MDC 


3. 


ccc 


11. 


DCCCVII 


19. 


LXXII 


4. 


MMM 


12. 


XL 


20. 


CCLI 


5. 


VII 


13. 


XC 


21. 


DCLXVI 


6. 


LXXX 


14. 


IX 


22. 


DCXIV 


7. 


XXII 


15. 


XD 


23. 


MD^LVI 


8. 


XVIII 


16. 


XM 


24. 


Mi>CCXXIX 



REVIEW OF ARITHMETIC 



Express the following numbers in Roman numerals : 

1. 14 4. 81 7. 281 10. 314 13. 1837 

2. 42 5. 73 a 509 11. 573 14. 1789 

3. 69 6. 67 9. 812 12. 874 15. 80,003 

Standard Mathematics Sheet. — To avoid errors in solving problems 
the work should be done in such a way as to show each step and to make 
it easy to check the answer when found. Paper of standard size, 8| in. 
by 11 in., should be used. Rule each sheet as in the following diagram, 
set down each example with its proper number in the margin, and clearly 
show the different steps required for the solution. To show that the 
answer obtained is correct, the proof should follow the example. 

Standard Mathematics Sheet 







8i in. 


• 

1. 


t 


Mary Smith — 100 
Vocational Mathematics 

10-2-12 No. 10 


1,203 2^ 
2,672 2j;f 
31,118 23 
480 1^ 
39 
19,883 

'66,396 Ans. 


2. 


Proof: 


9 


3. 





. The pupil should write or print her name and class, the date when the 
problem is finished, and the number of the problem on the Standard 



4 VOCATIONAL MATHEMATICS FOR GIRLS 

Mathematics Sheet. If the question contains several divisions or prob- 
lems, they should be tabulated — (a), (6), etc. — at the left of the prob- 
lems inside the margin line. A line should be drawn between problems 
to separate them. 

Addition 

Addition is the process of finding the sum of two or more 
numbers. The result obtained by this process is called the 
sum or amount 

The sign of addition is an upright cross, +, called plus. The 
sign is placed between the two numbers to be added. 

Thus, 9 inches + 7 inches (read nine inches plus seven inches). 

The sign of equality is two short horizontal parallel lines, =, 
and means equals or is equal to. 

Thus, the statement that 8 feet + 6 feet = 14 feet, means that six feet 
added to eight feet (or 8 feet plus 6 feet) equals fourteen feet. 

To find the sum or amount of two or more numbers. 

Example. — An agent for a flour mill sold the following num- 
ber of barrels of flour during the day : 1203, 2672, 31,118, 480, 
39, and 19,883 bbl. How many barrels did he sell during the 

day? 

[The abbreviation for barrels is bbl.] 

The sum of the units column is 3 + 9 + 
+ 8 + 2 + 8 = 26 units, or 20 and 6 more ; 
20 is tens, so leave the 5 under the units 
column and add the 2 tens in the tens column. 
The sum of the tens column 182 + 8 + 3 + 8 
+ 1+7 + = 29 tens. 29 tens equal 2 hun- 
dreds and 9 tens. Place the 9 tens under 
Sum 55,395 bbl. the tens column and add the 2 hundreds 

to the hundreds column. 2+8 + 4 + 1+6 
+ 2 = 23 hundreds ; 23 hundreds are equal to 2 thousands and 3 hundreds. 
Place the 3 hundreds under the hundreds column and add the 2 thousands 
to the next column. 2 + 9 + 1 + 2+1 = 15 thousands, or 1 ten-thousand 
and 6 thousands. Add the 1 ten-thousand to the ten-thousands column 



1,203 


2^ 


2,672 


2? 


31,118 


2^ 


480 


^ 


39 




19,883 





REVIEW OF ARITHMETIC 5 

and the sum is 1 + 1 + 3 = 5. Write the 5 in the ten-thousands column. 
Hence, the sum is 55,396 bbl. 

Test. — Repeat the process, beginning at the top of the right-hand 
column. 

4 

Exactness is very important in arithmetic. There is only 
one correct answer. Therefore it is necessary to be accurate 
in performing the numerical calculations. A check of some 
kind should be made on the work. The simplest check is to 
estimate the answer before solving the problem. If there is 
a great discrepancy between the estimated answer and the 
answer in the solutioiij the work is probably wrong. It is 
also necessary to be exact in reading the problem. 

EXAMPLES 

1. Write the following numbers as figures and add them : 
Seventy-five thousand three hundred eight ; seven million two 
hundred five thousand eight hundred forty-nine. 

2. In a certain year the total output of copper from the 
mines was worth $ 58,638,277.86. Express this amount in words. 

3. Solve the following : 

386 + 5289 + 53666 + 3001 + 291 + 38 = ? 

4. The cost of the Panama Canal was estimated in 1912 to 
be $ 375,000,000. Express this amount in words. 

5. A farmer's wife received the following number of eggs 
in four successive weeks ; 692, 712, 684, and 705 eggs. How 
many eggs were received during the four weeks ? 

6. A woman buys a two-family house for $6511.00. She 
makes the following repairs : mason-work, $ 112.00 ; plumb- 
ing, $ 146.00 ; carpenter work, $ 208.00 ; painting and decora- 
ting, $ 319.00. How much does the house cost her ? 

7. Add the following numbers, left to right : 

a. 108, 219, 374, 876, 763, 489, 531, 681, 104 ; 
h. 3846, 5811, 6014, 8911, 7900, 3842, 5879. 



6 VOCATIONAL MATHEMATICS FOR GIRLS 

8. According to the census of 1910 the population of the 
United States, exclusive of the outlying possessions, consisted 
of 47,332,277 males and 44,639,989 females. What was the 
total population? 

9. Wire for electric lights was run around four sides of 
three rooms. If the first room was 13 ft. long and 9 ft. wide ; 
the second 18 ft. long and 18 ft. wide ; and the third 12 ft. 
long and 7 ft. wide, what was the total length of wire re- 
quired? Remember that electric lights require two wires. 

10. Find the sum : 

46 lb. + 136 lb. + 72 lb. + 39 lb. + 427 lb. + 64 lb. + 139 lb. 

Subtraction 

Subtraction is the process of finding the difference between 
two numbers, or of finding what number must be added to a 
given number to equal a given sum. The minuend is the num- 
ber from which we subtract; the subtrahend is the number 
subtracted ; and the difference or remainder is the result of the 
subtraction. 

The sign of subtraction is a short horizontal line, — , called 
minus, and is placed before the number to be subtracted. 

Thus, 12 — 8 = 4 is read twelve minus (or less) eight equals four. 

To find the difference of two numbers. 

Example. — A house was purchased for $ 8074.00 twenty- 
five years ago. It was recently sold at auction for $ 4869.00. 

What was the loss ? 

Write the smaller number under the 

Minuend $8074.00 greater, with units of the same order in 

Subtrahend $4869.00 ^® same vertical line. 9 cannot be taken 

Remainder $3205.00 ^""^^ ^» ^ ^^^^^^ ^ *®° ^ ^°^*«- '^^ ^ 

ten that was changed from the 7 tens 

makes 10 units, which added to the 4 units makes 14 units. Take 9 
from the 14 units and 6 units remain. Write the 6 under the unit col- 
umn. Since 1 ten was changed from 7 tens, there are 6 tens left, and 6 
from 6 leaves 0. Write under the tens column. Next, 8 hundred can- 



REVIEW OF ARITHMETIC 7 

not be taken from hundred, so 1 thousand (ten hundred) is changed 
from the thousands column. 8 hundred from 10 hundred leave 2 hun- 
dred. Write the 2 under the hundreds column. Since 1 thousand has 
been taken from the 8 thousand, there are left 7 thousand to subtract the 
4 thousand from, which leaves 3 thousand. Write 3 under the thousand 
column. The whole remainder is $3206.00. 

Proof. — If the sum of the subtrahend and the remainder equals the 
minuend, the answer is correct. 

EXAMPLES 

1. Subtract 1001 from 79,999. 

2. A box contained one gross (144) of wood screws. If 48 
screws were used on a job, how many screws were left in the 
box? 

3. What number must be added to 3001 to produce a sum 
of 98,322 ? 

4. Barrels are usually marked with the gross weight and tare 
(weight of empty barrel). If a barrel of sugar is marked 329 
lb. gross weight and 19 lb. tare, find the net weight of sugar. 

5. A box contains a gross (144) of pencils. If 109 are 
removed, how many remain? 

6. A farmer received 1247 quarts of milk in October and 
1189 quarts in November. What was the difference ? 

7. A housewife purchases a $ 800.00 baby grand piano for 
$ 719.00. How much does she save ? 

8. No. 1 cotton yarn contains 840 yards to the pound, 
while No. 1 worsted yarn contains 560 yards to the pound. 
What is the difference in length? 

9. A young lady saved $453.00 during five years. She 
spent ^189.00 on a sea trip. How much remained? 

10. 69,221-3008=? 

11. The population of New York City in 1900 was 3,437,202 
and in 1910 was 4,766,883. What was the increase from 1900 
to 1910 ? 



8 VOCATIONAL MATHEMATICS FOR GIRLS 

12. If there are 374,819 wage-earning women in a certain 
city having a total population of 3,366,416 persons, how many of 
the residents are not wage-earning women ? 

13. In the year 1820 only 8385 immigrants arrived in the 
United States. In 1842, 104,565 immigrants arrived. How 
many more arrived in 1842 than in 1820 ? 

14. The first great shoemaker settled in Lynn, Mass., in 
1636. How many years is it since he arrived in Lynn ? 

» 

Multiplication 

Multiplication is the process of finding the product of two 

numbers. 

ThuSf 8x3 may be read 8 multiplied by 3, or 8 times 3, and means 
8 added to itself 3 times, or 8 + 8 + 8 = 24 and 8 x 3 = 24. 

The numbers multiplied together are called factors. The 
mvltiplicand is the number multiplied; the multiplier is the 
number multiplied by ; and the result is called the product. 

The sign of multiplication is an oblique cross, x, which 
means multiplied by or tim£8. 

Thus, 7x4 may bq read 7 multiplied by 4, or 7 times 4. 

To find the product of two numbers. 

Example. — A certain set of books weighs 24 lb. What is 

the weight of 17 sets ? 

Write the multiplier under the multipli- 

Multiplicand 24 lb. cand, units under units, tens under tens. 

Multiplier 17 etc. 7 times 4 units equal 28 units, which 

J^ are 2 tens and 8 units. Place the 8 under 

OA the units column. The 2 tens are to be 

T^ 7 ^ 17\o ii_ added to the tens product. 7 times 2 tens 

Product 408 lb. - . , . .v o * i« * i 

are 14 tens + the 2 tens are 16 tens, or 1 

hundred and 6 tens. Place the 6 tens in the tens column and the 1 hun- 
dred in the hundreds column. 168 is a partial product. To multiply by 
the 1, proceed as before, but as 1 is a ten, write the first number, which 
is 4 of this partial product, under the tens column, and the next number 
under the hundreds column, and so on. Add the partial products, and 
their sum is tte whole product, or 408 lb. 



REVIEW OF ARITHMETIC 9 

« 

EXAMPLES 

1. A milliner ordered 58 spools of wire, each spool contain- 
ing 100 yards. How many yards did she order ill all ? 

2. Each shoe box contains 12 pairs of shoes. How many 
pairs in 423 boxes ? 

3. Multiply 839 by 291. 

4. A mechanic sent in the following order for bolts : 12 
bolts, 6 lb. each ; 9 bolts, 7 lb. each ; 11 bolts, 3 lb. each ; 6 
bolts, 2 lb. each; and 20 bolts, 3 lb. each. What was the 
total weight of the order ? 

5. Find the product of 1683 and «09. 

To multiply by 10, 100, 1000, ete., annex as many ciphers to 
the multiplicand as there are ciphers in the mvUiplier. 

Example. — 864 x 100 = 86,400. 

EXAMPLES 

Multiply and read the answers to the following : 

1. 869 X 10 a 100 X 500 

2. 1011 X 100 9. 1000 X 900 

3. 10,389 X 1000 10. 10,000 x 500 

4. 11,298x30,000 11. 10,000x6000 

5. 58,999 X 400 12. 1,000,000 x 6000 

6. 681,719x10 13. 1,891,717x400 

7. 801,369 X 100 14. 10,000,059 x 78,911 

Division 

Diyision is the process of finding how many times one num- 
ber is contained in another. The dividend is the number to be 
divided; the divisor is the number by which the dividend is 
divided; the quotient is the result of the division. When a 
number is not contained an equal number of times in another 
number, what is left over is called a remainder. 



12 VOCATIONAL MATHEMATICS FOR GIRLS 

REVIEW EXAMPLES 

1. A farmer's daughter raised on the farm 5 loads of pota- 
toes containing 38 bu., 29 bu., 43 bu., 39 bu., and 29 bu. 
respectively. She sold 12 bu. to each of three families, and 
34 bu. to each of four families. How many bushels were 
left ? 

2. Five pieces of cloth are placed end to end. If each 
piece contains 38 yards, what is the total length ? 

3. I bought a chair for $ 3, a mat for $ 1, a table for 
$4, and gave in payment a $20 bill. What change did I 
receive ? 

4. A teacupful contains 4 fluid ounces. How many teacup- 
fuls in 64 fluid ounces ? 

5. No. 30 cotton yarn contains 25,200 yards to a pound. 
How many pounds of yarn in 630,000 yards ? 

6. The consumption of water in a city during the month 
of December was 116,891,213 gallons and during January 
115,819,729 gallons. How much was the decrease in con- 
sumption ? 

7. An order to a machine shop called for 598 sewing 
machines each weighing 75 pounds. What was the total weight ? 

8. If a strip of carpet weighs 4 lb. per foot of length, find 
the weight of one measuring 16' 9" in length. 

9. Multiply 641 and 225. 

10. Divide 24,566 by 319. 

11. An order was given for ties for a railroad 847 miles 
long. If each' mile required 3017 ties, how many ties would be 
needed ? 

12. How many gallons of milk are used every day by 
two hospitals, if one uses 25 gallons per day and the other 6 
gallons less ? 



REVIEW OF ARITHMETIC 13 

Factors 

The factors of a number are the integers which when multi- 
plied together produce that number. 

Thus, 21 is the product of 3 and 7 ; hence, 3 and 7 are the factors of 21. 

Separating a number into its factors is called factoring, 
A number that has no factors but itself and 1 is a prime 
number. 

The prime numbers up to 25 are 2, 3, 5, 7, 11, 13, 17, 19 and 23. 

A prime number used as a factor is 2l priyne factor. 

Thus, 3 and 5 are prime factors of 15. 

Every prime number except 2 and 5 ends with 1, 3, 7, or 9. 

To find the prime factors of a number. 

Example. — Find the prime factors of 84. 

2 )84 The prime number 2 divides 84 evenly, leaving the quotient 

2)42 ^^» which 2 divides evenly. The next quotient is 21 which 3 



3)21 



divides, giving a quotient 7. 7 divided by 7 gives the last 
quotient 1 which is indivisible. The several divisors are the 
IL prime factors. So 2, 2, 3, and 7 are the prime factors 
1 of 84. 
Pboof. — The product of the prime factors gives the number. 

EXAMPLES 

Find the prime factors : 

1. 63 4. 636 7. 1155 

2. 60 5. 1572 8. 7007 

3. 250 6. 2800 9. 13104 

Cancellatioii 

To reject a factor from a number divides the number by that 
factor ; to reject the same factors from both dividend and divisor 
does not affect the quotient. This process is called cancellation. 

This method can be used to advantage in many everyday cal- 
culations. 

Example. — Divide 12 x 18 x 30 by 6 x 9 x 4. 



14 VOCATIONAL MATHEMATICS FOR GIRLS 



2 2 15 By *'^^ method it is not 

Dividend 12 X 18 X M ,_ „ ,. , necessary to multiply be- 

Divisor % X 9 X 4 = ^^ Q«o«w««. fore dividing. Indicate 

[s ^ ^ the division by writing 

^ ^ r the divisor under the divi- 

1 dend with a line between. 

Since 6 is a factor of 6 
and 12f and 9 of 9 and 18, respectively, they may be cancelled from both 
divisor and dividend. Since 2 in the dividend is a factor of 4 in the 
divisor it may be cancelled from both, leaving 2 in the divisor. Then the 
2 being a factor of 30 in the dividend, is cancelled from both, leaving 15. 
The product of the uncancelled factors is 30. Therefore, the quotient 
is 30. 

Proof. — If the product of the divisor and the quotient equal the 
dividend, the answer is correct. 

EXAMPLES 

Indicate and find quotients by cancellation : 

1. Divide 36 x 27 x 49 x 38 x 50 by 70 x 18 x 15. 

2. What is the quotient of 36 x 48 X 16 divided by 27 X 24 
X8? 

3. How many pounds of tea at 50 cents a pound must be 
given in exchange for 15 pounds of butter at 40 cents a 
pound? 

4. There are 16 ounces in a pound ; 30 pounds of steel will 
produce how many horseshoes, if each weighs 6 ounces ? 

5. Divide the product of 10, 75, 9, and 96 by the product of 
5, 12, 15, and 9. 

6. I sold 16 dozen eggs at 30 cents a dozen and took my 
pay in butter at 40 cents a pound ; how many pounds did I 
receive ? 

7. A dealer bought 16 cords of wood at $ 4 a cord and sold 
them for $ 96 ; find the gain per cord. 



REVIEW OF ARITHMETIC 15 



Greatest Common Divisor 

The greatest common divisor of two or more numbers is the 
greatest number that will exactly divide each of the numbers. 

To find the greatest common divisor of two or more numbers. 

Example. — Find the greatest common divisor of 90 and 

160. 

90 = 2x3x5x3 2)90 150 First Method 

150 =2x3x5x5 • 5 )45 75 The prime factors com- 

Ans. 30 = 2 X 3 X 5 3 )9 15 ™<^» ^^ both 90 and 150 

Q g are 2, 3, and 5. Since 

2 X 3 X 5 = 30 Ans. *^® greatest common di- 

visor of two or more num- 

90)150(1 l>ers is the product of 

QQ their common factors, 30 

^vQ^/^ is. the greatest common 

w;^^.-^ divisor of 90 and 160. 



Second Method 



60 

GHreatest Common Divisor 30)60(2 

^Q To find the greatest 

— common divisor when 

the numbers cannot be readily factored, divide the larger by the smaller, 
then the last divisor by the last remainder until there is no remainder. 
The last divisor wiU be the greatest common divisor. If the greatest com- 
mon divisor is to be found of more than two numbers, find the greatest 
common divisor of two of them, then of this divisor and the third num- 
ber, and so on. The last divisor will be the greatest common divisor of 
all of them. 

EXAMPLES 

Find the greatest common divisor : 

1. 270,810. 3. 504,560. 5. 72,153,315,2187. 

2. 264,312. 4. 288,432,1152. 

Least Common Multiple 

The product of two or more numbers is called a multiple of 
each of them; 4, 6, 8, 12 are multiples of 2. The common 



16 VOCATIONAL MATHEMATICS FOR GIRLS 

multiple of two or more numbers is a number that is divisible 
by each of the numbers without a remainder ; 60 is a common 
multiple of 4, 5, 6. 

The least common multiple of two or more numbers is the 
smallest common multiple of the number; 30 is the least 
common multiple of 3, 5, 6. 

To find the least common multiple of two or more numbers. 

Example. — Find the least common multiple of 21, 28, 

^d 30. • . , „^, , 

.. First Method 

21 = 3 X 7 Take all the factors of the first number, all of 

28 = 2 X 2 X T the second not already represented in the first, etc. 
30 = 2 X 3 X 5 Thus, 

3 X 7 X 2 X 2 X 5 = 420 i. a JJf. 

Second Method 

2 )21 28 30 

3)21 14 15 

7 )7 14 5 

12 5 

2 X 3 X 7 X 1 X 2 X 5 = 420 i. a JIf. 

Divide any two or more numbers by a prime factor contained in them, 
like 2 in 28 and 80. Write 21 which is not divided by the 2 for the next 
quotient together with the 14 and 16. 3 is a prime factor of 21 and 15 
which gives a quotient of 7 and 6 with 14 written in the quotient undi- 
vided. 7 is a prime factor of 7 and 14 which gives a remainder of 1, 2 ; 
and 6 midivided is written down as before. The product 420 of all these 
divisors and the last quotients is the least common multiple of 21, 28, 
and 30. 

EXAMPLES 

Find the least common multiple : 

1. 18, 27, 30. 2. 15, 60, 140, 210. 3. 24, 42, 54, 360. 

4. 25, 20, 35, 40. 5. 24, 48, 96, 192. 

6. What is the shortest length of rope that can be cut into 
pieces 32', 36', and 44' long ? 



REVIEW. OF ARITHMETIC 17 

Fractions 

A fraction is one or more equal parts of a unit. If an apple 
be divided into two equal parts, each part is one-half of the 
apple, and is expressed by placing the number 1 above the 
number 2 with a short line between: ^. A fraction always 
indicates division. In ^, 1 is the dividend and 2 the divisor; 
1 is called the numerator and 2 is called the denominator, 

A common fraction is one which is expressed by a numerator 
written above a line and a denominator below. The nu- 
merator and denominator are called the terms of the fraction, 

A proper fraction is a fraction whose value is less than 1 j its 
numerator is less than its denominator, as |, |, f,, -J^. An 
improper fraction is a fraction whose value is 1 or more than 1 ; 
its numerator is equal to or greater than its denominator, as f, 
\^, A number made up of an integer and a fraction is a 
mixed number. Read with the word and between the whole 
number and the fraction : 4y»^, 3|^, etc. 

The value of a fraction is the quotient of the numerator 
divided by the denominator. • 



EXERCISE 



Bead the following : 






1. 1 3. 12^ 


s. H 


7- 9^ 


2. \i 4. 8J 


6. 6J 


8- 12^ 



». i 



Reduction of Fractions 

Reduction of fractions is the process of changing their form 
without changing their value. 

To reduce a fraction to higher terms. 

Multiplying the denominator and the numerator of the given 
fraction by the same number does not change the volume of the 
fraction. 



18 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — Reduce | to thirty-seconds. 

The denominator must be multiplied by 4 to 
5 X - = — - Ana, obtain 32 ; so the numerator must be multiplied 
o 4 32 by the same number in order that the value of 

the fraction may not be changed. 

EXAMPLES 

Change the following : 

1. |to27ths. 6. ^to75th8. 

2. l^toGOths. 7. iJtol44ths. 

3. |to40ths. a f^tol68ths. 

4. Jto56ths. 9. ||to522ds. 

5. ^^to50ths. 10. ^to9375ths. 

A fraction is said to be in its lowest terms when the numera- 
tor and the denominator are prime to each other. 

To reduce a fraction to its lowest terms. 

Dividing the numerator and the denominator of a fraction 
by the same number does not change the value of the fraction. 
The process of dividing the numerator and denominator of a 
fraction by a number common to both may be continued until 
the terms are prime to each other. 

Example. — Reduce || to fourths. 

The denominator must be divided by 4 to give 
12 __ 3 J the new denominator 4 ; then the numerator must be 

16 4 ' divided by the same number so as not to change the 

value of the fraction. 

If the terms of a fraction are large numbers, find their 
greatest common divisor and divide both terms by that. 

Example. — Reduce |^|| to fourths. 

(1) 2166)2888(1 (2) 2166^3 ^ 

2166 2888 4 

O. a D. 722)2166(3 

2166 



REVIEW OF ARITHMETIC 19 

EXAMPLES 

Reduce to lowest terms : 

2. If* 4. i* 6. ^y a ifi 10. ,igy^ 

To reduce an integer to an improper fraction. 
Example. — Reduce 25 to fifths. 

oe .• K 1 o K >i Ij^ 1 there are 4. In 26 there must be 

25 times 4 = ^4^ -4^« ok *• « i «/ 
» ^ 26 times |, or J-j^. 

To reduce a mixed number to an improper fraction. 

Example. — Reduce 16^ to an improper fraction. 

1 sevenths Since in 1 there are ^, in 16 there must 

112 be 16 times J, or i^. 

4 sevenths H^ + *=^^. 

116 sevenths, = J^^. 

EXAMPLES 

Reduce to improper fractions : 

1. 3| 3. 17^ 5. 13| 7. 359^ 

2. 16^ 4. 12^ 6. 27t^ a 482^1 
9. 25^ 10. Reduce 250 to 16ths. 

11. Change 156 to a fraction whose denominator shall be 12. 

12. In $730 how many fourths of a dollar ? 

13. Change 12f to 16ths. 14. Change 24| to 18ths. 

To reduce an improper fraction to an integer or mixed number 
divide the numerator by the denominator. 

Example; — Reduce ^^ to an integer or mixed number. 
24 

16)385 

oo Since ^ equal 1, ^^ will equal as many 

times 1 as 16 is contained in 386, or 24^^ 

65 24^1^ Ana, ^^^^ 

64 

1 



20 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Beduce to integers or mixed numbers : 

1- H 4- ^H^ 7. VV^ 10. m& 

2. 2^ 5. ^j^ a -Vj^ 11. Aiy^ 

3. 1^1 6. ^ 9. -HJHH^ 12. e 

When fractions have the same denominator their denomi- 
nator is called a common denominator. 
" Thus, JJ, T%, if'jj have a common denominator. 

The smallest common denominator of two or more fractions is 
their least common denominator. 

Thus, Ht i^^t 1^ become |, }, | when changed to their least common 
denominator. 

The common denominator of two or more fractions is a 
common multiple of their denominators. 

The least common denominator of two or more fractions is 
the least common multiple of their denominatorp. 

Example. — Reduce | and ^ to fractions having a common 

denominator. 

8^6^18 The common denominator must be a 

T T _ JJ common multiple of the denominators 4 

^ A t ~ 74 and 6, and since 24 is the product of the 

? ™ 2 1 *^^ 8^2* denominators, it is a common multiple of 

them. Therefore. 24 is a common denominator of } and J. 

To reduce fractions to fractions having the least common denominator. 

Example. — Reduce f, |, and -^ to fractions having the 

least common denominator. 

'>^ ^ f) 1^ '^^ I'^^JsX, common de- 

^'^ * -^ ^ nominator must be the 

* ir ?? ._ least common multiple of 

1 1 ^ the denominators 3, 6, 12, 

2 X 3 X 2 = 12 L.CM. which is 12. 

1 = ^; | = |^;tV = T^- •^^- Divide the least common 

multiple 12 by the denom- 
inator of each fraction, and multiply both terms by the quotient If the 



REVIEW OF ARITHMETIC 21 

denominators should be prime to each other, their product would be their 
least common denominator. 

EXAMPLES 

Reduce to fractions having a common denominator : 

2. 1,1 6. iyi,i 

3. hi 7. hhhi 
*• h !*¥> i ®- h A> f > i 

Reduce to fractions baying least common denominator: 

1- hh^ 5. ft, A, 4 

2. i i, A 6. f , f , J, I 

3- A> A? i 7. Which fraction is larger, 

Addition of Fractions 

Only fractions with a common denominator can be added. 
If the fractions have not the same denominator, reduce them 
to a common denominator, add their numerators, and place 
their sum over the common denominator. The result should be 
reduced to its lowest terms. If the result is an improper 
fraction, it should be reduced to an integer or mixed number. 

Example. — Add |, |^, and ^^. 

1. 2)4 6 16 ^ ,,. 

^ common multi- 

^)^ ^ ^ pie of the de- 

13 4 48 2/. C, M. nominators is 

this by the de- 
nominator of each fraction and multiplying both terms by the quotient 
give }}, J5, JJ. The fractions are now like fractions, and are added by 
adding their numerators and placing the sum over the common denomi- 
nator. Hence, the sum is y^, or 2/j. 



22 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — Add 5f , 7^, and 6/^. 

^5 ~ ^'So First find the sum of the fractions, 

'^A = '^M which is fS, or 1|§. Add this to the 

6^2^ = 6J^ sum of the integers, 18. 18 + 1}J = 

I8|f=19|f Arts, 1»M- 

EXAMPLES 

1. Find the " over-all " dimension of a drawing if the 
separate parts measure f/\ f ", y, and f", respectively. 

2. Find the sum of ^, f , ^, ^, and f^. 

3. Find the sum of 3f , 4|, and 2^^. 

4. A seam -^^ of an inch wide is made on both sides of a 
piece of cloth 27 inches wide. What is the width after the 
seams are made ? 

5. I bought cotton cloth valued at $ 6 J, silk at $ 13f , hand- 
kerchiefs for $2^, and hose for $2 J. What was the whole 
cost ? 

6. A ribbon was cut into two pieces, one 8|" and the other 
5 j^/' long. If ^g-" was allowed for waste in cutting, what was 
the length of the ribbon ? 

7. Three pieces of cloth contain 38J, 12^, and 53^ yards re- 
spectively. What is their total length in yards ? 

8. Add : lOi, 7f 11, it. 

9. Add : 136^, 184|, 416^, 125 J. 

Subtraction of Fractions 

Only fractions with a common denominator can be sub- 
tracted. If the fractions have not the same denominator, 
reduce them to a common denominator and write the differ- 
ence of their numerators over the common denominator. The 
result should be reduced to its lowest terms. 



REVIEW OF ARITHMETIC 23 

Example. — Subtract f from f . 

The least common denominator of f 
f-| = f-| = f Ana, and f is 6. f = f, and f = f Their 

difference is |. 

Example. — From 11 J subtract 5f . 

-i-ii__-i/\g When the fractions are changed to 

yi 5 — A 5 their least common denominator, they are 

^ "■ —4 llj — 4|. f cannot be subtracted from J, 

^i ^^ ^2* -^'^' hence 1 is taken from 11 units, changed to 

sixths, and added to the ), which makes f . 10} — 4j = 6} = 6^. 

EXAMPLES 

1. From eleven yards of cloth, If yards were cut for a 
jacket and S^ yards for a coat. How many yards were left ? 

2. From a firkin of butter containing 27|^ lb. there were 
sold 3 J lb. and 11^ lb. How many pounds remained ? 

3. The sum of two fractions is f . One of the fractions is 
^. Find the other. 

4. Laura had $7^ and gave away $2^ and $3^. How 
much remained ? 

5. The sum of 2 numbers is 37^ and one of the numbers is 
28f . Find the other number. 

6. By selling goods for $ ^3^, I lost $ 27|. What was the 
cost? 

7. A man sells 9J yards from a piece of cloth containing 
34 yds. How many yards remain ? 

8. Mr. Brown sold goods for $ 56^, gaining $ 12. What 
did they cost ? 

9. A dealer had 208 tons of coal and sold 92f tons. How 
much remained ? 

10. If I buy a ton of coal for $ 6\ and sell for $ 7^, how 
much do I gain ? 



24 VOCATIONAL MATHEMATICS FOR GIRLS 

14. There were 48|^ gallons in the tank. First 4^ gallons 
were used, then 5 J gallons, and last 2| gallons. How many 
gallons were left in the tank ? 

15. What is the difference between -^ and ^ j ? 

16. What is the difference between 32| and 3^ ? 

17. A piece of dress goods contains 60 yd. If four cuts 
of 12 J^, 9 1, 18f, and 10^ yd. respectively are made, what 
remains ? 

Multiplication of Fractions 

To multiply fractionsy multiply the numerators together for the 
new numerator and multiply the denominators together for the 
new denominator. 

Cancel when possible. The word of between two fractions 
is equivalent to the sign of multiplication. 

To multiply a mixed number by an integer, multiply the whole 
number and the fraction separately by the integer tJien add the 
products. 

To multiply two mixed numbers, change each to an improper 
fraction and multiply. 

Example. — Multiply | by f . 

^ multiplied by } is the same as } o/ f . 3 and 5 are prime to each other 
so that answer is f . This method of solution is the same as multiplying 
the numerators together for a new numerator and the denominators for 
a new denominator. Cancellation shortens the process. 

Example. — Find the product of 124f and 5. 

124i 

p. If the fraction and integer are mul- 

— 3T ft 8 — If — Q 8 tiplied separately by 6, the result is 6 

3f 6 X f - V - ^f ^.j^gg J _ Y _ 3j^ and 6 times 124 = 



620 

623| Ans. 



620. 620 + 3} =623}. 



REVIEW OF ARITHMETIC 25 

EXAMPLES 

1. William earns 83^ cents a day. How much will he 
earn in five weeks ? 

2. One bag of flour costs 75 cents. How much will three 
barrels cost ? A barrel h6lds 8 bags. 

3. Erom a barrel of flour containing 196 lb., 24^ lb. were 
taken. At another time ^ of the remainder was taken. How 
many pounds were left ? 

4. Multiply f of f by I of |. 

5. Multiply 26f by 9f 

6. Find the cost of 19| yd. of cloth at 16^ cents a yard. 

7. At $ 12^ each, how many tables can be bought for 
$280? 

a I paid $ 6f for a barrel of flour and sold it for $ ^ more. 
How much did I sell it for ? 

9. What is the cost of 18 yards of cloth at 15| cents a yard ? 

10. If coal cost $7^ a ton, how much will 8^ tons cost ? 

11. Multiply : 32f by 8|. 

Division of Fractions 

To divide one fraction by another, invert the divisor and 
proceed as in multiplication of fractions. Change integers and 
mixed numbers to improper fractions. 

Example. — Divide f X | by f x |. 

ixf-h(fxf)= 

2 

4 S S ^ S '^^ divisor { x f is inverted and the 

^X-X^X^ = -. Ana. result obtained by the process of cancel- 
^ P ^ P ^ lation. 



26 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — Divide 3156f by 5. 

631^ Ans. 
5)3156| y^^^ ^^^ integer of a mixed 



30 



number is large, it may be 

15 divided as follows : 6 in 3166}, 

15 If = J ^1 times, with a remainder of 

g 1 J. This remainder divided by 

r 5 gives ^^, which is placed at 



the right of the quotieut. 



Example. — Divide 3682 by 5^. 

When the dividend is a large number and 
5i-) 3682 the divisor a mixed number, it is useful to re- 

2 2 member that multiplying both dividend and di- 

TT Vqaj visor by the same number does not change the 

i-^ quotient. In this example we can multiply 

"""tt Ans. }yoth. dividend and divisor by 2 and then divide 

as with whole numbers. The quotient is 669^^. 

A fraction having a fraction for one or both of its terms is 
called a complex fraction. 

To reduce a complex fraction to a simple fraction. 

42 
Example.— Reduce ^ to a simple fraction. 

7| = ^ = '^^V- = ¥xA=if Ans. 

Change 4J and 7f to improper fractions, ^ and y, respectively. Per- 
form the division indicated with the aid of cancellation and the result will 
be If 

EXAMPLES 

1. Divide fl by f 7. 296-^10^=? 

2. Divide ^^ by f. a 28,769 -^7|=? 

3. Divide -If by i. 7j__^ 

4. Divide^ by i. ' if~' 

5. Divide f by |. iof^ _ 

6. 384f ^5 = ? ' I Xf 



REVIEW OF ARITHMETIC 27 

REVIEW PROBLEMS IN FRACTIONS 

1. Two and one half yards of cloth cost $ 2.75. What is 
the price per yard ? 

2. An 8^t. can of milk is bought from a farmer for .60 
cents. What is the cost per quart ? 

3. I paid 56 cents for f of a yard of lace. What was the 
price per yard ? 

4. A farmer's daughter sold a weekly supply of eggs for 
$5.70. If she received 28^ cents a dozen, how many dozen 
did she sell ? 

5. If a narrow piece of goods, 6J yd. long, is cut into pieces 
6f inches long, how many pieces can be cut? How much 
remains ? Allow \ in. for waste. 

6. What is the cost of 18|^ pounds of crackers at 17^ cents 
a pound ? 

7. A gallon (U. S. Standard capacity) contains 231 cubic 

inches. 

a. Give number of cubic inches in ^ gallon. 

6. Give number of cubic inches in 1 quart. 

c. Give number of cubic inches in 1 pint. 

d. Give number of cubic inches in ^ pint. 

8. A woman earns $ 2^ a day. If she spends $ If, how 
much do6s she save ? How many weeks (six full working 
days) will it take to save $ 90 ? 

9. I paid 56 cents for | of a yard of lace. What was the 
price per yard ? 

10. A furniture dealer sold a table for $ 14^, a couch for 
$ 45|, a desk for $ llf, and some chairs for $ 27^. Eind the 
amount of his sales. 

11. A woman had $ 200. She lost \ of it, gave away ^ the 
remainder, and spent $ 20|. How much had she left ? 

12. I gave $ 16^ for 33 yards of cloth. How much did one 
yard cost ? 



28 VOCATIONAL MATHEMATICS FOR GIRLS 

Drill in the Use of Fractions 

Addition 

1. i + i = ? 19. i + TV = ? 37. ^ + i = ? 

2. i + i = ? 20. H-i = ? 38. ^ + i = ? 

3. i + i=? 21. i + J=? 39. ;fe + i = ? 

4. i + TV = ? 22. H-tJj = ? 40. H + f-? 

5. i + TV = ? 23. i + TV = ? «• l + i = ? 

6. i + f = ? 24. i + T^ = ? 42. i + A = ? 
7- i + TV = ? 25. tV + A = ? «• T^ + |=? 
a i + i = ? 26. T\ + i=? 44. H-tV = ? 
9. i + i = ? 27. T»ff + i = ? 45. tV + H = ? 

10- 1 + T»ir = ? 28. TV + T»ff = ? 46. U + -^=? 

11. i + i = ? 29. T>ff + | = ? 47. A+A = ? 

12. i + f = ? 30. T»ir + i = ? 48. i + Tfj = ? 

13. i + i = ? 31. i + i = ? 49. i + i = ? 

14. | + i = ? 32. H-i = ? 50. i+i = ? 

15. | + i = ? 33. | + i = ? 51. i + i=? 

16. | + T'ir = ? 34. | + tV=? 52. i + TJff = ? 
". | + A = ? 35. f + A = ? 53. | + tV=? 
la 1 + ,^ = ? 36. i + TV = ? 5*- l+l\ = ? 

Subtraction 

1. i-i = ? ft i-i=? 15. |-i = ? 

2. i-i = ? 9. i-i = ? 16. f-i»ff=? 

3. i-i = ? 10. i-T»ir=? 17. |-^=? 

4. i-TV = ? "• i-l!V = ? 18- 1-5^ = ? 

5- i-liV = ? 12. i-A = ? 19. 1-| = ? 

6- i-|i^ = ? 13. |-i = ? 20. i-A = ? 

7- i-?V = ? 1*- |-i = ? 21. i-i = ? 



9 
9 



22. 


i -lV = ? 


23. 


i -1>V = ? 


24. 


i -T^ = ? 


25. 


i -A = ? 


26. 


A -tV = ? 


27. 


t^%-tV = ? 



REVIEW OP ARITHMETIC 29 

33. f -i =? 44. i -A = ? 



«• I -A = 5 



9 



35. I -^ = ? 46. H-l^ = ? 

36. i -T^ = ? 47. ;,V-Ti^ = ^ 



? 






37. ii-ii^ = ? 48. ^-^ = ? 

... .. 38. \ -T^ = ? 49. I -I =? 

28.tV-t'f = ? 39. ||-^ = ? 50. |-i=? 

29. tV -T^ = ? «. .^_^ = ? 51. i -i =? 

*>.tV-1^ = ? *l--ife-liV = ? 52. |-tV = ? 

31. i -I =? 42. if-^ = ? 53. ^ -^ = ? 

32. f -i =? 43.^-11 = ? 54. I -^ = ? 

1. i X i = ? 19. i X ^ = ? 37. ^ X i = ? 

2.|Xi=? 20. ixi=? 38. ^Xi=? 

3. iX\ =? 21. ixi=? 39. ^Xi=? 

4. ^X^\ = ? 22. ^ XT»y = ? 40. ^XtV=? 
5- iX^ = ? 23. ^ X^ = ? 41. ^Xjlj = ? 

6. iX-^ = ? 24. i X^V = ? 42. isS-X5>j = ? 

7. |Xi=? 25. TlirX^=? 43. i^Xi=f 
aixi=? 26. TVxi=? 44. ^ljXi=^ 
9. ixi =? 27. tVxI =? 45. ^Xi =? 

W. 1X^3^=? 2a ^XtV = ? 46- T!^XtV=? 

11. iXisV = ? 29. tJ5X^ = ? 47. ^X-5^=? 

12. ix^ = ? 30. ^^x-^ = ? 4a ,Vx^V=? 

13. |X^=? 31. |xi=? 49. ^Xi=? 

14. |xi=? 32. fxi=? 50. |Xi=? 

15. I X j = ? 33. I X i = ? 51. I X i = ? 

16. |XtV = ? 34. I XtV = ? 52. i Xt'j=? 

17. |X^7 = ? 35. f X^ = ? 53. i X^j=? 
ia|x^ = ? 36. I X^ = ? 54. |. X^V=? 



9 

9 

? 



30 



VOCATIONAL MATHEMATICS FOR GIRLS 









Division 






1. 


i-^i -? 


19. 


i ^i =? 


37. 


l>^-^i =? 


2. 


i^i =? 


20. 


i -^i =? 


38. 


A-i =? 


3. 


1-^i =? 


21. 


i -^i =? 


39. 


t^^i =? 


4. 


i-^TV=? 


22. 


i ->-tV = ? 


40. 


1!V-«-tV = ? 


5. 


i^U^ = ? 


23. 


i -,v = ? 


41. 


sV • ^ — ^ 


6. 


i-irV=? 


24. 


i ^^T=? 


42. 


ij^^=^ 


7. 


i^i =? 


25. 


tV-^1 =? 


43. 


1^-i =? 


8. 


i-^i =? 


26. 


TV-^i =? 


44. 


A-^i =? 


9. 


i-^i =? 


27. 


TV-^i =? 


45. 


T^-S-i =? 


10. 


i-^iV = ? 


28. 


tV-^tV = ? 


46. 


Ti^-^T^ = ? 


11. 


i^lJ^=? 


29. 


1 _t_ 1 — 9 


47. 


^^-h = '^ 


12. 


i-^l^=? 


30. 


lV-^l!»f = ? 


48. 


^-1^ = ? 


13. 


I^i =? 


31. 


1 -i =? 


49. 


i -^i =? 


14. 


l-^i =? 


32. 


1 -i =? 


50. 


i -^i =? 


15. 


l-i =? 


33. 


1 +i =? 


51. 


i -i =? 


16. 


|-^iV = ? 


34. 


f -^tV = ? 


52. 


i *tV = ? 


17. 


1-^7=? 


35. 


f -^li»J = ? 


53. 


i +tV = ? 


18. 


1^1^=? 


36. 


i +iiV=? 


54. 


i -A = ? 



Decimal Fractions 

A power is the product of equal factors, as 10 x 10 = 100. 
10 X 10 X 10 = 1000. 100 is the second power of 10. 1000 is 
the third power of 10. 

A decimal fraction or decimal is a fraction whose denominator 
is 10 or a power of 10. A common fraction may have any 
number for its denominator, but a decimal fraction must always 
have for its denominator 10, or a power of 10. A decimal is 
written at the right of a period (.), called the decimal point. 
A figure at the right of a decimal point is called a decimal 
figure. 



REVIEW OF ARITHMETIC 



31 



A mixed decimal is an integer and a decimal ; as^ 16.04. 

To read a decimal, read the decimal as an integer, and give 
it the denomination of the right-hand figure. To write a deci- 
mal, write the numerator, prefixing ciphers when necessary to 
express the denominator, and place the point at the left. 
There must be as many decimal places in the decimal as there 
are ciphers in the denominator. 



EXAMPLES 

9 

Read the following numbers : 



1. .7 

2. .07 

3. .007 

4. .700 

5. .125 

6. .0625 



7. .4375 

a .03125 

9. .21875 

10. .90625 

11. .203125 

12. .234375; 



13. .0000054 

14. 35.18006 

15. .0005 

16. 100.000104 

17. 9.1632002 
la 30.3303303 



19. 9.999999 

20. .10016 

21. .000155 

22. .26 

23. .1 

24. .80062 



Express decimally : 

1. Four tenths. 

2. Three hundred twenty-five thousandths. 

3. Seventeen thousand two hundred eleven hundred-thou- 
sandths. 

4. Seventeen hundredths. 6. Five hundredths. 

5b Fifteen thousandths. 7. Six ten-thousandths. 

a Eighteen and two hundred sixteen hundred-thousandths. 
9. One hundred twelve hundred-thousandths. 
10. 10 millionths. 11. 824 ten-thousandths. 

12. Twenty-nine hundredths. 

13. 324 and one hundred twenty-six millionths. 

14. 7846 himdred-inillionths. 



32 VOCATIONAL MATHEMATICS FOR GIRLS 
^®* loooooooj TOT? 10000> A> To 008 OIF* 

17. One and one tenth. 

18. One and one hundred-thousandth. 

19. One thousand four and twenty-nine liundredths. 

Reduction of Decimals 

Ciphers anneoced to a decimal do not change the value of 
the decimal; these ciphers are called decimal ciphers. For 
each cipher prefixed to a decimal, the value is diminished ten- 
fold. The denominator of a decimal — when expressed — is 
always 1 with as many ciphers as there are decimal places in 
the decimal. 

To reduce a decimal to a common fraction. 

Write the numerator of the decimal omitting the point for the 
numerator of the fra/ction. For the denominator wnte 1 with as 
many ciphers annealed, as there are decimal places in the dedrrval. 
Then reduce to lowest terms. 

Example. — Reduce .25 and .125 to common fractions. 

1 Write 26 for the numerator and 

95 = ^^ _« $!^ __ 1 J - 1 for the denominator with two O's, 

1OO'~^00"~4 * which makes ^Jy^; ^ reduced to 

4 lowest terms is J. 

1 

1 9^ — ^^^ — j^^^ _ 1 >!« « '126 is reduced to a common frac- 

~ 1000 "" ^000 ~" 8 ' tion in the same way. 

8 

Example. — Reduce .37^ to a common fraction. 

37^ has for its denominator 1 

3Ii=,i = ^X^ = ? Ans ^^*^^'^^"^^^^^^io- 
100 100 2 Ji/i^ 8 * This is a complex fraction 

4 which reduced to lowest terms 

is}. 



REVIEW OF ARITHMETIC 33 

EXAMPLES 

Reduce to common fractions : 

1. .09375 a 2.26 11. .16f 16. .87^ 

2. .15625 7. 16.144 12. .33^ 17. .66| 

3. .016625 a 26.0000100 13. .06^ la .36J 

4. .609375 9. 1084.0025 14. .140626 19. .83 ^ 

5. .678125 10. .121- 15. .984376 20. .62| 

To reduce a common fraction to a decimal. 

Annex decimal ciphers to the numerator and divide by the de- 
nominator. Point off from the right of the quotient as many 
pla/ces as there are ciphers annexed. If there are not figures 
enough in the quotient, prefix ciphers. 

The division will not always be exact, i.e, ^ = .142|^ or .142"'". 



ExAUPIiE. 


— Reduce 


f to a decimal. 

.76 
4)3.00 
28 

20 
1 = .76 

EXAMPLES 


• 








Beduce to decimals : 












1- iu 


6. i 


u. tV 


la 


H 


21. 


sU 


2- Th 


7. H 


12. ^ 


17. 


16i 


22. 


25.12J 


^- shs 


8. « 


1^- IS^STF 


la 


66| 


23. 


33i 


*• i 


9- ^ 


14. 12^ 


19. 


M 


24. 


A 



5. I 10. 7i^ 15. ^ 20. I 25. tIy 

Addition of Decimals 

To add decimals, write them so that their decimal points are in 
a column. Add as in integers, and place the point in the sum 
directly wider the points above it. 



34 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — Find the sum of 3,87,2.0983, 5.00831, .029, 
.831. 

3.87 

2 0983 Place these numbers, one under the other, with 

K 005^^1 decimal points in a column, and add as in addition 

' of integers. The sum of these numbers should 

.UJy jjj^yg j.jjg decimal point in the same column as the 

'831 numbers that were added. 

11.83661 Ans. 

EXAMPLES 

Find the sum : 

1. 5.83, 7.016, 15.0081, and 18.3184. 

2. 12.031, 0.0894, 12.0084, and 13.984. 

3. .0765, .002478, .004967, .0007862, .17896. 

4. 24.36, 1.358, .004, and 1632.1. 

5. .175, 1.75, 17.5, 175., 1750. 

6. 1., .1, .01, .001, 100, 10., 10.1, 100.001. 

7. Add 5 tenths; 8063 millionths ; 25 hundred-thousandths ; 
48 thousandths; 17 millionths; 95 ten-millionths ; 5, and 5 
hundred-thousandths ; 17 ten-thousandths. 

8. Add 24f , 17^, .0058, 7^, 93^- 

9. 32.58, 28963.1, 287.531, 76398.9341. 
10. 145., 14.5, 1.45, .145, .0145. 

Subtraction of Decimals 

To subtract decimals, tvrite the smaller number under the 
larger with the decimal point of the subtrahend directly under the 
decimal point of the minuend. Subtract as in integers, and place 
the point directly under the points above. 

Example. — Subtract 2.17857 from 4.3257. 

Write the lesser number under the greater, 
4.32570 Minuend ^^^^ the decimal points under each other. 

2.17857 Subtrahend Add a to the minuend, 4.3267, to give it the 
2.14713 Remainder same, denominator as the subtrahend. Then 

subtract as in subtraction of integers. Write 
the remainder with decimal point under the other two points. 



REVIEW OF ARITHMETIC 35 

EXAMPLES 

Subtract : 

1. 69.0364-30.8691 = ? 3. .0626 - .03125 = ? 

2. 48.7209-12.0039 = ? 4. .00011 - .000011 = ? 

5. 10-.1 + .0001 = ? 

6. From one thousand take five thousandths. 

7. Take 17 hundred-thousandths from 1.2. 

8. From 17.37^ take 14.16^. ' 

9. Prove that ^ and .600 are equal. 

10. Find the difference between -^^ and yf§^. 

Multiplication of Decimals 

To multiply decimals proceed as in integers, and give to tJie 
product as many decimal figures as there are in both multiplier 
and multiplicand. When there are not figures enough in the 
product, prefix ciphers. 

Example. — Find the product of 6.8 and .63. 

6.8 Multiplicand 
.63 Multiplier ^'^ ^® ^^® multiplicand and .63 the multiplier. 

ofu Their product is 4.284 with three decimal figures, 

the number of decimal figures in the multiplier 

and multiplicand. 



408 



4.284 Product 

Example. — Find the product of .06 and .3. 

.06 Multiplicand The product of .06 and .3 is .016 with a cipher 
.3 Multiplier prefixed to make the three decimal figures re- 

.016 Product quired in the product. 

EXAMPLES 

Find the products : 

1. 46.26 X. 126 3. .016 X. 06 

2. 8.0626 X. 1875 4. 26.863 x 4^ 



36 VOCATIONAL MATHEMATICS FOR GIRLS 

5. 11.11x100 a .325x121 

6. .5625x6.28125 9. .001542 x .0052 

7. .326 X 2.78 10. 1.001 x 1.01 

To multiply by 10, 100, 1000, etc,,, remove the point one place 
to the right for each cipher m the multiplier. 

This can be performed without writing the multiplier. 

Example.— Multiply 1.625 by 100. 

1.626 X 100 = 162.6 

To multiply by 200, remove the point to the right and multiply 
by 2, 

Example. — Multiply 86.44 by 200. 

86.44. 

2 

17,288 

EXAMPLES 

Find the product of : 

1. 1 thousand by one thousandth. 

2. 1 million by one millionth. 

3. 700 thousands by 7 hundred-thousandths. 

4. 3.894 X 3000 5. 1.892 x 2000. 

Division of Decimals 

To divide decimals proceed as in integers, and give to the quo- 
tient as many decimal figures as the number in the dividend ex- 
ceeds tliose in the divisor. 

Example. — Divide 12.685 by .5. 

The number of decimal figures in 

Divisor . 5)12.685 Dividend the quotient, 12.685, exceeds the num- 

25.37 Quotient her of decimal figures in the divisor, .6, 

by two. So there must be two deci- 
mal figures in the quotient. 



REVIEW OF ARITHMETIC 37 

Example. — Divide 399.552 by 192. 

, When the divisor is an integer, 

^•^^^ Q^iOtient the point in the quotient should be 

Divisor 192)399.552 Dividend placed directly over the point in 

384 the dividend, and the division per- 

1555 formed as in integers. This may 

-I rog be proved by multiplying divisor 

— :r^ by quotient, which would give the 

^^^ dividend. 

192 

Example. — Divide 28.78884 by 1.25. 

When the divisor contains 

23.031 •*• Quotient decimal figures, move the point 

Divisor 1.25.)28. 78.884 Dividend in both divisor and dividend as 

250 many places to the right as 

3yg there are decimal places in the 

OTK divisor, which is equivalent to 

— — ^ multiplying both divisor and 

l^ dividend by the same number 

^*^ and does not change the quo- 

134 tient. Then place the point in 

125 the quotient as if the divisor 

"~9 Remainder ^®^® ^'^ integer. In this ex- 
ample, the multiplier of both 
dividend and divisor is 100. 

EXAMPLES 

Find the quotients : 

1. .0625 -f- .125 5. 1000 -^ .001 8. 1.225 -^ 4.9 

2. 315.432 -^ .132 6. 2.496 -^. 136 9. 3.1416 -f- 27 

3. .75^.0125 7. 28000^16.8 10. 8.33 -^ 5 

4. 125-^12| 

To divide by 10, 100, 1000, e^c, remove the point one place to 
the left for each cipher in the divisor. 

To divide by 200, remove the point two places to the left, and 
divide by 2. 



\ 



38 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Find the quotients : 

1. 38.64 -^ 10 6. 865.45^5000 

2. 398.42 -f- 1000 7. 38.28^400 

3. 1684.32 -^ 1000 8. 2.5^500 

4. 1.155 -^ 100 9. .5^10 

5. 386.54-- 2000 10. .001 -^ 1000 

REVIEW EXAMPLES 

1. Add 28.03, .1674, .08309, 7.00091, .1895. 

2. Subtract 1.00894 from 13.0194. 

3. Multiply 83.74 X 3.1416. 

4. Divide 3.1416 by 8.5. 

5. Perform the following calculations : .7854 X 35 x 7.5. 

6. Perform the following calculations : 

65.3 X 3.1416 X .7854 
600 X 3.5 X 8.3 

7. Change the following fractions to decimals : 

(«) lAr^ W A» (c) ^ , (d) y|^, (e) ^j, (/) ^^, (g) ^. 
a Change the following decimals to common fractions : 
(a) .33^, (b) .25, (c) .125, (d) .375, (e) .437^, (/) .875. 

Parts of 100 or 1000 

1. What part of 100 is 12^ ? 25 ? 33| ? 

2. What part of 1000 is 125 ? 250 ? 333| ? 

3. How much is ^ of 100 ? Of 1000? 

4. How much is i of 100 ? Of 1000? 

5. What is I of 100 ? Of 1000? 

Example. — How much is 25 times 24 ? 

100 times 24 = 2400. 
25 times 24 = } as much as 100 times 24 = 600. Ans. 



REVIEW OF ARITHMETIC 39 

Short Method of Multiplication 

To multiply by 

25, multiply by 100 and divide by 4 
33J, multiply by 100 and divide by 3 
16^, multiply by 100 and divide by 6 
12|, multiply by 100 and divide by 8 
9, multiply by 10 and subtract the multiplicand ; 
11, if more than two figures, multiply by 10 and add the 

multiplicand to the product ; 
11, if two figures, place the figure that is their sum between 

them. 

63 X 11 = 693 74 X 11 = 814 

Note that when the sum of the two figures exceeds nine, the one in the 
tens place is carried to the figure at the left. 

EXAMPLES 

Multiply by the short process : 

1. 81 by 11 = ? 10. 68byl6f=:? 

2. 75by33i = ? 11. 112 by 11 = ? 

3. 128 by 12^ = ? 12. 37 by 11 = ? 

4. 87 by 11 = ? 13. 4183 by 11 = ? 

5. 19 by 9 = ? 14. 364by33i = ? 

6. 846 by 11 = ? 15. 8712 by 12^ = ? 

7. 88 by 11 = ? 16. 984byl6f = ? 
a 19 by 11 = ? 17. 36 by 25 = ? 

9. 846byl6| = ? 18. 30by333J = ? 

Aliquot Parts of $ 1.00 

The aliquot parts of a number are the numbers that are 
exactly contained in it. The aliquot parts of 100 are 5, 20, 
12^, 16|, 33i, etc. 

The monetary unit of the United States is the dollar, con- 
taining one hundred cents, which are written decimally. 



40 VOCATIONAL MATHEMATICS FOR GIRLS 

6^ cents = $ ^V ^^ cents = $ ^ = quarter dollar 

8| cents = $ ^^ ^H ^®^*s = $ | 

12^ cents = $ ^ 50 cents = $ ^ = half dollar 
16| cents = $ ^ 

10 mills = 1 cent, ct. = $ .01 or $ 0.01 
5 cents = 1 " nickel " = $ .05 
10 cents = 1 dime, c?. = $ .10 
10 dimes = 1 dollar, $ = $ 1.00 
10 dollars = 1 eagle, E. = $ 10.00 

Example. — Wliat will 69 pairs of stockings cost at 16| 
cents a pair ? 

69 pairs will cost 69 x 16§ cts., or 69 x $ J = ^- = $!!{ = $ 11.60. 

Example. — At 25^ a peck, how many pecks of potatoes 
can be bought for $ 8.00 ? 

8-4-J = 8xf = 32 pecks. Ans, 

Review of Decimals 

1. For work on a job qne woman receives $ 13.75, a second 
woman $ 12.45, a third woman $ 14.21, and a fourth woman 
$ 21.85. What is the total amount paid for the work ? 

2. A pipe has an inside diameter of 3.067 inches and an 
outside diameter of 3.428 inches. What is the thickness of 
the metal of the pipe ? 

3. At 4^ cts. a pound, what will be the cost of 108 boxes of 
salt each weighing 29 lb. ? 

4. A dressmaker receives $ 121.50 for doing a piece of 
work. She gives $ 12.25 to one of her helpers and $ 10.50 
to another. She also pays $ 75.75 for material. How much 
does she make on the job ? 

5. An automobile runs at the rate of 9^ miles an hour. 
How long will it take it to go from Lowell to Boston, a dis- 
tance of 26.51 miles ? 



REVIEW OF ARITHMETIC 41 

6. A man uses a gallon of gasoline in traveling 16 miles. 
If a gallon costs 23 cents, what is the cost of fuel per mile ? 

7. Which is cheaper, and how much, to have a 13^ cents 
an hour woman take 13J hours on a piece of work, or hire a 
17^ cents an hour woman who can do it in 9^ hours ? 

8. On Monday 1725.25 lb. of coal are used, on Tuesday 
2134.43 lb., on Wednesday 1651.21 lb., on Thursday 1821.42 
lb., on Friday 1958.82 lb., and on Saturday 658.32 lb. How 
many pounds of coal are used during the week ? 

9. If, in the example above, there were 10,433.91 lb. of 
coal on hand at the beginning of the week, how much was left 
at the end of the week ? 

10. The distance traveled in an automobile is measured by an 
instrument called a speedometer. A man travels in a week the 
following distances: 87.5 mi., 49.75 mi., 112.60 mi., 89.7 mi., 
119.3 mi., and 93.75 mi. What is the total distance traveled ? 

U. An English piece of currency corresponding to our five- 
dollar bill is called a pound sterling and is worth $4,866^. 
How much more is a five-dollar bill than a pound ? 

12. An alloy is made of copper and zinc. If .66 is copper 
and .34 is zinc, how many pounds of zinc and how many 
pounds of copper will there be in a casting of the alloy 
weighing 98 lb. ? 

13. A train leaves New York at 2.10 p.m. and arrives in 
Philadelphia at 4.15 p.m. The distance is 90 miles. What is 
the average rate per hour of the train ? 

14. The weight of a foot of ^" steel bar is 1.08 lb. Find 
the weight of a 21-foot bar. 

15. A steam pump pumps 3.38 gallons of water to each 
stroke and the pump makes 51.1 strokes per minute. How 
many gallons of water will it pump in an hour ? 

16. At 12^ cents per hour, what will be the pay for 23^ days 
if the days are 10 hours each ? 



42 VOCATIONAL MATHEMATICS FOR GIRLS 

Compound Numbers 

A number composed of different kinds of concrete units that 
are related is a compound number : as, 3 bu. 2 pk. 1 qt. 

A denomination is a name given to a unit of measure or of 
weight. A number having one or more denominations is also 
called a denominate number. 

Reduction is the process of changing a number from one 
denomination to another without changing its value. 

Changing to a lower denomination is called reduction descend- 
ing : as, 2 bu. 3 pk. = 88 qt. Changing to a higher denomi- 
nation is called reduction ascending ; as, 88 qt. = 2 bu. 3 pk. 

Linear Measure is used in measuring lines or distance 

Table 

12 inches (in.) = 1 foot, ft. 

3 feet = 1 yard, yd. 

5 J yards, or 16 J feet = 1 rod, rd. 
820 rods, or 5280 feet = 1 mile, mi. 
1 mi. = 320 rd. = 1760 yd. = 5280 ft. = 63,360 in. 

Square Measure is used in measuring surfaces. 

Table 

144 square inches = 1 square foot, sq. ft. 

9 square feet = 1 square yard, sq. yd. 
30J square yards 1 ^ j ^^^ ^^ ^ ^ 
272} square feet J 
160 square rods = 1 acre, A. 
640 acres = 1 square mile, sq. mi. 

1 sq. mi. = 640 A. = 102,400 sq. rd. = 3,097,600 sq. yd. 

Cubic Measure is used in measuring volumes or solids. 

Table 

1728 cubic inches = 1 cubic foot, cu. ft. 

27 cubic feet = 1 cubic yard, cu. yd. 

16 cubic feet = 1 cord foot, cd. ft. 

8 cord feet, or 128 cu. ft. = 1 cord, cd. 
1 cu. yd. = 27 cu. ft. = 46,656 cu. in. 



REVIEW OF ARITHMETIC 43 

Liquid Measure is used in measuring liquids. 

Table 

4 gills (gi.)=l pint, pt. 

2 pints = 1 quart, qt. 

4 quarts = 1 gallon, gal. 
1 gal. = 4 qt. = 8 pt. = 82 gi. 
A gallon contains 231 cubic inches. 
The standard barrel is 31} gal., and the hogshead 63 gal. 

Dry Measure is used in measuring roots^ gradn^ vegetables^ 
etc. 

Table 

2 pints = 1 quart, qt 
8 quarts = 1 peck, pk. 
4 pecks = 1 bushel, bu. 
1 bu. = 4 pk. = 82 qt. = 64 pints. 

The bushel contains 2150.42 cubic inches; 1 dry quart contains 
67.2 cu. in. A cubic foot is ff of a bushel. 

Ayoirdupois Weight is used in weighing all common articles ; 
aS; coal, groceries, hay, etc. 

Table 

16 ounces (oz.) = 1 pound, lb. 
100 pounds = 1 hundredweight, cwt. ; 

or cental, ctl. 
20 cwt., or 2000 lb. = 1 ton, T. 
1 T. = 20 cwt. = 2000 lb. = 32,000 oz. 

The long ton of 2240 pounds is used at the United States Custom 
House and in weighing coal at the mines. 

Measure of Time. 

Table 

60 seconds (sec.) = 1 minute, min. 

60 minutes = 1 hour, hr. 

24 hours = 1 day, da. 

7 days = 1 week, wk, 

366 days = 1 year, yr. 

366 days = 1 leap year, 

100 years = 1 century. 



44 VOCATIONAL MATHEMATICS FOR GIRLS 

Counting. 

Table 



12 thiDgs = 1 dozen, doz. 

12 dozen = 1 gross, gr. 

12 gross = 1 great gross, G. gr. 



Paper Measure. 



Table 

24 sheets = 1 quire 2 reams = 1 bundle 

20 quires = 1 ream 6 bundles = 1 bale 

Reduction Descending 

Example. — Reduce 17 yd. 2 ft. 9 in. to inches. 

1 yd. = 3 ft. 
17 yd. = 17 X 3 = 51 ft. 
51 + 2 = 53 ft. 
1 ft. = 12 in. 

63 ft. = 53 X 12 = 6.36 in. 
636 + 9 = 646 in. Ans. 

EXAMPLES 

Reduce to lower denominations: 

1. 46 rd. 4 yd. 2 ft. to feet. 

2. 4 A. 15 sq. rd. 4 sq. ft. to square inches. 

3. 16 cu. yd. 25 cu. ft. 900 cu. in. to cubic inches. 

4. 15 gal. 3 qt. 1 pt. to pints. 

5. 27 da. 18 hr. 49 min. to seconds. 

Reduction Ascending 

Example. — Reduce 1306 gills to higher denominations. 

4 )1306 gi. Since in 1 pt. there are 4 gi., in 1306 gi. 

2 )326 pt. + 2 gi. there are as many pints as 4 gi. are contained 

4 )163 qt. times in 1306 gi., or 326 pt. and 2 gi. remainder. 

40 gal. + 3 qt. In the same way the quarts and gallons are 

40 gal. 3 qt. 2 gi. Ans. found. So there are in 1306 gi., 40 gal. 3 qt. 

2gi. 



REVIEW OF ARITHMETIC 45 

EXAMPLES 

Reduce to higher denominations : 

1. Reduce 225,932 in. to miles, etc. 

2. Change 1384 dry pints to higher denominations. 

3. In 139,843 sq. in. how many square miles, rods, etc. ? 

4. How many cords of wood in 3692 cu. ft. ? 

5. How many bales in 24,000 sheets of paper ? 

A denominate fraction is a fraction of a unit of weight or 
measure. 

To reduce denominate fractions to integers of lower denominations. 

Change the fraction to the next lower denomination. Treat 
the fractional part of the product in the same way, and so pro- 
ceed to the required denomination. 

Example. — Reduce ^ of a mile to rods, yards, feet, etc. 

f of 320 rd. = ^Af^ rd. = 228^ rd. 

^of yyd. = ttyd. =8}yd. 

^ of 3 ft. = Of ft. 

f of 12 in. = y in. = 5^ in. 

j of a mile = 228 rd. 3 yd. ft. 6f in. 

The same process applies to denominate decimals. 
To reduce denominate decimals to denominate numbers. 
Example. — Reduce .87 bu. to pecks, quarts, etc. 



Change the decimal fraction to 

the next lower denomination. Treat 

the decimal part of the product in the 

same way, and so proceed to the re- 

q"q7 q4. quired denomination. 

3 pk. 3 qt. 1.68 pt. Ans. 



.87 bu. 
4 




.84 qt. 
2 


3.48 pk. 




1.68 pt. 




.48 
8 


pk. 



46 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Reduce to integers of lower denominations : 

1. f of an acre. 3. ^ of a ton. 

2. .3125 of a gallon. 4. .51625 of a mile. 

5. Change f of a year to months and days. 

6. .2364 of a ton. 

7. What is the value of | of 1^ of a mile ? 

a Reduce f^ bu. to integers of lower denominations. 
9. .375 of a month. 
10. ^j acre are equal to how many square rods, etc. ? 

Addition of Compound Numbers 

Example. — Find the sum of 7 hr. 30 min. 45 sec, 12 hr» 
25 min. 30 sec, 20 hr. 15 min. 33 sec, 10 hr. 27 min. 46 sec 

The sum of the seconds = 164 sec. = 
2 min. 34 sec. Write the 34 sec. under 
the sec. column and add the 2 min. to 
the min. column. Add the other columns 
50 39 34 in the same way. 

60 hr. 39 min. 34 sec. Ana, 

Subtraction of Compound Numbers 

Example. — From 39 gal. 2 qt. 2 pt. 1 gi. take 16 gal. 2 qt. 
3 pt. 3 gi. 

J ^ ^ . As 3 gi. cannot be taken from 1 gi., 4 gi. 

9 9 1 or 1 pt. are borrowed from the pt. column 

-,(, o q q *"^<1 added to the 1 gi. Subtract 3 gi. from 

rr — X — T — — the 6 gi. and the remainder is 2 gi. Continue 

on , o .. o • ^ in the same way until all are subtracted. 

22 gal. 3 qt. 2 gi. Ans. _, ^, . ^ . _ i o * /^ * o ^ 

° Then the remamder is 22 gal. 3 qt. pt. 2 gi. 



hr. 


min. 




7 


30 


46 


12 


26 


30 


20 


16 


33 


10 


27 


46 



REVIEW OF ARITHMETIC 



47 



Multiplication of Compound Numbers 
Example. — Multiply 4 yd. 2 ft. 8 in. by 8. 

8 times 8 in. = 64 in. = 6 ft. 4 in. Place the 
4 in. under the in. column, and add the 6 ft. to 
the product of 2 ft. by 8, which equals 21 ft. =7 yd. 
Add 7 yd. to the product of 4 yd. by 8 = 39 yd. 



yd. 


ft. 


in. 


4 


2 


8 
8 


39 





4 


39 yd. 


4 


in. Ans. 



Division of Compound Numbers 
Example. — Find -^ of 42 rd. 4 yd. 2 ft. 8 in. 



rd. yd. 


ft. 


In. 


36)42 4 
36 

7 


2 


8(1 rd. 


3i 
86 
SSi 
+ 4 
36)4iii yd. (1 yd 
36 


36)24i(0 ft. 
12 
294 

+ 8 
. 36)302(8Jf in. 
280 


3 




22 


22Jft. 
12 


1 rd. 1 yd. 8^ in. 



^ of 42 rd. = 1 rd. ; re- 
mainder, 7 rd. = 38J yd. ; 
add 4 yd. = 42J yd. ^ of 
42J yd. = 1 yd. ; remainder, 
7i yd., = 22J ft. = 24J ft. 
^ of 24J ft. = ft. 24 J ft. 
=294 in. ; add 8 in. =302 in. 
■^ of 302 in. = m in. 



Difference between Dates 

Example. — Find the time from Jan. 25, 1842, to July 4, 
1896. 



1896 
1842 



7 
1 



4 
26 



64 yr. 6 mo. 9 da. Ans, 



It is customary to consider 30 days 
to a month. July 4, 1896, is the 1896th 
yr., 7th mo., 4th da., and Jan. 26, 1842, 
is the 1842d yr., Ist. mo., 25th da. 
Subtract, taking 30 da. for a month. 



48 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — What is the exact number of days between 
Dec. 16, 1895, and March 12, 1896 ? 

Dec. 15 Do not count the first day mentioned. There 

Jan. 31 are 15 days in December, after the 16th. Jan- 

Feb. 29 uary has 81 days, February 29 (leap year), 

Mar. 12 and 12 days in March ; maldng 87 days. 

87 days. Ana. 

EXAMPLES 

1. How much time elapsed from the landing of the Pil- 
grims, Dec. 11, 1620, to the Declaration of Independence, 
July 4, 1776? 

2. Washington was born Feb. 22, 1732, and died Dec. 14, 
1799. How long did he live? 

3. Mr. Smith gave a note dated Feb. 25, 1896, and paid it 
July 12, 1896. Find the exact number of days between its date 
and the time of payment. 

4. A carpenter earning $ 2.50 per day commenced Wednes- 
day morning, April 1, 1896, and continued working every week 
day until June 6. How much did he earn ? 

5. Find the exact number of days between Jan. 10, 1896, 
and May 5, 1896. 

6. John goes to bed at 9.15 p.m. and gets up at 7.10 a.m. 
How many minutes does he spend in bed ? 

To multiply or divide a compound number by a fraction. 

To multiply by a fractiorij multiply by the numerator , and 
divide the product by the denominator. 

To divide by a fraction^ multiply by the denominator, and divide 
the product by the numerator. 

When the multiplier or divisor is a mixed number, reduce to 
an improper fraction^ and proceed as above. 



REVIEW OF ARITHMETIC 49 

EXAMPLES 

1. How much is f of 16 hr. 17 min. 14 sec. ? 

2. A field contains 10 A. 12 sq. rd. of land, which is f 
of the whole farm. Find the size of the farm. 

3. If a train runs 60 mi. 35 rd. 16 ft. in one hour, how far 
will it run in 12^ hr. at the same rate of speed ? 

4. Divide 14 bu. 3 pk. 6 qt. 1 pt. by f 

5. Divide 5 yr. 1 mo. 1 wk. 1 da. 1 hr. 1 min. 1 sec. by 3f . 

REVIEW EXAMPLES 

1. A time card on a piece of work states that 2 hours and 
15 minutes were spent on a skirt, 1 hour and 12 minutes on a 
waist, 2 hours and 45 minutes on a petticoat, and 1 hour and 
30 minutes on a jacket. What was the number of hours spent 
on all the work ? 

2. How many parts of a sewing machine, each weighing 14 
oz., can be obtained from 860 lb. of metal if nothing is allowed 
for waste ? 

3. How many feet long must a dry goods store be to hold 
a counter 8' 6", a bench 14' 4", a desk 4' 2", and a counter 
7' 5"f placed side by side, if 3' 3" are allowed between the 
pieces of furniture and between the walls and the counters ? 

4. How many gross in a lot of 968 buttons ? 

5. Find the sum of 7 hr. 30 min. 45 sec, 12 hr. 25 min. 
30 sec, 20 hr. 15 min. 33 sec, 10 hr. 27 min. 46 sec. 

6. If a train is run for 8 hr. at the average rate of 50 
mi. 30 rd. 10 ft. per hour, how great is the distance covered ? 

7. A telephone pole is 31 ft. long. If 4 ft. 7 in. are under 
ground, how high (in inches) is the top of the pole above the 
street ? 

8. If 100 bars of iron, each 2|' long, weigh 70 lb., what is 
the total weight of 2300 bars ? 



50 VOCATIONAL MATHEMATICS FOR GIRLS 

9. If a cubic foot of water weighs 62^ lb., how many 
ounces does it weigh ? 

10. A farmer's wife made 9 pounds 7 ounces of butter and 
sold it at 41 cents a pound. How much did she receive ? 
U. A peck is what part of a bushel ? 

12. A quart is what part of a bushel ? of a peck ? 

13. I have 84 lb. 14 oz. of salt which I wish to put into 
packages of 2 lb. 6 oz. each. How many packages will 
there be ? 

14. If one bottle holds 1 pt. 3 gi., how many dozen bottles 
will be required to hold 65 gal. 2 qt. 1 pt. ? 

15. How many pieces 5^" long can be cut from a rod 16' 8" 
long, if 5" are allowed for waste ? 

16. What is the entire length of a .railway consisting of five 
different lines measuring respectively 160 mi. 185 rd. 2 yd., 
97 mi. 63 rd. 4 yd., 126 mi. 272 rd. 3 yd., 67 mi. 199 rd. 5 yd., 
and 48 mi. 266 rd. 5 yd. ? 

Percentage 

Percentage is a process of solving questions of relation by 
means of hundredths or per cent (%). 

Every question in percentage involves three elements : the 
rate per cent, the base, and the percentage. 

The rate per cent is the number of hundredths taken. 

The base is the number of which the hundredths are taken. 

The percentage is the result obtained by taking a certain per 
cent of a number. 

Since the percentage is the result obtained by taking a cer- 
tain per cent of a number, it follows that the percentage is the 
product of the base and the rate. The rate and base are always 
factors, the percentage is the product. 

Example. — How much is 8 % of $ 200 ? 

8 % of ^200 = 200 X .08 = $ 16. (1) 



REVIEW OF ARITHMETIC 51 

In (1) we have the three elements: 8% is the rate, $200 is the base, 
and $ 16 is the percentage. 

Since $ 200 x .08 = J| 16, the percentage ; 

tl6 -^ .08 = $ 200, the base ; 
and $ 16 -$- $ 200 = .08, the rate. 

If any two of these elements are given, the other may be 

found : 

Base X Rate = Percentage 

Perceyitage -^ Ba^e = Ba^e 

Percentage -j- Ba^se = Rate 

Per cent is commonly used in the decimal form, but many 
operations may be much shortened by using the common frac- 
tion form. 

1 % = .01 = T^ i % = .00^ or .006 

10%= .10 = tV 33i%=.33i = i 

100 % = 1.00 = 1 8i % = .08^ = .0825 
12^ % = .121. or .125 = 1 I % = .00^ = .00125 

There are certain per cents that are used so frequently that 
we should memorize their equivalent fractions. 

H%=^ 33i%=i 66f%=| 

10% =,1, mfo=i 76% =f 

12^% =i 40%= I 80% =f 

16i%=i 50%=^ 83i%=| 

20%=^ 60% =1 87i%=i 

25% =i 62^% = I 

EXAMPLES 

1. Find 75 % of $ 368. 

2. Find 15 % of $ 412. 

3. 840 is 33^ % of what number ? 

4. 616 is 16 % of what number ? 

5. What per cent of 12 is 8 ? 



52 VOCATIONAL MATHEMATICS FOR GIRLS 

6. What per cent of a foot is 8 inches ? 11 inches ? 4 inches ? 

7. A technical high school contains 896 pupils ; 476 of the 
pupils are girls. What per cent of the school is girls ? 

8. Out of a gross of bottles of mucilage 9 were broken. 
What was the per cent broken ? 

Trade Discount 

Merchants and jobbers have a price list. From this list 
they give special discounts according to the credit of the cus- 
tomer and the amount of supplies purchased, etc. If they 
give more than one discount, it is understood that the first 
means the discount from the list price, while the second denotes 
the discount from the remainder. 

EXAMPLES 

1. What is the price of 200 spools of cotton at $ 36.68 per 
M. at40% off? 

2. Supplies from a dry goods store amounted to $ 68.75. If 
12^ % were allowed for discount, what was the amount paid ? 

3. A dealer received a bill amounting to $212.75. Suc- 
cessive discounts of 15%, 10%, and 5% were allowed. 
What was the amount to be paid ? 

4. 2 % is usually discounted on bills paid within 30 days. 
If the following are to be paid within 30 days, what will be 
the amounts due ? 

a. $ 30.19 c. $399.16 e. $1369.99 

b. 2816.49 d. 489.01 /. 918.69 

5. Millinery supplies amounted to $ 127.79 with a discount 
of 40 % and 15 %. What was the net price ? 

6. What single discount is equivalent to a discount of 45 % 
and 10 % ? 

7. What single discount is equivalent to 20 %, and 10 % ? 



REVIEW OF ARITHMETIC 53 

Simple Interest 

Money that is paid for the use of money is called interest. 
The money for the use of which interest is paid is called the 
principal, and the sum of the principal and interest is called 
the amount. 

Interest at 6 % means 6 % of the principal for 1 year ; 12 
months of 30 days each are usually regarded as a year in com- 
puting interest. There are several methods of computing 
interest. 

Example. — What is the interest on $ 100 for 3 years at 6 % ? 

$100 
.06 
$ 6.00 interest for one year. Or, jj^ x J^ x | = $ 18. Am. 

3 



% 18.00 interest for 3 years. Ans. 

$ 100 + $ 18 = $ 118, amount. 

Principal x Rate X Time = Interest 

Example. — What is the interest on $ 297.62 for 6 yr. 3 mo. 
at6%? 

a 297 .62 3 

M Or, -?- X ?^^?^X 21 = li§750:55 = 1^93.76. 



$17.8672 ' 100 1 i 200 

6i 2 

4.4643 
89.2860 Note. — Final results should not include 



$93.7503 $93.76. Ans, mills. Mills are disregarded if less than 6, 

and called another cent if 5 or more. 

EXAMPLES 

1. What is the interest on $ 586.24 for 3 months at 6 % ? 

2. What is the interest on $ 816.01 for 9 months at 5 % ? 

3. What is the interest on $ 314.72 for 1 year at 4 % ? 

4. What is the interest on $ 876.79 for 2 yr. 3 mo. at ^ % ? 

5. What is the interest on $ 2119.70 for 6 yr. -2 mo. 13 da. 
at 5i%? 



54 VOCATIONAL MATHEMATICS FOR GIRLS 

The Six Per Cent Method 

By the 6 ^c method it is convenient to find first the interest 
of % 1, then multiply it by the principal. 

Example. — r What is the interest on % 60.24 at 6 % for 2 yr. 
8 mo. 18 da. ? 

Interest on $ 1 for 2 yr. =2 x $ .06 = $.12 
Interest on f 1 for 8 mo. = 8 x $ .OOJ = .04 
Interest on $ 1 for 18 da. = 18 x $ .OOOJ = .003 
Interest on $ 1 for 2 yr. 8 mo. 18 da. % .163 
Interest on $ 60.24 is 60.24 times % .163 = % 8.19. Ans, 

Second Method. — Interest on any sum for 60 days at 6 % is 
yJ-^ of that sum and mxiy he expressed by momng the decimal point 
two places to the left. The interest for 6 days may be expressed 
by moving the decimal three places to the left. 

Example. — What is the interest on $ 394.50 for 96 days at 

6%? 

$3.9460, interest on $394.60 for 60 days at 6 ^. 
1.9726, interest on $394.60 for 30 days at 6 ^. 
.3946, interest on $ 394.60 for 6 days at 6 9^). 
$6.3120, interest on $394.60 for 96 days at 6 <^. Ana, $ 6.31. 

Example. — What is the interest on $ 529.70 for 78 days at 
8% 



? 



$6,297, interest on $629.70 for 60 days at 6 %. 

1.689, interest on $629.70 for 18 days (6 days x 3). 
$6,886, interest on $629.70 for 78 days at 6 ^. 

.886 + $2,296 = $9,181. Am. $9.18. 



EXAMPLES 

Find the interest and amount of the following : 

1. S 2350 for 1 yr. 3 mo. 6 da. at 6 %. 

2. $ 125.75 for 2 yr. 5 mo. 17 da. at 7 %. 

3. $ 950.63 for 3 yr. 7 mo. 21 da. at 5 %. 

4. $ 625.57 for 2 yr. 8 mo. 28 da. at 8 %. 



REVIEW OF ARITHMETIC 55 

Exact Interest 

When the time includes days, interest computed by the 6% 
method is not strictly exact, by reason of using only 30 days 
for a month, which makes the year only 360 days. The day is 
therefore reckoned as ^hf ^^ ^ 7©*^, whereas it is -^ of a year. 

To compute exact interest, find the exact time in days, and con- 
sider 1 day^s interest as ^-J-j of 1 year's interest. 

Example. — Find the exact interest of $ 368 for 74 days at 
7%. 

^368 X .07 = $26.06, 1 year's interest. 
74 days' interest is ^ of 1 year's interest. 
^ of $ 25.06 = $ 5.08. Ans, 

EXAMPLES 

Find the exact interest of : 

1. $324 for 15 da. at 5 %. 

2. $ 253 for 98 da. at 4 %. 

3. $624 for 117 da. at 7 %. 

4. $ 620 from Aug. 15 to Nov. 12 at 6 %. 

5. $ 153.26 for 256 da. at 5| %. 

6. $ 540.25 from June 12 to Sept. 14 at 8 %. 

Rules for Computing Interest 

The following will be found to be excellent rules for finding the inter- 
est on any principal for any number of days. 

Divide the principal by 100 and proceed as follows: 

2 % — Multiply by number of days to run, and divide by 180. 
2^ % — Multiply by number of days, and divide by 144. 

3 % — Multiply by number of days, and divide by 120. 

S^ % — Multiply by number of days, and divide by 102.86. 



56 



VOCATIONAL MATHEMATICS FOR GIRLS 



4 % — Multiply by number of days, and divide by 90. 

5 % — Multiply by number of days, and divide by 72. 

6 % — Multiply by number of days, and divide by 60. 

1 fjo — Multiply by number of days, and divide by 61.43. 
8 ^0 — Multiply by number of days, and divide by 45. 



Savings Bank Compound Interest Table 

Showing the amount of $ 1, from 1 year to 16 years, with compound 
interest added semiannually, at different rates. 



Pbb Cent 


8 


4 


5 


6 


7 


8 


9 


iyear 


101 


102 


102 


103 


103 


1 04 


104 


1 year 


103 


104 


105 


106 


107 


108 


109 


\\ years 


104 


106 


107 


109 


110 


112 


114 


2 years 


106 


108 


1 10 


112 


114 


116 


119 


2} years 


107 


1 10 


113 


115 


1 18 


121 


124 


3 years 


109 


1 12 


115 


1 19 


122 


126 


130 


3J years 


110 


114 


1 18 


122 


127 


131 


136 


4 years 


1 12 


1 17 


121 


126 


131 


136 


142 


4J years 


114 


119 


124 


130 


136 


1 42 


148 


5 years 


1 16 


121 


128 


134 


141 


148 


155 


6J years 


1 17 


124 


131 


138 


145 


153 


162 


6 years 


1 19 


126 


134 


142 


151 


160 


169 


6J years 


121 


129 


137 


146 


1 56 


166 


177 


7 years 


123 


131 


141 


151 


161 


173 


185 


7i years 


124 


134 


144 


156 


167 


180 


193 


8 years 


126 


137 


148 


160 


173 


187 


2 02 


8i years 


128 


139 


162 


166 


179 


194 


2 11 


9 years 


130 


142 


1 55 


170 


185 


2 02 


220 


9J years 


132 


146 


159 


176 


192 


2 10 


2 30 


10 years 


134 


148 


163 


180 


198 


2 19 


2 41 


11 years 


138 


164 


1 72 


191 


2 13 


2 36 


2 63 


12 years 


142 


160 


180 


203 


2 28 


2 56 


2 87 


13 years 


147 


167 


190 


2 16 


2 44 


2 77 


3 14 


14 years 


161 


173 


199 


2 28 


2 62 


2 99 


3 42 


15 years 


166 


180 


2 09 


2 42 


2 80 


3 24 


3 74 



REVIEW OF ARITHMETIC 57 

EXAMPLES 

Solve the following problems by using the tables on page 56 : 

1. What is the compound interest of $1 at the end of 
8^ years at 6 % ? 

2. What is the compound interest of $ 1 at the end of 11 
years at 6 % ? 

3. How long will it take $400 to double itself at 5 %, 
compound interest ? 

4. How long will it take $580 to double itself at 6^%, 
compound interest ? 

5. How long will it take $615 to double itself at 8 %, 
simple interest? 

6. How long will it take $784 to double itself at 7%, 
simple interest ? 

7. Find the interest of $684 for 94 days at 3 %. 
a Find the interest of $ 1217 for 37 days at 4 %. 

9. Find the interest of $ 681.14 for 74 days at 4J %. 

10. Find the interest of $414.50 for 65 days at 5 %. 

11. Find the interest of $384.79 for 115 days at 6 %. 

Ratio and Proportion 

Ratio is the relation between two numbers. It is found 
by dividing one by the other. The ratio of 4 to 8 is 4 -^ 8 = |^. 

The terms of the ratio are the two numbers compared. The 
first term of a ratio is the antecedent, and the second the con- 
sequent. The sign of the ratio is (:). (It is the division sign 
with the line omitted.) Ratio may also be expressed fraction- 
ally, as J^ or 16 : 4 ; or ^^ or 3 : 17. 

A ratio formed by dividing the consequent by the antece- 
dent is an inverse ratio : 12 : 6 is the inverse ratio of 6 : 12. 

The two terms of the ratio taken together form a couplet 



58 VOCATIONAL MATHEMATICS FOR GIRLS 

Two or more couplets taken together form a compound ratio. 

Thus, 2:6 6 : 11 

A compound ratio may be changed to a simple ratio by- 
taking the product of the antecedents for a new antecedent, 
and the product of the consequents for a new consequent ; as, 
6x2:11x6, or 12; 55. 

Antecedent -j- Consequent = Ratio 

Antecedent -r- Ratio = Consequent 
Ratio X Consequent = Aiitecedent 

To multiply or divide both terms of a ratio by the same 
number does not change the ratio. 

Thus 12 : 6 = 2 

3x12:3x6 = 2 

EXAMPLES 

Find the ratio of 

1. 20 : 300 Fractions with a common de- 

2. 3 bu. : 3 pk. nominator have the same 
3 21 • 16 ratio as their numerators. 

*• 12:i 7. ^:|^,||:^,||:|J 

6. 16:(?) = J 

Proportion 

An equality of ratios is a proportion. 

A proportion is usually expressed thus : 4 : 2 : : 12 : 6, and is 
read A: is to 2 as 12 is to 6. 

A proportion has four terms, of which the first and third are 
antecedents and the second and fourth are consequents. The 
first and fourth terms are called extremes^ and the second and 
third terms are called means. 

The product of the extremes equals the product of the 
means. 



REVIEW OF ARITHMETIC 59 

To find an extreme^ divide the product of the uneans by the given 
extreme. 

To find a mean, divide theprodvjct of the extremes by the given 
mean, 

EXAMPLES 

Supply the missing term : 

1. 1 : 836 : : 25: ( ) 4. 10 yd. : 50 yd. : : $20 : ($ ) 

2. 6:24::( ):40 5. $f :$3|::( ):5 

3. ( ):15::60:6 

Simple Proportion 

An equality of two simple ratios is a simple proportion. 
Example. — If 12 bushels of charcoal cost $ 4, what will 60 
bushels cost ? 

19 . ftft . • «4 . r« ^ There is the same relation between the cost 

. . . ^p f\j9 ) of 12 bu. and the cost of 60 bu. as there is be- 

'^^* = $20. Ans, tween the 12 bu. and the 60 bu. |4is the 

third term. The answer is the fourth term. 
It must form a ratio of 12 and 60 that shall equal the ratio of $4 to the 
answer. Since the third term is less than the required answer, the first 
must be less than the second, and 12 : 60 is the first ratio. The product 
of the means divided by the given extreme gives the other extreme, or % 20. 

EXAMPLES 

Solve by proportion : 

1. If 150 yd. of edging cost $ 6, how much will 1200 yd. cost ? 

2. If 250 pounds of lead pipe cost $ 15, how much will 1200 
pounds cost ? 

3. If 5 men can dig a ditch in 3 days, how long will it take 
2 men? 

4. If 4 men can shingle a shed in 2 days, how long will it 
take 3 men ? 

5. The ratio of Simon's pay to Matthew's is |. Simon 
earns $ 18 per week. What does Matthew earn ? 



60 VOCATIONAL MATHEMATICS FOR GIRLS 

6. What will 11 1 yards of cambric cost if 50 yards cost 
$ 6.76 ? 

7. If it takes 7^ yards of cloth, 1 yard wide, to make a 
suit, how many yards of cloth, 44 inches wide, will it take to 
make the same suit ? 

8. If 21 yards of silk cost $ 52.50, what will 35 yards cost ? 

9. A farm valued at $5700 is taxed for $38.19. What 
should be the tax on property valued at $ 28,500 ? 

10. If there are 7680 minims in a pint of water, how many 
pints are there in 16,843 minims ? 

11. There are approximately 15 grains in a gram. How 
many grams in 641 grains ? 

12. In a velocity diagram a line '31 in. long represents 
45 ft. What would be the length of a line representing 30 ft. 
velocity ? 

13. When a post 11.5 ft. high casts a shadow on level ground 
20.6 ft. long, a telephone pole nearby casts a shadow 59.2 ft. 
long. How high is the pole ? 

14. If 10 grams of silver nitrate dissolved in 100 cubic cen- 
timeters of water will form a 10 % solution, how much silver 
nitrate should be used in 1560 cubic centimeters of water ? 

15. A ditch is dug in 14 days of 8 hours each. How many 
days of 10 hours each would it have taken ? 

16. If in a drawing a tree 38 ft. high is represented by 1^^", 
what on the same scale will represent the height of a house 
47 ft. high ? 

17. What will be the cost of 21 motors if 15 motors cost 
$ 887 ? 

18. If goods are bought at a discount of 25 % and are sold 
at the list price, what per cent is gained ? (Assume $ 1 as 
the list price.) 



REVIEW OF ARITHMETIC 61 

18. If a sewing machine sews 26 inches per minute on heavy 
goods, how many yards will it sew in an hour ? 

19. If a girl spends 28 cents a week for confectionery, how 
much does she spend for it in three months ? 

20. If a pole 8 ft. high casts a shadow 4^ ft. long, how high 
is a tree which casts a shadow 48 ft. long ? 

Involution 

The product of equal factors is a power. 

The process of finding powers is involution. 

The product of two equal factors is the second power, or 
square, of the equal factor. 

The product of three equal factors is the third power, or cube, 
of the factor. 

42 = 4x4 is 4to the second power, or the square of 4. 

2^ = 2 X 2 X 2 is 2 to the third power, or the cube of 2. 

3* = 3x3x3x3is3to the fourth power, or the fourth power of 4. 



EXAMPLES 




Find the powers : 




1. 6« 3. 1* 5. (2^)2 


7. 9» 


2. 1.1^ 4. 262 6. 2* 


8. .152 


Evolution 





One of the eqiuil factors of a power is a root. 

One of two equal factors of a number is the square root. 

One of three equal factors of a number is the cube root of it. 

The square root of 16 = 4. The cube root of 27 = 3. 

The radical sign (^) placed before a number indicates that 
its root is to be found. The radical sign alone before a number 
indicates the square root. 

Thus, V9 = 3 is read, the square root of 9 = 3. 



62 VOCATIONAL MATHEMATICS FOR GIRLS 

A small figure placed in the opening of the radical sign is 
called the index of the root, and shows what root is to be 
taken. 

Thus, \/8 = 2 is read, the cube root of 8 is 2. 

Square Root 

The square of a number composed of tens and units is equal 
to the square of the tens, plus twice the product of the tens by 
the units, plus the square of the units. 

ten^ -h 2 X tens x units + units? 
Example. — What is the square root of 1225 ? 



12'25(30 + 6 = 86 


Separating 


re»w2, 302 =900 


into periods of 


2 X tens = 2 x 30 = 60 326 


two figures 


2 X tens + units = 2 x 30 + 6 = 66 325 


each, by a 






check mark ('), 



beginning at units, we have 12'26. Since there are two periods in the 
power, there must be two figures in the root^ tens and units. 

The greatest square of even tens contained in 1226 is 000, and its 
square root is 30 (3 tens). Subtracting the square of the tens, 000, the 
remainder consists of 2 x (tens x units) + units. 

326, therefore, is composed of two factors, units being one of them, 
and 2 x tens — units being the other. But the greater part of this factor 
is 2 X tens (2 x 30 = 60). By trial we divide 326 by 60 to find the other 
factor (units), which is 6, if correct. Completing the factor, we have 
2 X tens + units = 66, which, multiplied by the other factor, 6, gives 826. 
Therefore the square root is 30 + 6 = 36. 

The area of every square surface is the product of two equal 
factors, length, and width. 

Finding the square root of a number, therefore, is equivalent 
to finding the length of one side of a square surface, its area 
being given. 

1. Length x Width =Area 

2. Area -i- Length = Width 

3. Area -i- Width = Length 



REVIEW OF ARITHMETIC 63 

Short Method 

Example. — Find the square root of 1306.0996. 

13^06.09^96 (36.14 Beginning at the decimal point, separate the 

9 number into periods of two figures each, point- 



66) 406 ing whole numbers to the left and decimals to 

896 the right. Find the greatest square in the left- 

721)1009 hand period, and write its root at the right. 

721 Subtract the square from the left-hand period, 

7224)28896 and bring down the next period for a dividend. 

28896 Divide the dividend, with its right-hand 

figure omitted, by twice the root already found, 
and annex the quotient to the root, and to the divisor. Multiply this 
complete divisor by the last root figure, and bring down the next period 
for a dividend, as before. 

Proceed in this manner till all the periods are exhausted. 
When occurs in the root, annex to the trial divisor, bring down 
the next period, and divide as before. 

If there Is a remainder after all the periods are exhausted, annex deci- 
mal periods. 

If, after multiplying by any root figure, the product is larger than the 
dividend, the root figure is too large and must be diminished. Also the 
last figure in the complete divisor must be diminished. 

For every decimal period in the power, there must be a decimal figure 
in the root. If the last decimal period does not contain two figures, 
supply the deficiency by annexing a cipher. 

EXAMPLES 

Find the square root of : 

1. 8836 5. yjl^l 9. V3.532 ^ 6.28 

2. 370881 6. 72.5 10. V625+1296 

3. 29.0521 7. .009^9^ 11. J_x:^ 



4. Am56 8. 1684.298431 12. 



V9 
3969 



5625 

13. What.is the length of one side of a square field that has 
an area equal to a field 75 rd. long and 45 rd. wide ? 



CHAPTER II 
MENSURATION 

The Circle 

A circle is a plane figure bounded by a curved line, called 
the circumference, every point of which is equidistant from the 
center. 

The diameter is a straight line drawn, 
from one point of the circumference 
to another and passing through- the 
center. 

The ratio of the circumference to 
the diameter of any circle is always a 
constant number, 3.1416+, approxi- 
mately S^, which is represented by 
the Greek letter ir {pi). 

C = Circumference 
D = Diameter 




The radius is a straight line drawn from the center to the 
circumference. 

Any portion of the circumference is an arc. 

By drawing a number of radii a circle may be cut into a 
series of figures, each one of which is called a sector. The area 
of each sector is equal to one half the product of the arc and 
radius. Therefore the area of the circle is equal to one half of 
the product of the circumference and radius. 

1 See Appendix for explanation and directions concerning the use of formulas. 

64 



MENSURATION 65 

2 

In this formula A equals area, ir = 3.1416, and -B* = tlie 
radius squared. 

In this formula D equals the diameter and G the circum- 
ference, 

4 4 

Example. — What is the area of a circle whose radius is 

3ft.? 

xZ)2 



A-rB?^ ^ = 



4 

9 



-4=irx9 ^=^ = ir9 = 28.27 sq.ft. Ans, 

Example. — What is the area of a circle whose circumfer- 
ence is 10 ft. ? 

8.1416 2 2 

ix-i5_ xlx 10 = -^5_ = 7.1 sq.ft. ^ns. 
2 3.1416 2 3.1416 ^ 

Area of a Ring. — On examining a flat iron ring it is clear that 
the area of one side of the ring may be found by subtracting 
the area of the inside circle from the area of the outside circle. 

Let D = outside diameter 
d = inside diameter 
A = area of outside circle 
a = area of inside circle 

(1) ^ = :^=.7854Z>» 




66 



VOCATIONAL MATHEMATICS FOR GIRLS 



(2) 

. (3) A 
Let 



a = 

-a 

B 
B 



4 



=.7854 (P 



4 4 
area of circular ring =s A — a 



-cP) 



Example. — If the outside diameter of a flat ring is 9" and 

the inside diameter 7", what is the area of one side of the 

ring? 

B = .7854 (2>2 - cP) 

B = .7864 (81 - 49) = .7854 x 32 = 25.1328 sq. in. Am. 

Angles 

We make two common uses of angles : (1) to measure a cir- 
cular movement, and (2) to measure a difference in direction. 
A circle contains 360°, and the angles at the center of the 
circle contain as many degrees as their corresponding arcs on 
the circumference. 

Angle FOE has as many degrees as arc PE. 

A right angle is measured by a quarter 
of the circumference of the circle, which 
is90^ 

The angle AOG is a right angle. 

The angle ACy made with half the cir- 
cumference of the circle, is a straight angle, and the two right 
angles, AOO and GOC, which it contains, are supplementary 
to each other. When the sura of two angles is equal to 90®, 
they are said to be complementary angles, and one is the com- 
plement of the other. When the sum of two angles equals 180**, 
they are supplementary angles, and one is said to be the supple- 
ment of the other. 




MENSURATION 



67 



The number of degrees in an angle may be measured by a 
protractor. The distance around a semicircular protractor is 




Pbotractob— Semicircular, having 180°. 

divided into 180 parts, each division measuring a degree. It 
is used by placing the center of the protractor on the vertex 
and the base of the protractor on one side of the angle to be 
measured. Where the other side of the angle cuts the circular 
piece of the protractor, the size of the angle may be read in 
degrees. 



EXAMPLES 

1. What is the area of a circular piece of velvet 8" in 
diameter ? 

2. What is the distance around the edge of a hat 6" in 
diameter ? 

3. Name the complements of angles of 30^ 45^ 65^ 70°, 
85°. 

4. Name the supplements of angles of 55°, 140°, 69°, 98° 44', 
81° 19^. 

5. What is the diameter of a wheel that is 12' 6" in circum- 
ference ? 



68 



VOCATIONAL MATHEMATICS FOR GIRLS 



6. What is the area of one side of a flat iron ring 14" inside 
diameter and 18" outside diameter ? 

7. The wheel of a child's carriage is 30" in diameter. 
What is the length of the rubber tire that fits it ? 

8. How much ribbon is needed to bind the edge of a circu- 
lar cloth that exactly covers the top of a center table 28" in 
diameter ? 

9. A straw hat measures 30" around the rim. What is 
the diameter of the hat ? 

10. If a circular dining room table measures 12' 6" in cir- 
cumference, what is the greatest distance across the table ? 



Triangles 

A triangle is a plane figure bounded by three straight lines. 
Triangles are classified according to the relative lengths of 
their sides and the size of their angles. 

A triangle having equal sides is called equilateral. One 
having two sides equal is isosceles. A triangle having no 
sides equal is called scalene. 

If the angles of a triangle are equal, the triangle is equi- 
angular. 

If one of the angles of a triangle is a right angle, the tri- 
angle is a right triangle. In a right triangle the side opposite 
the right angle is called the hypotenuse and is the longest side. 
The other two sides of the right triangle are the legs, and are 
at right angles to each other. 







Equilateral Isosceles 



Scalene 



BlQHT 



MENSURATION 



69 



Kinds of Triangles 
Right Triangles 



In a right triangle the 
square of the hypotenuse 
equals the sum of the 
squares of the other two 
sides or legs. 

If the length of the hy- 
potenuse and one leg of a 
right triangle is known, 
the other side may be 
found by squaring the 
hypotenuse and squaring 
the leg, and extracting the 
square root of their dif- 
ference. 



Example. — If the hypotenuse of a right angle triangle is 
30" and the base is 18'', what is the altitude ? 



A 



802 = 30 X 30 

182 = 18 X 18 

900-324 

VEw 



900 
324 
576 
24". Ans, 




JS" 



Areas of Triangles 

The area of a triangle may be found when the length of the 
thi'ee sides is given by adding the three sides together, divid- 
ing by 2, and subtracting from this sum each side separately. 
Multiply the four results together and find the square root of 
their product. 



70 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — What is the area of a triangle whose sides 
measure 15, 16, and 17 inches, respectively ? 



V24x 9 x8'x7 = \/l2096 

V12096 = 109.98 sq. in. Ana, 



16 






16 






17 






)48 
24- 


15 


= 9 


24- 


16 


= 8 


24- 


17 


= 7 



Area of a Triangle = ^ Ba^e X Altitzide 

Example. — What is the area of a triangle whose base is 
17" and altitude 10"? 

1 ^ 

^ = - X 17 X ^jJ = 85 sq. in. Ans. 



EXAMPLES 

1. A ladder 17 ft. long standing on level ground reached to 
a window 12 ft. from the ground. If it is assumed that the 
wall is perpendicular, how far is the foot of the ladder from 
the base of the wall ? 

2. Find the area of a triangular piece of cloth having the 
base 81" and the height measured from the opposite angle 56". 

3. Find the length of the hypotenuse of a right triangle 
with equal legs and having an area of 280 sq. in. 

4. Find the length of a side of a right triangle with equal 
legs and an area of 72 sq. in. 

5. Find the hypotenuse of a right triangle with a base of 
8" and the altitude of 7". 

6. What is the area of a triangle whose sides measure 12, 
19, and 21 inches ? 

7. What is the altitude of an isosceles triangle having sides 
8 ft. long and a base 6 ft. long ? 



MENSURATION 



71 



Quadrilaterals 

Four-sided plane figures are called quadrilaterals. Among 
them are the trapezoid, trapezium, rectangle, rhombus, and rhom- 
boid. 



Squaab 



Bbctanqle 



Rhomboid 



7/7 



Rhombus 




Tbapbzium 



Tbapbzoid 



Paballblogbam 



Kinds of Quadrilaterals 

A rectangle is a quadrilateral which has its opposite sides 
parallel and its angles right angles. Its area equals the prod- 
uct of its base and altitude. 

A= ha 

A trapezoid is a quadrilateral having only two sides parallel. 
Its area is equal to the product of the altitude by one half the 
sum of the bases. 

A = 



(b + c)x ^a 
In this formula c = length of longest side 

b = length of shortest side 
a = altitude 



ni\ 



A trapezium is a four-sided figure with no two sides parallel. 
The area of a trapezium is found by dividing the trapezium 
into triangles by means of a diagonal. Then the area may be 
found if the diagonal and perpendicular heights of the triangles 
are known. 



72 



VOCATIONAL MATHEMATICS FOR GIRLS 



Example. — In the trapezium ABOD if the diagonal is 43' 
and the perpendiculars 11' and 17', respectively, what is the 
area of the trapezium ? 

43 X V- =^p = 236| sq. ft., area of ABC 
43 X 4^ = 4^=365^ sq. ft., area of ADG 

602 sq. ft., total area 

Arts, 

To find the areas of irregular figures, 
draw the longest diagonal and upon this 
diagonal drop perpendiculars from the ver- 
tices of the figure. These perpendiculars will form trapezoids 
and right triangles whose areas may be determined by the pre- 
ceding rules. The sum of the areas of the separate figures will 
give the area of the whole irregular figure. 




Polygons 

A plane figure bounded by straight lines is a polygon. A 
polygon which has equal sides and equal angles is a regular 
polygon. 

The apothem of a regular polygon is the line drawn from the 
center of the polygon perpen- 
dicular to one of the sides. 

A five-sided polygon is a 
pentagon. 

A six-sided polygon is a 
hexagon. 

An eight-sided polygon is an octagon. 

The shortest distance between the opposite sides of a regu- 
lar hexagon is the perpendicular distance between them, and 
is equal to the diameter of the inscribed circle. 

The diameter of the circumscribed circle is the long diame- 
ter of a regular hexagon. 

The perimeter of a polygon is the sum of all its sides. 





Pentagon 



Hexagon 



MENSURATION 73 

The area of a regular polygon equals one half the product of 
the apothem and the perimeter. 

Formula -4 = i dP 

In this formula P = perimeter 

a = apothem 

Ellipse 

Only the approximate circumference of an ellipse can be ob- 
tained. 

The circumference of an ellipse equals one half the product of 
the sum of two diameters and ir. 

If di = major diameter 

dj = minor diameter 
(7= circumference 




then C = ^±^,r 

The area of an ellipse is equal to one fourth the product of 
the major and minor diameters by w. 

If A= area 

di = major diameter 
dz = minor diameter 

then A = w^ 

4 

EXAMPLES 

1. Find the area of a trapezium if the diagonal is 93' and 
the perpendiculars are 19' and 33'. 

2. What is the area of a trapezoid whose parallel sides are 
18 ft and 12 ft., and the altitude 8 ft. ? 

3. What is the distance around an ellipse whose major 
diameter is 14" and minor diameter 8" ? 



74 VOCATIONAL MATHEMATICS FOR GIRLS 

4. In the map of a country a district is found to have two 
of its boundaries approximately parallel and equal to 276 and 
216 miles. If the breadth is 100 miles, what is its area ? 

5. If the greater and lesser diameters of an elliptical man- 
hole door are 2' 9" and 2' &', what is its area ? 

6. Find the area of a trapezium if the diagonal is 78'' and 
the perpendiculars 18" and 27". 

7. The greater diameter of an elliptical funnel is 4 ft. 6 in., 
and the lesser diameter is 4 ft. What is its area ? 

8. Find the perimeter of a hexagon having each side 15" 
long. 

9. What is the area of a pentagon whose apothem is 4y 
and whose side is 5" ? 

Volumes 

The volume of a rectangular-shaped bar is found by multi- 
plying the area of the base by the length. If the area is in 
square inches, the length must be in inches. 

The volume of a cube is equal to the cube of an edge. 

The contents or volume of a cylindrical solid is equal to the 
product of the area of the base by the height. 

If S = contents or capacity of cylinder 

R = radius of base 
H= height of cylinder 
V = 3.1416+ or ^ (approx.) 

8 = irB'H 

Example. — Find the contents of a cylindrical tank whose 
inside diameter is 14" and height 6'. 

S = tR^H 

H= 6' = 72" 

^ = yx7x7x72 = 11,088 cu. in. 




MENSURATION 



75 



The Pyramid 

The volume of a pyramid equals one 
third of the product of the area of the base 
and the altitude. 

V=\ba 

The volume of a frustum of a pyramid 
equals the product of one third the alti- 
tude and the sum of the two bases and the 
square root of the product of the bases. 




The surface of a regular pyramid is equal to the product of 
the perimeter of the bases and one half the slant height. 

S^Pxish 

The Cone 

A cone is a solid generated by a right triangle revolving on 
one of its legs as an axis. 

The altitude of the cone is the perpendicular distance from 
the base to the apex. 

The volume of a cone equals the product of the area of the 
base and one third of the altitude. 

or F= .2618 L^H 

Example. — What is the volume of a cone 1^" 
in diameter and 4" high ? 

Area of base = .7864 x } 



7.0686 



= 1.7671 sq. in. 




F=.2618D2fi- 

= .2618 X J X 4 = 2.3662 cu. in. Ans. 

The lateral surface of a cone equals one half the product of 
the perimeter of the base by the slant height. 



76 



VOCATIONAL MATHEMATICS FOR GIRLS 



Example. — What is the surface of a cone having a slant 
height of 36 in., and a diameter of 14 in. ? 

C = irZ> = 14 X V = 44" 
^^^ = 792 sq. in. Ans, 



Frustum of a Cone 

The frustum of a cone is the part of a cone included between 
the base and a plane or upper base which is parallel to the 
lower base. 

The volume of a frustum of a cone equals the product of one 
third of the altitude and the sum of the two bases and the 
square root of their product. 



When 



altitude 
upper base 
lower base 



H 

R 

F= \ H(B-^B' + VBB') 




The lateral surface of a fi^stum of a cone equals one half the 
product of the slant height and the sum of the perimeters 
of the bases. 

The Sphere 

The volume of a sphere is equal to 

3 

where R is the radius. 

The surface of a sphere is equal to 

The Barrel 

To find the cubical contents of a barrel, (1) multiply the 
square of the largest diameter by 2, (2) add to this product 




MENSURATION 77 

the square of the head diameter, and (3) multiply this sum by 
the length of the barrel and that product by .2618. 

Example. — Find the cubical contents of a barrel whose 
largest diameter is 21" and head diameter 18", and whose 
length is 33". 

212 = 441 X 2 = 882 V= [(Z>2 x 2) + ^2] x Z X .2618 
182 = 324 _^ 39798 

1206 .2618 

33 10419.11 cu. in. 

3618 
3618 10419.11 



39798 231 



= 45.10 gal. Ans, 



Similar Figures 

Similar figures are figures that have exactly the same shape. 
The areas of similar figures have the same ratio as the 
squares of their corresponding dimensions. 

Example. — If two boilers are 15' and 20' in length, what is 
the ratio of their surfaces ? 

JJ = }, ratio of lengths 

— = — , ratio of surfaces 
42 16 

One boiler is ^^ as large as the other. Ans. 

The volumes of similar figures are to each other as the cubes 
of their corresponding dimensions. 

Example. — If Jiwo iron balls have 8" and 12" diameters, 
respectively, what is the ratio of their volumes ? 

j^ = I, ratio of diameters 

= ^, ratio of their volumes. Ans, 

One ball weighs ^ as much as the other. 



78 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

1. Find the volume of a rectangular box with the following 
inside dimensions : 8" by 10" and 4' long. 

2. The radius of the small end of a bucket is 4 in. Water 
stands in the bucket to a depth of 9 in., and the radius of the 
surface of the water is 6 in. (1) Find the volume of the water 
in cubic inches. (2) Find the volume of the water in gallons 
if a cubic foot contains 7.48 gal. 

3. What is the volume of a steel cone 2^" in diameter and 
6" high ? 

4. Find the contents of a barrel whose largest diameter is 
22", head diameter 18", and height 35". 

5. What is the volume of a sphere 8" in diameter ? 

6. What is the volume of a pyramid with a square base, 
4" on a side and 11" high ? 

7. What is the surface of a wooden cone with a 6" diameter 
and 14" slant height ? 

8. Find the surface of a pyramid with a perimeter of 18" 
and a slant height of 11". 

9. Find the volume of a cask whose height is 3J-' and the 
greatest radius 16", and the least radius 12", respectively. 

10. How many gallons of water will a round tank hold which 
is 4 ft. in diameter at the top, 5 ft. in diameter at the bottom, 
and 8 ft. deep ? (231 cu. in. = 1 gal.) 

11. What is the volume of a cylindrical ring having an 
outside diameter of 6y, an inside diameter of 5^^", and a 
height of 3f " ? What is its outside area ? 

12. If 9 tons of wild hay occupy a cube 7' x 7' x 7', how 
many cubic feet in one ton of hay ? 

13. A sphere has a circumference of 8.2467". (a) What is 
its area ? (b) What is its volume ? 



MENSURATION 79 

14. If it is desired to make a conical can with a base 3.5" in 
diameter to contain ^ pint, what must the height be ? 

15. What is the area of one side of a flat ring if the inside 
diameter is 2|-" and the outside diameter 4 J" ? 

16. There are two balls of the same material with diameters 
4" and 1", respectively. If the smaller one weighs 3 lb., how 
much does the larger one weigh ? 

17. If the inside diameter of a ring is 5 in., what must the 
outside diameter be if the area of the ring is 6.9 sq. in. ? 

18. How much less paint will it take to paint a wooden ball 
4" in diameter than one 10" in diameter ? 

19. What is the weight of a brass ball 3^" in diameter if 
brass weighs .303 lb. per cubic inch ? 

20. A cube is 19" on its edge, (a) Find its total area. 
(b) Its volume. 

21. If a barrel of water contains about 4 cu. ft., what is 
the approximate weight of the barrel of water? (1 cu. ft. 
of water weighs 62.5 lb.) 

22. A conical funnel has an inside diameter of 19.25" at the 
base and is 43" high inside, (a) Find its total area, (b) Find 
its cubical contents. 

23. A pointed heap of corn is in the shape of a cone. How 
many bushels in a heap 10' high, with a base 20' in diameter ? 
A bushel contains 2150.42 cu. in. 

24. Find the capacity of a rectangular bin 6 ft. wide, 5 ft. 
6 in. deep, and 8 ft. 3 in. long. 

25. Find the capacity of a berry box with sloping sides 5.1" 
by 5.1" on top, 4.3" by 4.3" at the bottom, and 2.9" in depth. 

26. Find the capacity of a cylindrical measure 13" in 
diameter and 6" deep. 

27. How many tons of nut coal are in a bin 5 ft. wide and 
8 ft. long if filled evenly to a depth of 4 ft. ? Average nut coal 
weighs 52 lb. to a cubic foot. 



CHAPTER III 

INTERPRETATION OF R£STTLTS 

Reading a Blue Print. — Everyone aliould know how to read 
a blue print, which iB the name given to working plana and 
drawings with white lines upon a blue background. The blue 
print ia the language which the architect uses to the builder, 
the machinist to the pattern maker, the engineer to the foreman 



EiTBBiOE View of Cohplbtkd Hoosb 

of construction, and the designer to the workman. Through 
following the directions of the blue print the carpenter, metal 
worker, and mechanic are able to produce the object wanted 
by the employer and his designer or draftsman. 

Blue Print of a House. — An architect, in drawing the plans 
of a house, usually represents the following views : the ex- 
terior views to show the appearance of the house when it ia 
finished ; views of each floor, including the basement, to show 



INTERPRETATION OF RESULTS 

r/agtiont Cap 




West Elbtation 



East ELKViTiOK 

the location of rooms, windows, doors, and stairs. Detailed 
plans of sections are drawn for the contractors to show the 
method of construction. 



82 



VOCATIONAL MATHEMATICS FOR GIRLS 



//jg^ton* Ctft 




North Elevation 



^/"/agilone. Cap 







South Elevation 



Pupils should be able to form a mental picture of the appear- 
ance of a building constructed from any blue print plan set 
before them. They should have practice in reading the plans 
of the house and in computing the size of the rooms directly 
from the blue print. 



INTERPRETATION OP RESULTS 



1. "What is the height of the rooms on the tirst floor? 

2. What is the height of the rooms on the second floor? 

3. What ia the height of the cellar, first, and second floors ? 




GsouND FLOOa Plan 



84 VOCATIONAL MATHEMATICS FOR GIRLS 

1. What is the frontage of the house ? 

2. What is the depth of the house ? 

3. What is the length and width of the front porch ? 

4. What is the length and width of the living room ? the 
dining room ? the kitchen ? 



rf^fy-Tfry 



■ShinffU 



ea 







Shia^ki 



JBed £oom C 



4oyr 
® BedJioomB 




Second Floor Plan 



1. What is the size of each of the bedrooms? 
with aid of ground floor plan.) 

2. What are the dimensions of the bathroom ? 

3. How large is the storage room ? 



(Compute 



Two views are usually necessary in every working drawing, 
one the plan or top view obtained by looking down upon the 
object, and the other the elevation or front view. When an 



INTERPRETATION OF RESULTS 85 

object is very complicated, a third view, called an end or 
profile view is shown. 

All the information, such as dimensions, etc., necessary to construct 
whatever is represented by the blue print must be supplied on the draw- 
ing. If the blue print represents a machine, it is necessary to show all 
the parts of the machine put together in their proper places. This is 
called an assembly drawing. Then there must be a drawing for each 
part of the building or the machine, giving information as to the size, 
shape, and number of the pieces. Then if there are interior sections, 
these must be represented in section drawings. 

Drawing to Scale. — As it is impossible to draw most objects 
full size on paper, it is necessary to make the drawings pro- 
portionately smaller. This is done by making all the dimen- 
sions of the drawing a certain fraction of the true dimensions 
of the object. A drawing made in this way is said to be drawn 
to scale, 

\\ \\ \\\ \\\\ \\\\\\.\ \\y \\ y \\ \\\ \y \ \ \\\ \\.\ \\ y \\ \ 

II 2 

Vg I z 

\\\M\\l\\\ \ \ \ \ \ 

Triangular Scale 

The dimensions on the drawing designate the actual size of 
the object — not of the drawing. If a drawing were made of 
an iron door 25 inches long, it would be inconvenient to repre- 
sent the actual size of the door, and the drawing might be made 
half or quarter the size of the door, but on the drawing the 
length would read 25 inches. 

In making a drawing " to scale," it becomes very tedious to 
be obliged to calculate all the small dimensions. In order to 
obviate this work a triangular scale is used. It is a rule with 
the different scales marked on it. By practice the student will 
be able to use the scale with as much ease as the ordinary 
rule. 

QUESTIONS AND EXAMPLES 

1. Tell what is the scale and the length of the drawing of 
each of the following : 





86 VOCATIONAL MATHEMATICS FOR GIRLS 

a. An object 14" long drawn half size. 

b. An object 26" long di*awn quarter size. 

c. An object 34" long drawn one third size. 

d. An object 41" long drawn one twelfth size. 

2. If a drawing made to the scale of |" = 1 ft. is reduced 
^ in size, what will the new scale be ? 

3. A drawing is made \ size. If the scale is doubled, how 
many inches to the foot will the new scale be ? 

4. On the ^^" scale, how many feet are there in 18 inches ? 

5. On. the Y^ scale, how many feet are there in 26 inches ? 

6. On the J" scale, how many feet are there in 27 inches ? 

7. If the drawing of a door is made \ size and the length of 
the drawing is 8^", what will it measure if made to scale 3" 
= lft.? 

8. What will be the dimensions of the drawing of a banquet 
hall 582' by 195' if it is made to a scale of yV" = 1 f t. ? 

Estimating Distances. — Everyone meets occasions in daily 
life when it is of utmost importance that distance or weight 
should be correctly estimated. 

Few people have a clear conception of even our common standards of 
measurements. This is due to the fact that the average person has never 
given the proper attention to them. Improvement will be noticed after a 
small amount of drill. To illustrate : if the distances of one inch, one 
foot, one yard, six feet, and ten feet are measured off in a classroom so 
that an actual view of standard distances is obtained, and then pupils are 
asked to estimate other and unknown distances, they will estimate with a 
greater degree of accuracy. Pupils should be able to estimate within 
J inch any distance up to a yard. 

The power of estimating longer distances, such as the distance between 
buildings, across streets, or between streets, may be developed by laying 
off on a straight road one hundred feet, three hundred feet, and five hun- 
dred feet sections, with the proper distance marked on each. 

The same plan applies to heights of buildings, etc. Standards of alti- 
tude may thus be established. 

Pupils should measure in their homes pieces of furniture and wall 
openings so that they may develop an eye for estimating distances. 



INTERPRETATION OF RESULTS 87 

1. Estimate the length and width of the schoolroom. Verify 
this estimate by actual measurement and express the accuracy 
of your estimate in per cent. 

2. Estimate the height and width of the school door. Verify 
this estimate by actual measurement and express the accuracy 
of the estimate in per cent. 

3. Estimate the width and length of the window panes; 
the width and length of the window sill. 

Estimating Weights. — What is true concerning the advan- 
tage of being able to estimate distances applies equally well to 
weights. 

In this, guesswork may be largely eliminated. A little mental figur- 
ing on the part of the pupil will usually produce clear results. Weight 
depends not only on volume but also on the density of the material. 
Regular blocks of wood are excellent to begin with, and later small 
spheres and rectangular blocks of different metals afford good material. 

1. Select blocks of wood, coal, iron, lead, tin, or copper, and 
estimate their respective weights. 

2. Estimate the weight of a chair. 

3. Estimate the weight of different persons. 

Methods of Solving Examples. — Every commercial, household, 
or mechanical problem or operation has two distinct sides : the 
collecting of data, and the solving of the problem. 

The first part, the collecting of data, demands a knowledge 
of the materials and conditions under which the problem is 
given, and calls for the exercise of judgment as to the neces- 
sary accuracy of the work. 

There are three ways by which a problem may be solved : 

1. Exact method. 

2. Rule of thumb method, by the use of a formula or a rule 
committed to memory. 

3. By means of tables. 

The exact method of solving a problem in arithmetic is the 
one usually taught in school and is the method obtained by 



88 VOCATIONAL MATHEMATICS FOR GIRLS 

analysis. Everyone should be able to solve a problem by the 
exact method. 

The Rule of Thumb Method. — Many of the problems that 
arise in home, office, and industrial life have been met before, 
and very careful judgment has been exercised in solving them. 
As the result of this experience and the tendency to abbreviate 
and devise shorter methods that give 'sufficiently accurate re- 
sults, we find many rule of thumb methods used by the house- 
wife, the storekeeper, the nurse, etc. The exact method would 
require considerable time and the use of pencil and paper, 
whereas in cases that are not too complicated the estimates, 
based on experience or rule, give a quick and accurate result. 

In solving problems involving the addition and subtraction 
of fractions, use the yardstick or tape to carry on the compu- 
tation. To illustrate : if we desire to add ^ and ^ of a yard, 
place the thumb over ^ of a yard divisions, then slide (move) the 
thumb along the divisions corresponding to ^ of a yard, and 
then read the number of divisions passed over by the thumb. 
In this case the result is 21 inches. 

The Use of Tables. — In the commercial world the tendency 
is to do everything in the quickest and the most economical 
way. To illustrate : hand labor is more costly than machine 
work, so, whenever possible, machine work is substituted for 
hand labor. The same tendency applies to calculations in the 
dressmaking shop or the office. The exact methods of doing 
examples are not the quickest, nor are they more easily under- 
stood and performed by the ordinary girl than the shorter 
methods. Since a great many of the problems in calculation 
that arise in the daily experiences of the office assistant, the 
housewife, the dressmaker, the nurse, etc. are about ordinary 
things and repeat themselves often, it is not necessary to work 
them anew each time, if, when they are once solved, results are 
kept on file in the form of tables. 

See pages 220, 222, and 254 for tables used in this book. 



PART II — PROBLEMS IN HOMEMAKING 

CHAPTER IV 
THE DISTRIBUTION OF INCOME 

The economic standing of every person in the community 
depends upon three things : (1) (earning capacity, (2) spend- 
ing ability, and (3) the saving habit. The first regulates the 
amount of income; the second determines the purchasing 
power after the amount is earned; the third paves the way 
to independence. 

The welfare of every person, whether single or married, 
depends upon the systematic and careful regulation of each 
of these three items. No matter how large or small his wages 
or salary, if he does not spend his money wisely and carefully, 
or save each week or month a certain per cent of his earnings, 
a young man or woman is not likely to make a success of life. 

A young woman usually has more to do with the spending of money 
than a young man. The wife is really the spender and the husband the 
earner in the ordinary home. Therefore, it becomes necessary for every 
young woman to know how to get one hundred cents out of a dollar. In 
order to do this, she must know how to distribute the income over such 
items as rent, food, clothing, incidental expenses due to sickness, pleas- 
ure, or self-improvement. The proportion spent for each item should be 
carefully regulated. 

Incomes of American Families 

The average family income of both foreign and native born heads is 
about $725 a year; that of families with native bom heads alone is 
about $ 800. Not more than one-fourth have incomes exceeding $ 1000. 
The daily wages of adult men range from $ 1.60 to $ 5.00. This amounts 
on the average from $460 to $1500 a year. 

The family, the head of which earns only a few hundred dollars a 
year, must either be contented with comparatively low standards of liv- 

89 



90 VOCATIONAL MATHEMATICS FOR GIRI^ 

ing or obtain additional income, either titrongh tlie labor of children or 
from boarders or lodgere. The foreign-bom workers resort to the labor 
of children and mothers more than do the native Americana. The second 
course la quite often adopted ao that the average incoma of workingmen's 
families is considerably greater than the average earnings of the heads of 
the families. 




ExPBHDrrUBES 



EXAMPLES 

1. The average workingman's family spends at leaat two- 
fifths of ita income for food. What per cent is spent for food ? 

2. If the income of a workingman's family is $ 800, and the 
amount spent for food is $ 350, what per cent ia spent for food ? 

3. One-fifth of the expenditure of workingmen's families ia 
for rent. What per cent ? 

4. A &.niily with an income of S 800 spends $ 12.50 a 
month for rent. What per cent of the income is spent for 
rent? Is this too much? 

5. A family's income is $760. The father contributes $601. 
What per cent of the income is contributed by the father? 

6. A family of six has an income of $ 840. The father 
contributes $592, mother $112, and one child the balance. 
What per cent is contributed by the mother and child? 



THE DISTRIBUTION OF INCOME 91 

7. A man and wife have an income of $ 971. The husband 
earns $ 514, the wife keeps boarders and lodgers, and provides 
the rest of the income. What per cent of the income is con- 
tributed by the boarders and lodgers ? 

Cost of Subsistence 

Shelter, warmth, and food demand from two-thirds to three- 
fourths of the income of most workingmen's families. This 
leaves for everything else — clothing, furniture, sickness, death, 
insurance, religion, education, amusements, savings — only one- 
third or one-fourth of the income. Between $ 200 and $ 250 a 
year may be considered the usual outlay of workingmen's fami- 
lies for all these purposes combined. It is in these respects 
that the greatest difference appears between the families of 
the comparatively poor and the families of the well-to-do. * The 
well-to-do spend not only more in absolute amount, but also a 
larger proportion of their incomes on these, in general, less 
absolutely necessary things. 

Clothes. — On the average, approximately one-eighth of the 
income in workingmen's families goes for clothes. To those 
who keep abreast of the fashions and who dress with some 
elegance, it may seem quite preposterous that a family of five 
should spend only $ 100 or less a year for clothing, but multi- 
tudes of working-class families are clad with warmth and with 
decency on such an expenditure. 

EXAMPLES 

1. If two-thirds of the average workingman's income is 
spent for shelter, warmth, and food, what per cent is used ? 

2. A family, receiving an income of $ 847, spends $ 579 for 
shelter, warmth, and food. What per cent is used ? 

3. If one-eighth of the income of the average workingmen's 
family is spent for clothes, what is the per cent ? 

4. A family receives an income of $ 768, and $ 94 is spent 
for clothes. What per cent is spent for clothes ? 



92 VOCATIONAL MATHEMATICS FOR GIRLS 

The High Cost of Living 

The average cost of living represents the amount that must 
be expended during a given period by the average family- 
depending on an average income. The maximum or minimum 
cost, however, is another phase of the problem. It no longer 
involves the amount of dollars and cents necessary to buy 
and pay for life's necessaries, but involves questions of home 
management and housekeeping skill, which cannot be stand- 
ardized. About 1907 food and other necessities of life began 
to increase in cost — and this has continued to the present day. 

EXAMPLES 

1. In 1906 a ton of stove coal cost $ 5.75, and in 1915 $ 8.75. 
What was the per cent of increase in the cost of coal ? 

2. In 1907 a suit of clothes cost $ 15. The same suit in 
1912 cost $ 19.75. What was the per cent of increase ? 

3. In 1908 a barrel of flour cost $ 6.10. The same barrel of 
flour cost in 1914 $ 8.25. What was the per cent of increase ? 

Division of Income 

A girl should always consider her income for the entire year 
and divide it with some idea of time and relative proportion. 
If she earns a good salary for only ten months of. the year, 
she must save enough during those months to tide her over the 
other two. For instance, if a teacher earns $ 60 a month for 
10 months of the year, her actual monthly income is $50. 
The milliner, the trained nurse, the actress, and sometimes even 
the girl working in the mill have the same problem to confront. 

No girl has a right to spend nearly all she earns on clothing, 
neither should she spend too much for amusement. We find 
from investigations that have been made that girls earning $ 8 
or $ 10 a week usually spend about half their income on board 
and laundry. Girls earning a larger income may pay more 
for board, but not quite so great a fractional part. In these 



THE DISTRIBUTION OF INCOME 93 

days, when the cost of living is so* high, a girl should consider 
carefully a position that includes her board and laundry, for in 
such a position she will be better off financially at the end 
of the year than her higher salaried sister, who has to pay 
for the cost of her own living. The housegirl can save about 
twice as much as the average stenographer. 

We find that the average girl needs to spend about one-fifth 
of her income for clothing. A poor manager will often spend 
as much as one-third and not be very well dressed at that, 
because she buys cheap materials, that have to be frequently 
replaced, and follows every passing fad and style. Choose 
medium styles and good materials and you will look more 
richly dressed. Keep the shoes shined, straight at the heel, 
and the strings fresh. Keep gloves mended, and as clean as 
possible. If you spend more on clothing than the allotted one- 
fifth, you will have to go without something else. It may be 
spending money, or it may be gift or charity money, and quite 
often it is the bank account that suffers. 

Every person should save some part of his income. One 
never knows when sickness, lack of employment, or ill health 
may come. Saving money is a habit and one that should be 
acquired the very first year that a person earns his own living. 

EXAMPLES 

1. A girl earns $ 12 a week for 42 weeks, and in this time 
spends $ 144 for clothing. Is she living within the per cent 
of her income that should be spent for clothing ? 

2. A salesgirl earns $ 8 a week. She spends $ 98 a year for 
clothes. Is she living within her income ? 

3. A girl earns $ 5 a week and pays half of it to her home. 
She has two car fares and a 14-cent lunch each day. How much 
should she spend on clothing each year ? How much has she 
for spending money each week ? Should she save any money ? 

4. Which girl is the better off financially, one earning $ 6 
a week as a housemaid or one earning $ 7 a week in a store ? 



94 VOCATIONAL MATHEMATICS FOR GIRLS 

Buying; Christmas Gifts 

Let the gift be something useful. Do not be tempted by the 
display of fancy Christmas articles, for it is on these that the 
merchant makes his profit for extra decorations and light. 
Think of the person for whom you are buying. She may not 
have the same tastes as you have, so give something that she 
will like rather than something she ought to like. For in- 
stance, a certain girl may be very fond of light hair-ribbons 
when you know that dark ones would be much more sensible, 
but at Christmas give the light ones. 

The stores always show an extra supply of fancy neckwear. 
A collar cannot be worn more than three days without becom- 
ing soiled, so even 25 cents is too much to pay for something 
that cannot be cleansed. Over-trimmed Dutch collars and 
jabots easily rip apart. Choose the plain ordinary ones that 
you would be glad to wear any day. You see whole counters 
of handkerchiefs displayed with embroidery, lace, and ruffles. 
A linen handkerchief, even of very coarse texture, is more 
suitable. 

Be careful also about bright colors, for everything about the 
store is so gay that ordinary things appear dull, but when 
you get them out against the white snow, they will be bright 
enough. 

EXAMPLES 

1. Shortly before Christmas I purchased ^ doz. handker- 
chiefs for $ 1.50. One month later I purchased the same kind 
of handkerchiefs at 16f cents each or 6 for $ 1.00. What per 
cent did I save on the second purchase ? 

2. I also bought a chiffon scarf for which I paid $2.25. 
Early in the fall I saw similar scarfs selling for $ 1.50. How 
much did I lose by not making my purchase at that time? 
What per cent did I lose ? 

3. I bought at Christmas two pairs of silk stockings at 
$ 1.50 per pair. If I had purchased the stockings in October 



THE DISTRIBUTION OF INCOME 



95 



they would have cost me $ 1.12^ per pair. How much would 
I have saved ? What per cent would I have saved ? 

An Expense Account Book 

Every person and every family should keep an expense 
account showing each year's record of receipts and expendi- 
tures. A sample form is shown in page 96. Rule sheets in a 
similar manner for the solution of the problems that follow. 

At the end of the year a summary should be made of receipts and dis- 
bursements in some such form as the following : 



Yearly Summary 

HeceipU 



DiahuraemenU 



Receipts 

Cash on hand January 1 
Salary, etc. 
Other Income 



Disbursements 

Savings and Insurance 

Rent 

Food 

Clothing 

Laundry 

Car fares 

Stamps and Stationery 

Health 

Recreation 

Education 

Gifts, Church, Charity 

Incidentals 

Balance on Hand December 31 



Totals 



Rule similar sheets for the solution of the following problems. 






96 



VOCATIONAL MATHEMATICS FOR GIRLS 





Details of 
Disbursements 








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THE DISTRIBUTION OF INCOME 97 

EXAMPLES 

1. A man and wife have an income of $ 1000 a year. The 
disbursements for the month of October are as follows : 

Kentf $15 ^ Tooth paste, $.18 

Telephone, 1.46 Provisions, 6.86 

Repair on coat, 6.80 Life insurance, 7.40 

Gas, .76 Coal, 7.60 

Dinner, 1.60 Outlook (1 year), 8.00 

Stationery, 2.61 Assistance, .60. 

Fares, .86 Shampoo, .60 

Groceries, 10.36 Fares, .60 

Fruit, .30 Rubbers, .90 

Theater, .60 Soap, .10 

Papers, .06 Church, .26 

Church, .26 Milk, .66 

Milk, .71 Ice, .40 

Ice, .46 Papers, .11 

Electricity, 1.00 Vase for D., .75 

Laundry, .60 Peroxide, .26 

Enter the above disbursements in the expense account book. 
Find the total amount. 

What per cent was spent for food? house? clothing? 
housekeeping ? luxuries ? savings ? 

2. The items of expense for the month of January, 1915, are : 
rent and water, $ 15 ; operating expense : light and heat, $ 11 ; 
food : meats, groceries, $ 30 ; labor or services, $ 16.65 ; cloth- 
ing, $ 15 ; physician, $ 1 ; carfares, % 2.85 ; books, $ 1.00 ; 
amusements, % 4 ; cigars, $ 1.00 ; gifts, $ 1.00 ; sundry ex- 
penses, $ 1.50. Treat as in Ex. 1. 

3. A family of two receives an income of $ 1200 a year. 
They spend per week $ 6.93 for food, $ 3.51 for rent, % 3.49 
for operating expenses, $ 5.81 for contingency. What is the 
amount for each itiem per month (4 weeks) ? per year 
(52 weeks) ? What is the per cent of each item ? 



98 



VOCATIONAL MATHEMATICS FOR GIRLS 



4. A young married woman has an income of $ 1200 a year 
— $ 100 a month. The following represents the way she 
spends her income a month : 



Savings bank, $5.00 

Rent, 25.00 

Insurance, 5.00 

Groceries, 4.70 

Meat and fish, 11.15 

Milk, 2.79 

Clothing, 12.00 

Heat and light, 5.00 

Laundry and supplies, 2.00 

Help, 4.00 

Repairs and replenishing, .50 



Ice (set aside in the winter months 
for the summer), f 0.25 

Necessary carfares (the house is 
located in the country), 2.70 

Recreation, 3.00 

Avocation, 3.00 

Literature, .50 

Church and charity, .80 

Remembrances, .75 

Fire insurance, .09 



Enter the above in the expense account book. 

How much was left toward the next month's expense ? Can 
you improve on this? What is the per cent for food? 
Clothing ? 

5. A girl 14 years of age has cost her parents an amount 
equal to the following items : 



Fo6d, .$597.16 
Clothing, 339.66 
Furniture, 88.65 



Carfare to school, 1 11.00 
Doctor, 70.00 
Dentist, 10.00 



What is the per cent for each item ? 

6. A family of seven — three grown people and four chil- 
dren — lived in a southern city on $ 600 — $ 50 per month. 
The expenses each month were as follows ; 



House rent, ^ 12.00 
Groceries, 12.00 
Washing, 5.00 



Bread, $2.50 
Beef, 2.60 
Vegetables, 2.00 



What is the balance for clothing and fuel ? What is the 
per cent of income spent for food ? Clothing ? Rent ? Suggest 
points of saving. 



THE DISTRIBUTION OF INCOME 



99 



7. A girl in New York City lives on $ 10 a week. The ex- 
penses are as follows : 



Board and washing, $ 300.00 
Luncheons and carfare, 100.00 



Clothing and vacation, $96.00 
Church and charity, 10.00 



How much can she save ? What is the per cent for cloth- 
ing ? Incidentals ? 

Can you suggest any improvements in the distribution of her 
income ? 

8. A family of four lives on $ 750 a year. The expenses 
are as follows : 



Rent, 1 180.00 

Fuel, 62.00 

Meat, oysters, cheese, 96.00 



Groceries, including vegetables, 
butter, eggs, milk, kerosene, 
soap, etc., $241.00 

Clothing, about 146.00 



How much is left for the savings bank ? What per cent for 
rent ? Food ? Clothing ? Operating expenses ? 



CHAPTER V 
FOOD 

Since half of the income of the average family is spent for 
food, it is important that this expenditure should be made 
intelligently. Experts of the United States Department of 
Agriculture estimate that the food waste in a great many of 
the American homes is as high as 20 % . The causes of waste 
may be classified as follows : Needlessly expensive material, 
providing little nutrition ; failure to select according to season ; 
great amounts thrown away; poor preparation; badly con- 
structed ovens. 

If this waste were checked, it would afford an increase in 
the purchasing power of the income which would appreciably 
lift the family to a higher plane of efficiency. The efficiency 
of every person depends upon the energy and constant repair 
of the body. A woman should know the cost of food and real- 
ize what food value she is receiving for her money. It may 
seem strange, but it is true, that "a Eoman feast, a Lenten 
fast, a Delmonico dinner, and the lunch of the wayside beggar 
contain the same few elements of nutrition." 

The art of cooking can transform the common but nutritious foods 
into the most appetizing dishes. Further than this, the freshness and 
attractiveness of the food, the way in which it is served, the sur- 
roundings — all affect the appetite and the power to digest. Cost, 
which must always be considered in the limited income In relation to 
the nutritive value of food, is influenced by an equally important factor 
— waste. 

The problem of feeding our bodies is primarily a question of supply 
and demand. Of course, the element of pleasure in eating is a properly 

100 



POOD 






normal one, for enjoyment aids digestion. We must, however, eat to live 
rather than live to eat. 

Every motion of the body and every thought in the brain destroy cer- 
tain tissues. This material must be replaced from the food we eat. The 
two objects of eating are tissue repair in the adult and tissue repair 
plus growth in the child. As soon as we realize that these two pur- 
poses should determine the character of the food we eat, then we 
shall know the importance of intelligent instead of haphazard choice of 
food. 

To repair the*body means to supply the elements needed to renew the 
tissues that are worn or destroyed. We can sepiurate the elements of the 
human body broadly into water, protein, carbohydrates, fats, and ash. 
Water composes 60 per cent of a normal man's body. In other words, 
a 200-pound man is composed of only 80 pounds of solids, of which 18 
per cent is composed of protein, 16 per cent of fat, 1 per cent of carbo- 
hydrates, and 6 per cent of ash. 

Water aids digestion and is necessary in the economy of life. Protein 
is the basis of bone, muscle and other tissues, and essential to the body 
structure. Fat is an important source of energy in the form of heat 
and muscular power. Carbohydrates are transformed into fat and are 
important constituents, though in small proportions in the human body. 
Ash is composed of potash, soda, and phosphates of lime, and is necessary 
in forming bone. The diet best fitted to supply all the needs of the healthy 
human organism must contain a correct proportion of these elements ; it is 
called the balanced ration. 



Nutritive Ingredients (or Nutrients) of Food 

What has thus far been said about the ingredients of food and the ways 
in which they are used in the body may be briefly summarized in the 
following manner : 

f Water 



Food as purchased 
contains 



Edible portion . . . 
e.g. flesh of meat, yolk 
and white of eggs, wheat, 
flour, etc. 

Refuse. 

6.^. bones, entrails, shells, 

bran, etc. 



Nutrients 



' Protein 
Fats 

Carbohydrates 
Mineral mat- 
ters. 



•I • • 
• ••• 



• • • 

r • • 
• • • 



• : 



•1(12 :• tVWCJA^iONAt MATHEMATICS FOR GIRLS 
.•VTi^ I •• • ••' 



Are stored in the body as fat 



Uses of Nutrients in the Body 

Protein Forms tissue .... 

e g. white (albumen) 

of eggs, curd (casein) 

of milk, lean meat, 

gluten of wheat, etc. 
£ a vS • • . ' . . • 

e.g. fat of meat, butter, 

olive oil, oils of com 

and wheat, etc. 
Carbohydrates .... 

e.g. sugar, starch, etc. 
Mineral matters (ash) . 

e,g. phosphates of lime, 

potash, soda, etc. 



Are transformed into fat . 



Repairs tissues 

All serve as 
fuel to yield 
energy in the 
forms of heat 
and muscular 
power. 



Share in forming bone, assist in digestion, etc. 



The views thus presented lead to the following definitions : (1) Food 
is that which, taken into the body, builds tissue or yields energy. 
(2) The most healthful food is that which best fills the needs of the man. 
(8) The cheapest food is that which furnishes the largest amount of 
nutriment at the least cost. (4 ) The best food is that which is at the same 
time most healthful and cheapest. 

EXAMPLES 

Carbohydrates are present in large proportions in all the cereals, bread, 
and potatoes, and are almost 100 % pure in sugar. There is a widespread 
notion that starch, which is a fat-producing element, is mostly contained 
in potatoes, and many people who wish to reduce flesh omit potatoes 
and substitute rice or larger quantities of bread or cereals. The fact is 
that the white potato contains only 15 % carbohydrates and the sweet 
potato 27 %, while rice has 77 % and the breads range from whole wheat 
bread at 49 % to soda crackers at 73 % and the cereals from oats at 69 % 
to rye, 78 %. 

1. How many ounces of carbohydrates in f lb. of white 
potatoes ? 

,2. Find the number of pounds of carbohydrates in 4 lb. of 
rice. 

3. Find the number of ounces of carbohydrates in a loaf of 
whole wheat bread (| lb.) 



FOOD 103 

4. How many ounces of carbohydrates in a 2 lb. package of 
Quaker Oats ? 

5. How many ounces of carbohydrates in 4 oz. of soda 
crackers ? 

EXAMPLES 

The proportion of ash in foods is small, and as the body requires 6 per 
cent, we must be sure to supply it in the food. Salt cod has the largest 
proportion, 26 per cent, and we find it in good quantities in butter, dried 
beef, smoked herring, and bacon. 

Of the proteins, lean meat is the one most easily digested and assim-> 
ilated. Curiously enough, dried beef has the largest proportion of pro- 
tein of any flesh meat, 30 per cent, while next in range are leg of lamb, 
beef steak, roast beef, and fowl, with about 18 per cent. 

Let us note the protein value of fish. Smoked herring, despised by 
many, contains 36 per cent of protein, salt cod and canned salmon 21 per 
cent, and perch, halibut, mackerel, and fresh cod average 18 per cent, 
equal in food value per pound to the best beef and fowl. The peanut has 
27 per cent of its weight protein, and peanut butter 29 per cent. 

Fat is found in large proportion in nuts, especially in walnuts, which 
contain 63 per cent, and cocoanuts 67 per cent. Bacon contains 67 per 
cent of fat, and butter 86 per cent. 

1. If a man weighs 189 pounds, how many pounds of water 
in his weight? How many pounds of solids? How many 
pounds of fat ? protein ? carbohydrates ? 

2. How many ounces of protein in a pound and a half dried 
beef? 

3. Give the number of ounces of protein in a pound fowl. 

4. Give the number of ounces of protein in 1^^ lb. of herring. 

5. How many ounces of fat in 1^ lb. of shelled walnuts ? 

Kitchen Weights and Measures 

Correct measurements are absolutely necessary to insure 
successful results in cooking. 

Sift flour, meal, powdered sugar and soda before measuring. 
Many articles settle hard or in lumps and should be stirred 
and pulverized before measuring. 



104 VOCATIONAL MATHEMATICS FOR GIRLS 

Measure all materials level full, leveling with knife. Do 
not pack powdered articles. Butter, lard, etc., should be 
packed in measure and leveled. 

A half spoonful should be taken lengthwise and not crosswise. 
A quarter spoonful should be taken by dividing a half crosswise. 
A third spoonful is obtained by dividing twice crosswise. 

Equivalents To Make One Pound 

8 teaspoons equal 1 tablespoon. 4 cups flour. 

4 tablespoons equal ^ cup. 2f cups com meal. 

2 cups equal 1 pint. 2} cups oatmeal. 

2 pints equal 1 quart. 6 cups rolled oats. 

4 quai'ts equal 1 gallon. 4| cups rye meal. 

4 cups flour equal 1 lb. 2 cups rice. 

2 cups sugar equal 1 lb. 2 cups granulated sugar. 

16 tablespoons dry ingredients 2} cups brown sugar. 

equal 1 cup. 2f cups powdered sugar. 

12 tablespoons liquid equal 1 cup. 3^ cups confectioner's sugar. 

2 cups butter. 

2 cups chopped meat. . 

4| cups ground coffee. 

t. is the abbreviation for teaspoonful; and tb., f or tablespoonful. 

EXAMPLES 

1. How many teaspoons in 4 tablespoons ? 

2. How many tablespoons in f cup ? 

3. How many cups are equivalent to 5 pints ? 

4. Give the number of tablespoons in a pint. 

5. Give the number of teaspoons in 3 quarts and 1 pint. 

6. A cup of flour weighs how many ounces ? What part 
of a pound ? 

7. How many cups will 56 tablespoons of baking soda fill ? 

8. A pint of liquid contains how many tablespoons ? 

9. A cup of sugar weighs how many ounces ? 

10. Two cups of corn meal is what part of a pound ? 



FOOD 105 

11. Give the weight in ounces and fractions of a pound of 
the following quantities : — 

(a) 1 cup of butter. (/) 1 .cup of powdered sugar. 

(b) 1 cup of rice, (g) 1 cup of brown sugar. 

(c) 3 cups chopped meat. (h) 1 cup of rye meal. 

(d) 1 cup of coffee. (i) 1 cup of oatmeal. 

(e) 1 cup of conf . sugar. 

12. What is the cost of each of the following : 

(a) 1 cup of oatmeal at 5 cts. a pound ? 

(b) 2 cups of sugar at 5 lbs. for 33 cts.? 

(c) 2^ cups of rice at 5 cts. a pound ? 

(d) ^ cup of milk at 8 cts. a quart ? 

(e) f cup of butter at 35 cts. a pound ? 
(/) 2 eggs at 38 cts. a dozen ? 

(g) I peck of potatoes at 72 cts. a bushel ? 

(h) 3^ level teaspoons of sugar at 8 cts. a pound ? 

(i) ^ cup of vinegar at 9 cts. a quart. 

Cost of Food 

In order to calculate the cost of food it is necessary to know 
price per pound, price per cupful, and even price per teaspoon- 
ful. The price should be calculated to three decimal places 
and the results tabulated as follows : 

Cost per pound or quart. 

Number of cupfuls in pound or quart. 

Cost per cupful. 

Cost per tablespoonful. 

Cost per teaspoonful. 

When it is once calculated the data may be used from day 
to day in calculating the cost of food. 

EXAMPLES 

1. What is the cost per teaspoonful of cocoa at 38 cents a 
pound ? (4 cups in a pound.) 



106 VOCATIONAL MATHEMATICS FOR GIRLS 

2. What is the cost of a third of a cup of powdered sugar 
at 10 cents a pound ? (2f cups in a pound.) 

3. What is the cost of a tablespoonful of cream at 23 cents 
a pint ? 

4. What is the cost of 2 teaspoonfuls of sugar at 6^ cents 
a pound? (2 cups in a pound.) 

5. What is the cost of 6 nuts at 20 cents a pound ? (29 
walnuts in a pound.) 

6. What is the cost of 6 tablespoons of coffee at 35 cents a 
pound ? (4^ cups of coffee in a pound.) 

7. What is the cost of 3 slices of toast at 5 cents a loaf ? 
(10 slices in a loaf.) 

8. What is the cost of a pat of butter at 38 cents a pound ? 
(16 pats of butter in a pound.) 

9. What is the cost of an ordinary serving of cornflakes 
at 10 cents a pound ? (15 servings in a pound.) 

10. What is the cost of a serving of cream (| of cup) at 
24 cents a pint ? 

11. What is the cost of an ordinary serving of macaroni at 
12 cents a pound ? (11 servings to the pound.) 

12. What is the cost of a serving of cheese at 20 cents a 
pound ? (9 servings in a pound.) 

13. What is the cost of a serving of cabbage salad if cab- 
bage is 3 cents a pound and two servings in a pound? (A 
tablespoonful of salad dressing of equal parts of oil and vinegar. 
Oil is 25 cents a half pint. Vinegar is 10 cents a quart.) 

14. What is the cost of a serving of stewed apricots at 18 
cents a pound ? (A half pound of sugar at 7 cents is added 
to the apricots. Nine servings in a pound.) 



FOOD 107 

15. What is . the cost of an ordinary serving of mashed 
potatoes at 25 cents a half peck ? (A teaspoonf ul of milk at 
8 cents a quart to each serving. A half pat of butter at 37 
cents a pound, sixteen pats in a pound. Twenty-one servings 
in a half peck.) 

16. What is the cost of a serving of grape jelly {^ oz.) at 
13 cents a pound ? 

Girls should know how to make out a tabulation of stand- 
ard food materials, the current price for such material at the 
local stores, and the cost of quantities commonly used in cook- 
ing, as one cup or one tablespoonful. They should, in addi- 
tion, know how to take common recipes that are used in cook- 
ing classes •and reckon the cost. This will aid in reckoning 
the cost of meals iand arranging them economically. In a like 
manner, the cost of meals for one day and for one week may 
be calculated to see how near they are living within their 
income. 

EXAMPLES 

1. A supper consisting of the following is served for 14 
people : codfish in tomato sauce, cereal muffins, cookies, and 
tea. What is the cost per person if the codfish costs 30 cents, 
the muffins 24 cents, the cookies 34 cents, the tea 10 cents, 
and fuel 5 cents ? 

2. What is the cost per person for the following meal 
when 14 are served ? The meal consists of milk toast, stewed 
prunes with lemon, chocolate layer cake, and tea. The milk 
toast costs 25 cents, the prunes 25 cents, the cake 50 cents, 
the tea 10 cents, and fuel 10 cents. 

3. In a pound of rolled oats, costing 8 cents, there are 4 
cups. What is the cost of a serving (\ cup) of rolled oats ? 

4. In a package of cream of wheat costing 14 cents there 
are 4^ cups. One eighth of a cup is necessary for a serving. 
What is the cost of a serving ? 



108 VOCATIONAL MATHEMATICS FOR GIRLS 



5. Compute the cost of a cup of white sauce from the fol- 
lowing recipe : 



1 cup milk 
4i t; flour 
4^ t. butter 
} t. salt 



milk, Oc a quart 
flour, 6c a pound 
butter, 39c a pound 
salt Ic a cup 



6. A dinner consisting of mashed potatoes, peas, rib roast, 
rolls, jelly, fruit salad, krummel torte, coffee, cream and sugar 
is served for six. What is the cost per person? Estimate 
portions from amounts given. 



Dishes 

Mashed potatoes 



Peas 

Kib roast 
Gravy 
Rolls 



Jelly 
Apple and 

grape salad 
Saratoga flakes 
Salad dressing 



Krummel Torte 



Coffee 
Sugar 
Sugar total 
Butter total 



AMouirre 
J pk. potatoes at 46c per pk. 
1} cups milk at 2c per cup 
8 tablespoons butter at 40c per lb. 
6 tablespoons or ^ can at 13c per can 
f of 4-lb. roast at 28c per lb. 
3 cups flour at .IJc per cup 
J cup milk at 2c per cup 
3 tablespoons sugar, 2 tablespoons butter, } yeast cake 

at 2c 
i glass at 10c per glass 
3 apples at 8c per doz. 
} lb. grapes at 10c per lb. 
\ package at 15c per package 
J cup vinegar at 8c per qt. 
1 egg at 30c per doz. 
3 tablespoons sugar at 7c per lb. 
1 tablespoon butter at 40c per lb. 
I package dates at 10c per package 
} cup nuts at 70c per lb., 3 cups per lb. 
IJ eggs at 30c per doz. 
i pt. whipping cream for torte as well as for coffee at 15o 

}pt. 

6 tablespoons at 34c per lb. 
3 teaspoons 

7 tablespoons = ^ cup at 7c per lb. 
6 tablespoons = } cup at 40c per lb. 



FOOD 



109 



7. The following breakfast and luncheon were served for 

six. What was the cost of each meal per person? 

Dishes Amount psk Pebson 

Orange 1 medium-sized, 30c a doz. 

Toast 2 thin slices, ^c a slice 

Butter 1 ordinary pat, Jc 

Egg 1 medium-sized, 3c 

Com flakes 1 ordinary serving, .2c 

Cream f cup, 16c J pt. 

Sugar 3 J level teaspoons, 7c lb. 

Coffee 2^ tb. at 34c per lb 



Macaroni 

and cheese 
Cabbage salad 
Cooked dressing 
Stewed apricots 
Doughnut 
Milk 

a The following 
cost per person ? 

Dishes 

Bib roast 1 

Brown gravy j 

Butter 

Mashed potatoes 

Peas 

Jelly 

Buns 

Apple and 

grape salad 
Cooked dressing 
Saratoga flakes 
Krummel Torte 

Dates 

Nuts 
Whipping cream 
Sugar 
Cream 



Luncheon 

Ordinary serving, 4c 
} cu. in., .02c 
Large serving, .02c 
1 tablespoon, .OOJc 
1 serving, 2c 
1 large, Ic 
1 cup, 3c 

dinner was served for six. 

Amount per Person 



What is the 



Fairly large serving, 9c 

Ordinary pat, Jc 
Ordinary serving, Jc 
Very small, Jc 
Very small, Ic 

2 buns, Ic apiece 
} apple, }c 

i oz. of grapes, Ic 
1 tablespoon, ^c 

3 portions, lOc 0, pkg. (12 portions) 

6 dates, 10c a lb. (30 dates in a lb.) 
6 nuts, 18c a lb. (22 nuts in a lb.) 

1 tablespoon, 16c J pt. 

2 teaspoons, 7c a lb. 

1 tablespoon, 25c a pt. 



110 VOCATIONAL MATHEMATICS FOR GIRLS 

9. The recipe for potato soup for a family of man, wife, and 
two cliildren is : 

3 large potatoes 2 tb. flour 

1 qt. milk 1^ t. salt 

2 slices onion dash pepper 

3 tb. butter 1 1. chopped parsley 

a. What is the recipe for five men, two women, and three 
children (consider a child's diet one-half a man's diet, and a 
woman's equal to a man's)? b. What is the recipe for one 
person (adult) ? 

10. The recipe for a vegetable soup for a family of husband, 
wife, and two children is : 

Beeff 1 lb. 1^ qt. water 

Bones, 1 lb. 5 tb. butter 

^ cup carrot 1 tb. finely chopped parsley 

^ cup turnip salt 

1^ cups potato pepper 

\ onion 

a. What is the recipe for a family of three men, two 
women, and a child ? 6. What is the recipe for a child ? 

11. The recipe for sour-milk biscuits for a family of hus- 
band, wife, and two children is : 

2i c. flour 1 tb. fat (lard or butter) 

1 1. salt 1 c. sour milk, or ^ c. sour milk 

^ t. soda ^ c water 

a. What is the recipe for a man, wife, two boarders, and 
five children ? 6. What is the recipe for one adult ? 

Food Values 

The heating value of food is measured by the amount of heat 
given off when burned. The food taken into the human system 
is oxidized slowly in order to give us the ability to do work ; 



FOOD 111 

the number of heat units that food is capable of giving a body 
represents the quantity of energy the food will provide. 

There are two units for measuring heat : the English and metric unit. 
The English unit is called a Calorie, and it represents the quantity of heat 
necessary to raise a pound of water four degrees on the Fahrenheit scale. 
The metric unit is also called a calorie and is the amount of heat neces- 
sary to raise a gram of water one degree on the Centigrade scale. The 
English unit is called a large Calorie and is represented by the large letter 
C while the metric unit is called a small calorie and is represented by the 
small letter c. 

All scientific experiments are conducted in the metric system, while 
our measurements in daily life are in the English system. It is only nec- 
essary to know the English unit, which is used in this book. 

The United States Department of Agriculture 

The Department Bulletin No. 28 gives the fuel value of foods. It may 
be well to know how the fuel value is determined. To illustrate : What 
is the fuel value of flour ? Careful experiments by the Department of 
Agriculture show that flour is composed of 10.6 ^o protein, 1.1 <j^ fat, and 
76.6 ^ carbohydrates. Other experiments have shown that : 

1 gram of protein yields 4100 Calories (C) 
1 gram of fat yields 9300 Calories (C) 
1 gram of carbohydrates yields 4100 Calories (C) 
or 1 ounce of protein yields 113 Calories (C) 

1 ounce of fat yields 256 Calories (C) 
1 ounce of carbohydrates yields 113 Calories (C) 

Then each ounce of flour contains 

0.106 ounce protein 

0.011 ounce fat 

0.763 ounce carbohydrates 

Since each ounce of protein yields 1 13 C, 0. 106 oz. will yield 113 x 0. 106, 
or 11.98 C. 0.011 oz. of fat will yield 256 x 0.011, or 2.81 C. 0.763 oz. 
of carbohydrates will yield 0.763 x 113, or 86.22 C. 

EXAMPLES 

1. Rice contains 6% protein, 79.5% carbohydrates, and 
0.7 % fat. What is the fuel value of 3 oz. rice ? 



112 VOCATIONAL MATHEMATICS FOR GIRLS 

2. Milk contains 4 % protein, 5 % carbohydrates, and 4 % 
fat. What is the fuel value of 8 oz. milk ? 

3. Beans contain 23.1 % protein, 57 % carbohydrates, and 
2 % fat. What is the fuel value of 5 oz. beans ? 

4. Chicken contains 24.4 % protein and 2 % fat. What is 
the fuel value of 7 oz. chicken ? 

5. Pork (shoulder) contains 16 % protein and 32.8 % fat. 
What is the fuel value of 2 lb. pork ? 

6. Butter contain^ 0.6 % protein, 0.5 % carbohydrates, and 
85 % fat. What is the fuel value of | lb. butter ? 

7. Eggs contain 14.9 % protein and 10.5 % fat. What is the 
fuel value of 7 oz. eggs ? 

8. Cornmeal contains 9.2% protein, 70.6% carbohydrates, 
and 3.8 % fat. What is the fuel value of 3 lb. cornmeal ? 

9. English walnuts contain 16.6% protein, 63.4% carbo- 
hydrates, and 16.1% fat. W^hat is the fuel value of \ lb. 
nuts? 

It is clear that a balanced ration need not be an expensive one. The 
amount of heat required by the body varies from 2000 to 3600 calories 
approximately, dependent upon age, occupation, and sex. A family of a 
working man, wife, and three children under sixteen years of age requires 
12,000 total calories, 1200 to 1800 of protein, or from 10 to 26 9^ of the 
total amount required. The quantity of food taken at each meal may 
vary, provided the total quantities each day reach the standard required. 
Some authorities suggest about four-twelfths for breakfast, three-twelfths 
for luncheon, and five-twelfths for dinner. 

There are two defects in American diet. First, we fail to have a bal- 
anced ration and, second, we think that the richer the food the more 
nourishing it is, and that its goodness is in proportion to the hours spent 
in its preparation. 

The protein is the most valuable and expensive part of the food supply 
and it is wise to have a list of proteins so that one can substitute the lesser 
for the more expensive. Protein, of which we need 18 %, is found more 
generally in fish than in meat, and the inexpensive peanut is an appe- 
tizing substitute; fat, of which we need 16 9^, can be had from th^ 



FOOD 113 

fat of all meats, and carbohydrates are better obtained from potatoes 
than from rich cakes, confectionery, and jellies. We are indebted' to 
modem inventions for a wide list of cooked and partially cooked foods 
which have economized the time of the busy housewife and which have 
enriched our breakfast table beyond that of othe.r nations. The breakfast 
cereals and the grains from which they are made, white bread, potatoes, 
sugar, butter, and other fats may be classed as carbohydrates, while meat, 
fish, eggs, milk, cheese, peas, beans, and cabbage are some of the repre- 
sentatives of the protein group. These carbohydrates and nitrogenous 
substances are not wholly such, but are more or less a mixture of other 
things. 

Making Up Menus 

In making up menus it is necessary to have them balance 
evenly. One should not have too much fat one day, too much 
starch the next, etc. The menus for each day should hold 
part of each kind of food, one meat (fish or eggs), one fat, one 
starch, one tonic vegetable, and one laxative vegetable or 
fruit. 

The summer menus must be compiled most carefully, for 
too much fat or too much meat tends to heat the body at an 
excessive rate and should therefore be avoided. 

Of the different food materials which are palatable, nutritious, and 
otherwise suited for nourishment, we should select those that furnish the 
largest amounts of available nutrients at the lowest cost. To do this it 
is necessary to take into account not only the price per pound, quart, or 
bushel of the different materials, but also the kinds and amounts of the 
actual nutrients they contain and their fitness to meet the demands of 
the body for nourishment. The cheapest food is that which supplies the 
most nutriment for the least money. The most economical food is that 
which is cheapest and at the same time best adapted to the needs of the 
user. 

There are various ways of comparing food materials with respect to the 
relative cheapness or expeusiveness of their nutritive ingredients. The best 
way of estimating the relative pecuniary economy of different food mate- 
rials is found in a comparison of the quantities of nutrients and energy 
which can be obtained for a given sum, say 10 cents, at current prices. 
This is illustrated in the table which follows : 



114 VOCATIONAL MATHEMATICS FOR GIRLS 



Comparative Cost op Digestible Nutrients and Energy in 
DippERENT Food Materials at Average Prices 

[It is estimated tliat a man at light to moderate muscular work requires 
about 0.23 pounds of protein and 3060 Calories of energy per day.] 







1 

• 


r1 « 


Amoukt fob 


10 Cbnts 


Kind of Food Matbbial 


5 
S 




^•3 
%2 






00 






OS 


OST OF 

TBI 






a 

1 


t5 








Cents 


^ 


Cents 


H^ 


Lbs. 


Lbs, 


Lbs. 


H 




Dollars 


Lis. 


Calories 


Beef, sirloin .... 


26 


1.60 


26 


0.40 


0.06 


0.06 


-^ 


410 


Do 


20 


1.28 


20 


.50 


.08 


.08 


—^ 


615 


Do 


15 


.96 


15 


.67 


.10 


.11 


— 


685 


Beef, round .... 


16 


.87 


18 


.63 


.11 


.08 


— . 


560 


Do 


14 


.76 


16 


.71 


.13 


.09 


.^ 


630 


Do 


12 


.66 


13 


.83 


.15 


.10 


.^ 


740 


Beef, shoulder clod . . 


12 


.75 


17 


.83 


.13 


.08 


— 


696 


Do 





.57 


13 


1.11 


.18 


.10 


— . 


796 


Beef, stew meat . . . 


5 


.35 


7 


2 


.29 


.23 


— . 


1,530 


Beef, dried, chipped . . 


25 


.98 


32 


.40 


.10 


.03 




315 


Mutton chops, loin . . 


16 


1.22 


11 


.63 


.08 


.17 


-^ 


890 


Mutton, leg .... 


20 


1.37 


22 


.50 


.07 


.07 


_^ 


445 


Do 


16 


1.10 


18 


.63 


.09 


.09 


— 


560 


Roast pork, loin . . . 


12 


.92 


10 


.83 


.11 


.19 


— 


1,036 


Pork, smoked ham . . 


22 


1.60 


13 


.45 


.06 


.14 


— 


735 


Do 


18 


1.30 


11 


.56 


.08 


.18 


— i 


916 


Pork, fat salt .... 


12 


6.67 


3 


.83 


.02 


.68 


— • 


2,960 


Codfish, dressed, fresh . 


10 


.93 


46 


1 


.11 


_^ 


— . 


220 


Halibut, fresh .... 


18 


1.22 


38 


.56 


.08 


.02 


— i 


265 


Cod, salt 


7 


.46 


22 


1.43 


.22 


.01 


— • 


466 


Mackerel, salt, dressed . 


10 


.74 


9 


1 


.13 


.20 


—^ 


1,136 


Salmon, canned . . . 


12 


.57 


13 


.83 


.18 


.10 


— . 


760 


Oysters, solids, 50 cents 


















per quart 


25 


4.30 


111 


.40 


.02 


— 


.01 


90 


Oysters, solids, 36 cents 


















per quart 


18 


3.10 


80 


.66 


.03 


.01 


.02 


126 



1 The cost of 1 pound of protein means the cost of enough of the given ma- 
terial to furnish 1 pound of protein, without regard to the amounts of the other 
nutrients present. Likewise the cost of energy means the cost of enough ma- 
terial to furnish 1000 Calories, without reference to the kinds and proportions 
of nutrients in which the energy is supplied. These estimates of the cost of 
protein and energy are thus incorrect in that neither gives credit for the value 
of the other. 



FOOD 



115 



COMPARATIVB CoST OP DiOBSTIBLB NUTRIBNTS AND EnBROT IN 

DiFFBRBNT FooD MATERIALS AT Ayeragb Pricbs — (Continued) 



Kind of Food Matxbial 



Lobster, canned . . . 
Butter 

Do 

Do 

Eggs, 36 cents per doz. . 
Eggs, 24 cents per doz. . 
Eggs, 12 cents per doz. . 

Cheese 

Milk, 7 cents per quart . 
Milk, 6 cents per quart . 
Wheat flour .... 

Do 

Com meal, granular . . 
Wheat breakfast food . 
Oat breakfast food . . 

Oatmeal 

Rice 

Wheat bread .... 

Do 

Do 

Rye bread 

Beans, white, dried . . 

Cabbage 

Celery 

Com, canned .... 
Potatoes, 90 cents per bu. 
Potatoes, 60 cents per bu. 
Potatoes, 45 cents per bu. 

Turnips 

Apples 

Bananas 

Oranges 

Strawberries .... 
Sugar 





1 

o 


^'^ 




Ajiount fob 


10 Cit 




£ 


^3 






v« 








5 

04 


5s 

O 


ig 


tl 


a 




1 


H 

C 




hS 


p 


s 




i 


Cents 


O* 


Cents 


1 

Lbs. 


2 

Lbs. 


Lbs. 


Dollars 


Lbs. 


18 


1.02 


46 


.56 


.10 


.01 


—. 


20 


20.00 


6 


.50 


.01 


.40 


— 


25 


25.00 


7 


.40 


— . 


.32 


— ~ 


30 


80.00 


9 


.33 


~— 


.27 


— 


24 


2.09 


39 


.42 


.05 


.04 




16 


1.39 


26 


.63 


.07 


.06 




8 


.70 


13 


1.25 


.14 


.11 


— 


16 


.64 


8 


.63 


.16 


.20 


.02 


^ 


1.09 


11 


2.85 


.09 


.11 


.14 


3 


.94 


10 


3.33 


.11 


.13 


.17 


3 


.31 


2 


3.33 


.32 


.03 


2.46 


2} 


.26 


2 


4 


.39 


.04 


2.94 


^ 


.32 


2 


4 


.31 


.07 


2.96 


7i 


.73 


4 


1.33 


.13 


.02 


.98 


7i 


.53 


4 


1.33 


.19 


.09 


.86 


4 


.29 


2 


2.50 


.34 


.16 


1.66 


8 


1.18 


5 


1.25 


.08 


— 


.97 


6 


.77 


5 


1.67 


.13 


.02 


.87 


5 


.64 


4 


2 


.16 


.02 


1.04 


4 


.51 


3 


2.50 


.20 


.03 


1.30 


5 


.65 


4 


2 


.15 


.01 


1.04 


6 


.29 


3 


2 


.35 


.03 


1.16 


2i 


2.08 


22 


4 


.05 


.01 


.18 


5 


6.65 


77 


2 


.02 


— 


.06 


10 


4.21 


23 


1 


.02 


.01 


.18 


H 


1.00 


5 


6.67 


a 


.01 


.93 


1 


.67 


3 


10 


.15 


.01 


1.40 


i 


.50 


3 


13.33 


.20 


.01 


1.87 


1 


1.33 


8 


10 


.08 


.01, 


.54 


H 


5.00 


8 


6.67 


.02 


.02 


.65 


7 


10.00 


27 


1.43 


.01 


.01 


.18 


6 


12.00 


40 


1.67 


.01 




.13 


7 


8.75 


47 


1.43 


.01 


.01 


.09 


6 


— 


3 


1.67 


^— 


— 


1.67 



I 



CcUoriss 

225 

1,705 

1,365 

1,125 

260 

385 

770 

1,186 

885 

1,030 

5,440 

6,540 

6,540 

2,235 

2,395 

4,500 

2,025 

2,000 

2,400 

8,000 

2,340 

3,040 

460 

130 

430 

1,970 

2,950 

3,936 

1,200 

1,270 

370 

250 

216 

2,920 



116 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

1. What is the most economical part of beef for a soup ? 

2. What is the most economical part of mutton for boiling ? 

3. What is the most economical part of pork for a roast ? 

4. Is fresh or salt codfish more economical ? 

5. What is the fuel value of 3 oz. oatmeal ? 

6. What is the fuel value of 3 oz. rice ? 

7. What is the fuel value of 4 oz. strawberries ? 
a What is the fuel value of 6 oz. milk ? 

EXAMPLES 

Since several hundred Calories are required each day for a person's 
diet, it is most convenient in computing meals to think of our foods in 
100-Calorie portions. Therefore it is desirable to know how to compute 
this portion and tabulate it for future reference. 

1. 42 qt. of milk give 36,841 Calories. What is the weight 
of a 100-C portion ? 

2. 3^ lb. of flour give 1610.5 Calories. What is the weight 
of a 100-C portion ? 

3. ^ lb. of dates give 393.75 Calories. What is the weight 
of a 100-C portion ? 

4. If J of a cup of flaked breakfast food gives approximately 
100 C, what is the food value of 1 lb.? 

5. If ^ of a cup of skimmed milk gives approximately 100 
C, what is the food value of 1 qt.? 

6. A teaspoonful of fat gives 100 C. What is the food 
value of 1 lb. lard ? 

7. If ^ of a medium-sized egg gives a food value of 100 C, 
what is the food value of an egg ? 

8. 4 thin slices of bacon (1 oz.) give a food value of 100 C. 
What is the food value of 9 lb. of bacon ? 



FOOD 117 

9. If I oz. of sweet chocolate has a food value of 100 C, 
what is the food value of ^ lb.? 

10. Ten large pears have the value of 100 C, which is the 
same as for 2 doz. raisins. What is the food value of a single 
raisin? 

11. Eind the individual cost of feeding the following families 
per week and per day. Find the number of Calories per indi- 
vidual per day. (Arrange results in a column as suggested.) 

Family No. in Family Total Cost Total Calories 

A 6 

B 7 

C • 8 

D 8 

E 7 

F 6 

G 7 

H 4 

I 4 

J 6 

K 8 

L 6 

M 7 

N 14 

O 6 

Economical Use of Heat 

It is important to reduce waste by using as much as possible 
of the bone, fat, and trimmings, not usually served with the 
meat. If nothing better can be done with them, the bones and 
trimmings are profitably used in the soup kettle, and the fat 
can be saved for cooking to be used in place of more expensive 
butter and lard. The bits of meat not served with the main 
dish, or remaining after the first serving, may be seasoned and 
recooked in many palatable ways. Or they can be combined 
with vegetables, pie crust, or other materials, thus extending 
the meat flavor over a large quantity of less expensive food. 



13.60 


86224 


15.06 


90928.64 


11.21 


101966.75 


6.68 


33744.14 


15.01 


130657.04 


12.89 


93456.34 


17.77 


11063.91 


11.86 


90891.3 


10.28 


50490 


16.47 


69385.9 


10.37 


112197.3 


16.08 


930262 


30.89 


86006.8 


32.91 


141517 


12.31 


85582.8 



118 VOCATIONAL MATHEMATICS FOR GIRLS 

Different kinds and cuts vary considerably in price. Sometimes the 
cheaper cuts contain a larger proportion of refuse than the more expen- 
sive, and the apparent cost is really more than the actual cost of the 
more edible portion. Aside from this advantage, that of the more ex- 
pensive cuts lies in the tenderness and flavor, rather than in the nutritive 
value. Tenderness depends on the character of the muscle fibers and 
connective tissues of which the meat is composed. Flavor depends 
partly on the fat present in the tissues, but mainly on nitrogenous bodies 
known as extractives, which are usually more abundant or of more 
agreeable flavor in the more tender parts of the animal. The heat of 
cooking dissolves the connective tissues of tough meat and in a measure 
makes it more tender, but heat above the boiling point or even a little 
lower tends to change the texture of muscle fibers. Hence tough meats 
must be carefully cooked at low heat long applied in order to soften the 
connective tissue. For this purpose the fireless cooker may be used to 
great advantage. 

Steers and Beef 

Steers are bought from the farmer by the hundredweight 
(cwt.). They are inspected and then weighed. After they 
are killed and dressed, they are washed several times and sent 
to the cooler. The carcass must be left in the cooler several 
days before it can be cut. It is then divided into eight 
standard cuts and each piece weighed separately. 

Sixty per cent of the meat used in this country is produced 
in the Federally inspected slaughtering and packing houses, of 
which there are nearly 900, located in 240 cities. 

EXAMPLES 

1. A steer weighing 1093 lb. was purchased for $ 7.42 per 
cwt. What was paid for him ? 

2. The live weight of a steer is 1099 lb. ; the dressed weight 
641 lb. What is the difference ? What is the percentage of 
beef in the animal ? 

3. A steer with a dressed weight of 677 lb. was cut into the 
following parts : two ribs weighing 61 lb. each, 2 loins 103 lb., 
2 rounds 154 lb., and suet 21 lb. What was the percentage of 
each part to the total amount ? 



FOOD 119 

4. A steer with a dressed weight of 644 lb. was sold at 
$ 10.51 per ewt. What was paid ? 

5. If the value of ribs is 18^, loins 18^^, rounds 9|^, 
what is the value of cuts in problem 3 ? 

6. A housewife buys 8f lb. of meat every Monday, 9^ lb. 
on Wednesday^ and 10} lb. on Saturday. What is the total 
amount of meat purchased in a week ? 

7. The live weight of a low-grade steer was 947 lb. and 
dressed weight 475 lb. What is the per cent of dressed to 
live weight? .What did the steer sell for at 6^ cts. live 
weight ? What was the selling price per cwt. ? 

a A high-grade steer weighed live weight 1314 lb. and 
dressed weight 897 lb. What is the per cent of "dressed to 
live weight? What did the steer sell for at 9 cts. a pound 
live weight? What was the selling price per cwt.? Note 
the difference in the price between low- and high-grade steers 
due to the fact that the latter have a greater proportion of the 
higher priced cuts. 

9. A steer was killed weighing 632 lb. and sold for 
$ 10.38 cwt. a. What was the selling price ? b. What was 
the average price per pound ? c. What was the percentage 
of each cut to total value ? d. What was the total value of 
each cut ? 



Cuts 


Weight 


Pbioi p»b Pound (Wholesale) 


2 Ribs 


681b. 


1.17 


2 Loins 


100 


.18J 


2 Rounds 


160 


.09} 


2 Chucks 


160 


.08 


2 Fla.nkR 


30 


.06} 


2 Shanks 


26 


.06 


2 Briskets 


32 


.08} 


Navel End 


46 


.06 


Neck Piece 


8 


.01} 


2 Kidneys 


2 


.06 


Suet 


20 


.08 



632 lb. 



120 VOCATIONAL MATHEMATICS FOR GIRLS 



Cuts of Beef 

The cuta of beef differ with the locality and the packing 
house. The general method of cutting up a aide of beef is 
illustrated in the following figure. 

Stahdikd Bbef Cuts — Chicago Style 

1 — Jtound 

Rump Roast 
RouDd Steak 
Corned Beef 
Hambarger Sleak 
Dried Beef 
Shank — Soup Bone 

2 — Loin 

Slrlotn Steak 
Porterhonse Sleak 
Club Steak 
Beef Tenderloin 

S — Flank 

Flank Steak 
Hamburger Steak 
Corned Beet 



S — XanelEnd 
Short Riba 
Corned Beef 
Soap Meat 

G — BrUket 
Comed Bee( 
Soup Meat 
Pot Roast 



t — Fore Shank 
Soup Bone 

i — Chuck 

Shoulder Steak 
Shoulder Roast 
Pot Boaat 

Slews 



Standard Fork Cctb — Chicaoo Stvlb 



-Boston Bull 
Pickled Potk 
Pork Sboalder 
Fork Steak 



6 — Belly 

Spare Ribs 
Brisket Bacon 
Salt Pork 

Pock Eoasl 
Pork Chops , 

Fork Tenderloin 

7 — Fat Back 

Paprika Bacon 
Dry Salt Fat Backs 
Barrel Fork 



EXAMPLES 

Hogs are usaallj killed when Dine or ten months old. The velght 
iB 76% to 80% of live weight. The method of cutting up aside of pork 
differs considerably from that employed with other meats, A large por- 
tion of the carcfias of a dressed pig consists of almost clear fat. This fur- 
nishes the cuts wliicb are used for salt pork and bacon. 

1. A hog weighed at the end of 9 months 249 lb. When he 
was killed and dressed, he weighed 203 lb. What was the 
per cent of dressed to live weight? 

2. A hog weighing 261 lb. was sold for 8\ cents live weight. 
When he was dressed, he weighed 204 lb. What should he 
sell for per cwt. (dressed) in order to cover the price of 
purchase ? 



122 VOCATIONAL MATHEMATICS FOR Q-IRLS 

3. Sugar-cured hams and bacons are made by rubbing salt 
into the pieces and placing a brine solution of the following 
proportions over them in a barrel, before smoking them; 
8 lb. salt, 21 lb. brown sugar, 2 oz. saltpeter in four gallons of 
water for every 100 lb. of meat. What percentage of the solu- 
tion is salt? Sugar? (Consider a pint of water equal to a 
pound.) 

4. Sausages are made by mixing pork trimmings from the 
ham with fat and spices, and placing in casings. If 3 lb. of 
ham are added to 1 lb. fat pork, what is the percentage of lean 
pork? 

St&ndabd Mutton Cuts — Chicaoo Sttlb 
l~Leg 

Leg □( Mutton 
Mutton Chops 

2— Loin 

Loin Roast 
Mutton Cbopfl 

3— Hotel Back 
Rib Chops 



'0 — Chuck 

Shoulder Boast 
Stow 
Shoulder Chops 

EXAMPLES 
1. A butcher buys 169 sheep at S5.76 a head. He sells 
them so as to receive on the average $6.12^ for each. What 
does he gain ? 



FOOD 123 

2. A market man bought 19 dressed sheep for $81.75. 
What was the average price ? 

3. A sheep weighed 138 lb. live weight and 72 lb. dressed. 
What was the per cent of dressed to live weight ? 

4. A dressed sheep when cut weighed as follows ; 

Leg 23.11b. each Neck 3.41b. Breast 8.2 1b. 

Loin 18.4 lb. each Shoulder 6.1 lb. each Shank 5.3 lb. each 

Ribs 15.3 lb. each 

What was the total dressed weight ? What was the percent- 
age of each cut to the dressed weight ? 

Length of Time Required to Cook Mutton 

Boiling 
Mutton, per pound 16 minutes 

Baking 

Mutton, leg, rare, per pound ... 10 minutes 

Mutton, leg, well done, per pound . 15 minutes 

Mutton, loin, rare, per pound . . 8 minutes 

Mutton, shoulder, stuffed, per pound 16 minutes 

Mutton, saddle, rare, per pound . . 9 minutes 

Lamb, well done, per pound ... 15 minutes 

Broiling 

Mutton chops, French 8 minutes 

Mutton chops, English 10 minutes 

EXAMPLES 

Give the fraction of an hour required 

(a) To boil mutton (2 lb.). 

(b) To bake leg of mutton (3 lb.). 

(c) To bake loin of mutton (4 lb.). 

(d) To broil mutton chops (French). 

(e) To broil mutton chops (English). 
{f) To bake shoulder of mutton (5 lb.). 



124 VOCATIONAL MATHEMATICS FOR GIRLS 

Fish is a very economical kind of food. It can be obtained 
fresh at a reasonable figure in seacoast towns. 

1. During the year 1913, 170,000,000 lb. of fish were brought 
into Boston, and sold for $ 7,000,000. What was the average 
price per pound ? 

2. If 528,000,000 lb. of fish were caught in the waters of 
New England during the year 1913, it would represent one- 
quarter of the catch of the entire country. What is the catch 
of the entire country ? 

3. A pound of smoked ham at 24 cents contains 16 % protein, 
while a pound of haddock at 7 cents contains 18% protein. 
How much more protein in a pound of haddock than in a pound 
of ham ? (In ounces.) 

4. For the same value, how much more protein can you pur- 
chase in the haddock than in the ham ? 

5. A pound of pork chops at 25 cents contains 17 % protein ; 
a pound of herring at 8 cents contains 19 %. How much more 
protein is there in the pound of herring than in the pork chops ? 

6. For the same value, how much more protein can be pur- 
chased in the pound of herring than in pork chops ? 

7. A pound of sirloin steak at 30 cents gives the same amount 
of protein as the pork chops in example 6. For the same value 
how much more protein can be obtained from haddock than 
from the steak ? What per cent of protein per pound in had- 
dock ? Use data in Example 3. 

8. If fish can be purchased at any time at not over 12 cents 
per pound, and meats at not less than 20 cents per pound, what 
is the per cent of saving by buying fish ? 

9. If 5.3 % of the total expenses for foodstuffs is for fish, 
and 22 % of the family earnings goes for food, what is the 
amount spent for each ? Family income $ 894. 



POOD 125 

Economical Marketing 

The most economical way to purchase food is to buy in bulk. Fancy 
packages with elaborate labels must be paid for by the consumer. All 
realize the convenience of package goods, the saving in cost of preparation 
and cooking and the ease with which they are kept clean and wholesome, 
but the additional expense is enormous, in some instances as high as 300 ^ . 

EXAMPLES 

1. If the retail price of dried beef is 50 cents a pound, 
how much more per pound do I pay for dried beef, when I 
purchase a package weighing S^ oz. for 18 cents? What 
per cent more do I pay ? 

2. Wheat costs the farmer or producer 1^ cents per pound. 
I purchase a package of wheat preparation weighing 5 oz. for 
10 cents. How much more do I pay for wheat per pound than 
it costs to produce it ? What per cent more do I pay ? 

3. Good apples cost $ 2.75 per barrel. If I purchase a peck 
for 50 cents, at what rate am I paying for apples per barrel ? 
(A standard apple barrel contains 2^ bushels.) How much 
would I save a peck, if a few families in the neighborhood 
joined me in purchasing a barrel ? 

4. Codfish retails at 17 cents a pound. A group of families 
sent one of their members to the wharf and she purchased for 
60 cents a codfish weighing 6 lb. How much was saved per 
pound ? What per cent ? 

5. Print butter is molded by placing a quantity of tub 
butter in a mold. If the tub butter costs 34 cts. a pound and 
the print butter 42 cts. a pound, how much cheaper (per cent) 
is the tub butter than print butter? Does it afford the same 
nourishment? 

6. A pint can of evaporated milk costs 10 cents and con- 
tains the food element of 2^ quarts of fresh milk at 8 cents a 
quart. What is the saving per quart of milk ? 



126 VOCATIONAL MATHEMATICS FOR GIRLS 

Every housewife should possess the following articles in the 
kitchen so as to be able to verify everything she buys : 

1 good 20-lb. scale 1 dry quart measure 

1 peck measure 1 liquid quart measure 

1 half-peck measure 60-inch steel tape 

1 quarter peck measure - 8-oz. graduate 

The above should be tested and "sealed" by the Super- 
intendent of Weights and Measures. Check the goods bought 
and see if weight and volume agree with what was ordered. 

EXAMPLES 

1. If a gallon contains 231 cu. in., how many cubic inches 
are there in a quart ? 

2. If a bushel contains 2150.42 cu. in., how many cubic 
inches are there in a dry quart ? 

3. If a half-bushel basket or box, heaping measure, must 
contain five-eighths bushel, stricken ^ measure, how many cubic 
inches does the basket contain ? 

4. A box 12 by 14 by 16 inches when stricken full will 
hold a heaping bushel. How many cubic inches in the box ? 

5. A dealer often sells dry commodities by liquid measure. 
If a quart of string beans were sold by liquid measure for 16 
cts., how much would the customer lose ? What is the differ- 
ence in per cent between liquid and dry quart measure ? 

6. A grocer sold a peck of apples to a housewife. As he 
was about to place the apples in the basket, the woman called 
his attention to the fact that the measure was not " heaping." 
He placed four more apples in the measure. When she 
reached home she counted 24 apples. What would have been 
the per cent loss if she had not called his attention to the 
measure ? 

^ Stricken measure is measure that is not heaped, hut even full. 



FOOD 127 

7. A " five-pound " pail of lard was found to weigh 4 lb. 
11 oz. What per cent was lost to the customer ? 

8. A package (supposed to be a pound) sold for 12 cents 
and was found to weigh 14^ ounces. How much did the 
consumer lose ? 

9. A quart of ice cream was bought for 40 cents. The box 
was found to be 12^ % short. How much did the consumer 
lose? 

10. A girl bought a quart of berries for ten cents. J The box 
was found to contain 54.5 cu. in. How much was lost ? 

11. A pound of print butter cost 39 cents and was found to 
weigh 14^ ounces. How much did the consumer lose ? 



CHAPTER VI 

PROBLEMS ON THE CONSTRUCTION OF A HOUSE 

Most people live either in a flat or a house. Each has its 
advantages and its disadvantages. The work of a flat is all on 
one floor ; there are no stairs, halls, cellars, furnaces, and side- 
walks to care for, and when the building is heated by steam, 
there is only the kitchen fire or a gas range to look after. 
These are the advantages and they reduce the work of the 
home to very simple proportions. 

Then, too, it is possible to find comfortable flats at a moderate price in a 
neighborhood where it would be impossible to build a small house. How- 
ever, in these flats some of the rooms are not well lighted and ventilated, 
and one is dependent upon the janitor for many services which are not 
always pleasantly performed, though fees are constantly expected. The 
long flights of stairs are a great drawback, because people will not go out as 
much as they should, on account of the exhausting climb on their return. 

The small house, in country or city, brings more healthful 
mental and physical surroundings than the flat. Perfect venti- 
lation, light, sunshine, and freedom from all petty restrictions 
give a more vigorous tone to body and mind. If the house is 
in the suburbs and there is some land with it, where a few 
vegetables and flowers can be cultivated, it has an added charm 
and blessing in the form of healthful outdoor work : furnace, 
cellar, and grounds for the husband's . share ; house, from 
garret to cellar, for the wife's share. In a flat a man can 
escape nearly all duties about the house, but in the little house 
he must bear his share. 

If one lives in the suburbs, the time and money spent in going to and 
from the city is quite an item, but the cheaper rent usually more than 
balances the traveling expense. A person should not pay over 26% of 
income for rent. In case a person receives an income of $ 1600 or over, 
and has a savings bank deposit of about $ 1600, it is usually better to 

128 



CONSTRUCTION OF A HOUSE ' 129 

purchase a house than to rent. Money may be borrowed from either the 
cooperative bank or the savings bank. 

The total rent of a house a year should be at least 10 % of the value of 
the house and land : 6 % represents interest on the investment, and 4 % 
covers taxes and depreciation. In a flat the middle floor should cost 
approximately 10 % more than the first floor, and the top 10 % less than 
the first floor. 

EXAMPLES 

1. A single house and land cost $ 2800. Wliat should be 
considered the rent per year ? 

2. A two-family house cost $5600. (a) What should be 
the rent per month ? (6) What should be the rent of each flat ? 

3. A three-family house costs $ 6500. What should be the 
rent of each floor ? 

4. A family desires to build a cottage-style, gambrel roof 
house containing seven rooms, bath, reception hall, cemented 
cellar, and small storage attic. It is finished inside with North 
Carolina pine and has hard-pine floors, fir doors, open plumb- 
ing, two coats of plaster, furnace heat, and electric light. The 
first floor has three rooms and a reception hall. The second 
floor has three chambers, bath, and sewing room over the hall. 
The architect finds that the cost of materials in the summer 
and late fall varies as follows : 







Amount sa.vbd 


Itkm 


Summer 


BT BUILDING 

IN THE Fall 


Mason work 


$200 


a 16.00 


Brick and cement 


90 


7.20 


Lumber 


600 


60.00 


Finish 


126 


12.60 


Plumbing 


226 


22.60 


Heat (furnace) 


100 


10.00 


Paint and paper 


200 


20.00 


Plastering 


200 


16.00 


Electric wiring 


40 


3.20 


Electric light fixtures 


40 


4.00 


Labor (carpenters) 


460 




Profit to contractor 


213 


27.62 



130 VOCATIONAL MATHEMATICS FOR GIRLS 

(a) What is the total cost in each case ? (b) What is the 
difference in per cent ? What is the per cent difference in each 
item ? 

Economy of Space 

it 

Many persons who build houses, barns, and other buildings 
do not understand the fundamental fact that there is more 
space in a square building than in a long one, and that the 
further they depart from the square form the more their build- 
ing will cost in proportion to its size. For instance, a building 
20' by 20' has 400 square feet of floor space and requires 80 feet 
of outside wall, while one 10' by 40' will, with the same floor 
space, require 100 feet of wall. Accordingly more material 
and work will be required for the longer one. 

In many cases, of course, there are objections to having a 
building square. The longer building, for instance, gives 
more wall space and more light, and these may be desired 
items. The roof and floor items are about the same in either 
case. 

Preparation of Wood for Building Purposes 

In winter the forest trees are cut and in the spring the logs are floated 
down the rivers to sawmills, where they are sawed into boards of different 
thicknesses. To square the log, four slabs are first sawed off. After these 
slabs are off, the remainder is sawed into boards. 

As soon as the boards or planks are sawed from the logs, they are piled 
on prepared foundations in the open air to season. Each layer is sepa- 
rated from the one above by a crosspiece, called a strip, in order to allow 
free circulation of air about each board to dry it quickly and evenly. If 
lumber were piled up without the strips, one board upon another, the 
ends of the pile would dry and the center would rot. This seasoning or 
drying out of the sap usually requires several months. 

Wood that is to be subject to a warm atmosphere has to be artificially 
dried. This artificially dried or kiln-dried lumber has to be dried to a 
point in excess of that of the atmosphere in which it is to be placed after 
being removed from the kiln. This process of drying must be done grad- 
ually and evenly or the boards may warp and then be unmarketable. 



CONSTRUCTION OF A HOUSE 131 

Definitions 

Board Measure. — A board one inch or less in thickness is said 
to have as many board feet as there are square feet in its surface. 
If it is more than one inch thick, the number of board feet is 
found by multiplying the number of square feet in its surface 
by its thickness measured in inches and fractions of an inch. 

The number of board feet = length {in feet) x width {in feet) x thick- 
ness {in inches). 

Board measure is used for plank meafiure. A plank 2" thick, 10" wide, 
and 15' long, contains twice as many square feet (board measure) as a 
board 1'' thick of the same width and length. 

Boards are sold at a certain price per hundred (C) or per thousand (M) 
board feet. 

The term luinber is applied to pieces not more than four inches thick ; 
timber to pieces more than four inches thick ; but a large amount taken 
together often goes by the general name of lumber, A piece of lumber 
less than an inch and a half thick is called a board and a piece from one 
inch and a half to four inches thick is called a plank. 

Rough Stock is lumber the surface of which has not been dressed or 
planed. 

The standard lengths of pieces of lumber are 10, 12, 14, 16, 18 feet, etc. 

EXAMPLES 

1. How many board feet in a board 1 in. thick, 15 in. wide, 
and 15 ft. long ? 

2. How many board feet of 2-inch planking will it take to 
make a walk 3 feet wide and 4 feet long ? 

3. A plank 19' long, 3" thick, 10" wide at one end and 12" 
wide at the other, contains how many board feet ? 

4. Find the cost of 7 2-inch planks 12 ft. long, 16 in. wide 
at one end, and 12 in. at the other, at $ 0.08 a board foot. 

5. At $ 12 per M, what will be the cost of 2-inch plank for 
a 3 ft. 6 in. sidewalk on the street sides of a rectangular corner 
lot 56 ft. by 106 ft. 6 in. ? 



132 VOCATIONAL MATHEMATICS FOR GXHLS 

Frame and Koof 

After the excavation ia finished and the foundation laid, ttie ci 
tion of the l)UJldiDg itself Is begun. On the top of the foundation a lar) 
timber called a sill is placed. The timbers running at right angles to tt 
front sill are called side sills. The sills are joined at the comers by 
half-lap joint and held together by spikes. 



a. Outside studding de. Second-floor joisia t. Sheathing 

b. Rafters d^. First-floor joists j. Partition studs 

c. Plates g. Qirder or cross sill k. Partition heads 

d. Ceiling joists h. Sllla I. Piers 

The walls of the building are framed by placing eorner posls 4" by 6" 
on the four corners. Between these comer pneta there are placed smaller 
timbers called studding, 2" by 4", 13" apart. !Later the laths, 4' long, are 
nailed to this stndding. The upright timbers are often mortised into the 
sills at the bottom. When these uprights are all in position, a timber, called 
a plate, is placed on the top of tliem and they are spiked together. 

On the top of the plate is placed the roof. The principal timbers of 
the roof are tlie rafters. Different roofs have a different pitch or slope — 
that Is, form different angles with the plate. To obtain the desired pitch 
the carpenter uses the steel square. 



CONSTRUCTION OF A HOUSE 133 

A roof with one half pitch means that the height of the ridge of the 
roof above the level of the plate is equal to one half the width of the 
building. 

This illustrates a roof with one-half pitch. 




EXAMPLES 

Give the height of the ridge of the roof above the level of 
the plate of the following building : 





Pitch 


Width op Bciloino 


1. 


One-half 


32' 


2. 


One-fourth 


40' 


3. 


One-third 


36' 


4. 


One-sixth 


48' 



Building Materials 

Besides wood many materials enter into the construction of 
buildings; among these are mortar, cement, stone, bricks, 
marble, slate, etc. 

Mortar is a paste formed by mixing lime with water and sand in the 
correct proportions. (Common mortar is generally made of 1 part of 
lime to 5 parts of sand.) It is used to hold bricks, etc., together, and 
when stones or bricks are covered with this paste and placed together, 
the moisture in the mortar evaporates and the mixture ** sets *' by the 
absorption of the carbon dioxide from the air. Mortar is strengthened 
by adding cow's hair when it is used to plaster a house ; in such mortar 
there is sometimes half as much lime as sand. 

Plaster is a mixture of a cheap grade of gypsum (calcium sulphate), 
sand, and hair. When the plaster is mixed with water, the water com- 
bines with the gypsum and the minute crystals in forming interlace and 
cause the plaster to " set." 

When masons plaster a house, they estimate the amount of 
work to be done by the square yard. Nearly all masons use 
the following rule : Calculate the total area of walls and ceil- 



134 VOCATIONAL MATHEMATICS FOR GIRLS 

ings and deduct from this total area one-half the area of open- 
ings such as doors and windows. A bushel of mortar will 
cover about 3 sq. yd. with two coats. 

Example. — How many square yards of plastering are nec- 
essary to plaster walls and ceiling of a room 28' by 32' and 12' 
high? 

Areas of the front and back walls are 28 x 12 x 2 = 672 sq. ft. 

Areas of the side walls are 32 x 12 x 2 = 768 sq. ft. 

Area of the ceiling is 28 x 32 = 896 sq. ft. 

2336 sq. ft. 
2386 sq. ft. = ^^ sq. yd. = 259^ sq. yd. 

260 sq. yd. Ans. 
EXAMPLES 

1. What will it cost to plaster a wall 10 ft. by 13 ft. at 
$ 0.30 per square yard ? ' 

2. What will it cost to plaster a room 28' 6" by 32' 4" and 
9' 6" high, at 29 cents a square yard, if one-half its area is 
allowed for openings and there are two doors 8' by 3^' and 
three windows 6' by 3' 3" ? 

3. What will it cost to plaster an attic 22' 4" by 16' 8" and 
9' 4" high, at a cost of 32 cents a square yard ? 

Bricks used in Building 

Brickwork is estimated by the thousand, and for various 
thicknesses of wall the number required is as follows : 

8J-inch wall, or 1 brick in thickness, 14 bricks per superficial foot. 
12f-inch wall, or 1 J bricks in thickness, 21 bricks per superficial foot. 
17-inch wall, or 2 bricks in thickness, 28 bricks per superficial foot. 
21^inch wall, or 2^ bricks in thickness, 35 bricks per superficial foot. 

.EXAMPLES 

From the above table solve the following examples : 

1. How much brickwork is in a 17" wall (that is, 2 bricks 
in thickness) 180' long by 6' high ? 



CONSTRUCTION OF A HOUSE 135 

2. How many bricks in an 8 ^ wall, 164' 6" long by 6' 4" ? 

3. How many bricks in a 17" wall, 48' 3" long by 4' 8" ? 

4. How many bricks in a 21^" wall, 36' 4" long by 3' 6" ? 

5. How many bricks in a 12f" wall, 38' 3" long by 4' 2"? 

6. At $ 19 per thousand find the cost of bricks for a build- 
ing 48' long, 31' wide, 23' high, with walls 12f " thick. There 
are 5 windows (7' X 3') and 4 doors (4' x 8^'). 

To estimate the number of bricks in a wall it is customary 
to find the number of cubic feet and then multiply by 22, 
which is the number of bricks in a cubic foot with mortar. 

* 

7. How many bricks are necessary to build a partition wall 
36' long, 22' wide, and 18" thick ? 

8. How many bricks will be required for a wall 28' 6" 
long, 16' 8" wide, and 6' 5" high ? 

9. How many cubic yards of masonry will be necessary to 
build a wall 18' 4" long and 12' 2" wide ^nd 4" thick? 

10. At $ 19 per thousand, how much will the bricks cost to 
build an 8^", or one-brick wall, 28' 4" long and 8' 3" high ? 

11. At $20.60 per thousand, how much will the bricks cost 
to build a 12f " wall, 52' 6" long and 14' 8" high ? 

12. A house is 45' x 34' x 18', the walls are 1 foot thick, 
the windows and doors occupy 368 cu. ft. ; how many bricks 
will be required to build the house ? 

13. What will it cost to lay 250,000 bricks, if the cost per 
thousand is $ 8.90 for the bricks ; $ 3 for mortar ; laying, $ 8 ; 
and staging, $ 1.25 ? 

Stonework 

Stonework, like brickwork, is measured by the cubic foot 
or by the perch (16 J' x 1^ x 1') or cord. Practical men usu- 
ally consider 24 cubic feet to the perch and 120 cubic feet to 
the cord. The cord and perch are not much used. 



136 VOCATIONAL MATHEMATICS FOR GIRLS 

The usual way is to measure the distance around the cellar on the out- 
side for the length. This includes the corners twice, but owing to the 
extra work in making corners this is considered proper. * No allowance is 
made for openings unless they are very large, when one-half is deducted. 

The four walls may be considered as one wall with the same 
height. 

Example. — If the outside dimensions of a wall are 44' by 
31', 10' 6" high and 8" thick, find the number of cubic feet. 

44 25 

31 «« 2 



•"^^ ;^jai X ~ X i = 1050 cu. ft. Ans. 

_2 . ^^ ^ ;;2 

150 ft. length. ^ 

Cement 

Some buildings have their columns and beams made of 
concrete. Wooden forms are first set up and the concrete is 
poured into them. The concrete consists of Portland cement, 
sand, and broken stone, usually in the proportion of 1 part 
cement to 2 parts sand and 4 parts stone. The average weight 
of this mixture is 150 pounds per cubic foot. After the con- 
crete has " set," the wooden boxes or forms are removed. 

Within a few years twisted steel rods have been placed in the forms 
and the concrete poured around them. This is called reenforced con- 
crete and makes a stronger and safer combination than the whole concrete. 
It is used in walls, sewers, and arches. It takes a long time for the con- 
crete to reach its highest compressive and tensile strength. 

Cement is also used for walls and floors where a waterproof surface is 
desired. When the cement "sets," it forms a layer like stone, through 
which water cannot pass. If the cement is inferior or not properly made, 
it will not be waterproof and water will pass through it and in time 
destroy it. 

EXAMPLES 

1. If one bag (cubic foot) of cement and one bag of sand 
will cover 2f sq. yd. one inch thick, how many bags of cement 
and of sand will be required to cover 30 sq. yd. 2^" thick ? 



CONSTRUCTION OF A HOUSE 137 

2. How many bags of cement and of sand will be required 
to lay a foundation 1" thick on a sidewalk 20' by 8' ? 

3. How many bags of cement and of sand will it take to 
cover a walk, 34' by 8' 6", |" thick ? 

4. If one bag of cement and two of sand will cover 6 J sq. yd. 
I" thick, how much of each will it take to cover 128 sq. ft. ? 

5. How much of a mixture of one part cement, two parts 
sand, and four parts cracked stone will be needed to cover a 
floor 28' by 32' and 8" deep ? How much of each will be used ? 

Shingles 

Shingles for roofs are figured as being 16" by 4" and are 
sold by the thousand. The widths vary from 2" upward. 
They are put in bundles of 250 each. When shingles are laid 
on the roof of a building, they overlap so that only part of 
each is exposed to the weather. 

EXAMPLES 

1. How much will it cost for shingles to shingle a roof 
60 ft. by 40 ft., if 1000 shingles are allowed for 125 sq. ft. 
and the shingles cost $ 1.18 per bundle ? 

2. Find the cost of shingling a roof 38 ft. by 74 ft., 4" to 
the weather, if the shingles cost $ 1.47 a bundle, and a pound 
and a half of cut nails at 6 cents a pound are used with each 
bundle. 

3. How many shingles would be needed for a roof having 
four sides, two in the shape of a trapezoid with bases 30 ft. and 
10 ft., and altitude 15 ft., and two (front and back) in the 
shape of a triangle with base 20 ft. and altitude 15 ft.? 
(1000 shingles will cover 120 sq. ft.) 

Slate Roofing 

In order to make the exterior of a house fireproof the roof 
should be tile or slate. Slates make a good-looking and durable 



138 VOCATIONAL MATHEMATICS FOR GIRLS 

roof. They are put on, like shingles, with nails. Estimates 
for slate roofing are made on 100 sq. ft. of the roof.^ 
The following are typical data for building a slate roof : 

A square of No. 10 x 20 Monson slate costs about 9 8.35. 
Two pounds of galvanized nails cost $0.16 per pound. 
Labor, $ 3 per square. 
Tar paper, at 2} cents per pound, 1 J lb. per square yard. 

EXAMPLES 

Using the above data, give the cost of making slate roofs 
for the following : 

1. What is the cost of laying a square of slate ? 

2. What is the cost of laying slate on a roof 112' by 44' ? 

3. What is the cost of laying slate on a roof 166' by 64'? 

4. What is the cost of laying slate on a roof 118' by 52' ? 

5. What is the cost of laying slate on a roof 284' by 78' ? 

Clapboards 

Clapboards are used to cover the outside walls of frame 
buildings. Most clapboards are 4' long and 6" wide. They 
are sold in bundles of twenty-five. Three bundles will cover 
100 square feet if they are laid 4" to the weather. 

To find the number of clapboards required to cover a given 
area, find the area in square feet and divide by 1^, Allowance 
may be made for openings by deducting from area, 

EXAMPLES 

1. How many clapboards will be required to cover an area 
of 40 ft. by 30 ft.? 

2. How many clapboards will be necessary to cover an area 
of 38' by 42' if 66 sq. ft. are allowed for doors and windows ? 

3. How many clapboards will a barn 60 ft. by 50 ft. require 
if 10 % is allowed for openings and the distance from founda- 
tion to the plate is 17 ft. and the gable 10 ft. high ? 

^ Called a square. 



^^ 



CONSTRUCTION OF A HOUSE 139 

Flooring 

Most floors in houses are made of oak, maple, birch, or pine. 
This flooring is grooved so that the boards fit closely together 
without cracks between them. 

The accompanying figure shows the ends of c c g l^ 

pieces of matched flooring. Matched boards are 

also used for ceilings and walls. In estimating for matched flooring 
enough stock must be added to make up for what is cut away from the 
width in matching. This amount varies from J" to |" on each board ac- 
cording to its size. Some is also wasted in squaring ends, cutting up, and 
fitting to exact lengths. A common floor is made of unmatched boards 
and is usually used as an under floor. Not more than \^' per board is 
allowed for waste. 

Example. — A room 12 ft. square is to have a floor laid of 
unmatched boards 1|-" wide ; one-third is to be added for waste. 
What is the number of square feet in the floor ? What is the 
number of board feet required for laying the floor? 

12 X 12 = 144 sq. ft. = area. 144 x J = 48 

144. Ans, 144 

192 board measure for 

unmatched floor. 
192. Ans. 

EXAMPLES 

1. How much 1^ in. matched flooring 3" wide will be re- 
quired to lay a floor 16 ft. by 18 ft. ? One-fourth more is al- 
lowed for matching and 3 % for squaring ends. 

2. How much hard pine matched flooring |^" thick and 1^" 
wide will be required for a floor 13' 6" x 14' 10" ? Allow \ for 
matching and add 4 % for waste. 

3. An office floor is 10' 6" wide at one end and 9' 6" wide at 
the other (trapezoid) and 11' 7" long. What will the material 
cost for an unmatched maple floor |^" thick and IJ" wide at 
$ 60 per M, if 4 sq. ft. are allowed for waste ? 



140 VOCATIONAL MATHEMATICS FOR GIRLS 



4. How many square feet of sheathing are required for the 
outside, including the top, of a freight car 34' long, 8' wide, 
and 7 J^' high, if 37^% covers all allowances ? 

5. In a room 60' long and 20' wide flooring is to be laid ; 
how many feet (board measure) will be required if the stock 
is I" X 3" and \ allowance for waste is made ? 

Stairs 

The perpendicular distance between two floors of a building 
is called the rise of a flight of stairs. The width of all the 

steps is called the run. 
The perpendicular dis- 
tance between steps is 
called the width of risers. 
Nosing is the slight pro- 
jection on the front of 
each step. The board on 
each step is the tread. 

To find the number of 

stairs necessary to reach 

from one floor to another : 

Measure the rise first. 

S^^'^« Divide this by 8 inches, 

which is the most comfortable riser for stairs. The run should 

be 8J^ inches or more to allow for a tread of 9f inches with 

a nosing of 1 J inches. 

Example. — How many steps will be required, and what 
will be the riser, if the distance between floors is 118 inches ? 

118 H- 8 = 14i or 16 steps. 

118 -H 15 = 7{i inches each riser. Ans, 

EXAMPLES . 

1. How many steps will be required, and what will be the 
riser, (a) if the distance between floors is 8' ? (6) If the dis- 
tance is 9 feet ? 




CONSTRUCTION OF A HOUSE 141 

2. How many steps will be required, and what will be the 
riser, (a) if the distance between floors is 12' ? (b) If the dis- 
tance is 8' 8"? 

Lathing 

Laths are thin pieces of wood, 4 ft. long and 1|- in. wide, 
upon which the plastering of a house is laid. They are usu- 
ally put up in bundles of one hundred. They are nailed | in. 
apart and fifty will cover about 30 sq. ft. 

EXAMPLES 

1. At 30 cents per square yard what will it cost to lath and 
plaster a wall 12 ft. by 15 ft. ? 

2. At 45 cents per square yard what will it cost to lath and 
plaster a wall 18 ft. by 16 ft. ? 

3. What will it cost to lath and plaster a room (including 
walls and ceiling) 16 ft. square by 12 ft. high, allowing 34 sq. ft. 
for windows and doors, at 40 cents per square yard ? 

4. What will it cost to lath and plaster the following rooms 
at 41|^ cents per square yard ? 

a. 16' X 14' X 11' high with a door 8' x 2^ and 2 windows 2^ X 5'. 

b. 18' X 15' X 11' high with a door 10' X 3' and 4 windows 2^ X 5'. 

c. 20' X 18' X 12' high with a door 11' X 3' and 4 windows 2|'x 4'. 

d. 28' X 32' X 16' high with a door 10' X 3' and 4 windows 3' x5'. 

e. 28' X 30' X 15' high with a door 10' X 3' and 3 windows 3' x5'. 

Painting 

Paint, which is composed of dry coloring matter or pigment mixed 
with oil, drier, etc., is applied to the surface of wood by means of a 
brush to preserve the wood. The paint must be composed of materials 
which will render it impervious to water, or rain would wash it from the 
exterior of houses. It should thoroughly conceal the surface to which 
it is applied. The unit of painting is one square yard. In painting 
wooden houses two coats are usually applied. 



142 VOCATIONAL MATHEMATICS FOR GIRLS 

It is often estimated that one pound of paint will cover 4 sq. yd. for 
the first coat and 6 sq. yd. for the second coat. Some allowance is made 
for openings ; usually about one-half the area of openings is deducted, 
for considerable paint is used in painting around them. 

Table 

1 gallon of paint will cover on concrete . . . 300 to 376 superficial feet 

1 gallon of paint will cover on stone or brick 

work 190 to 226 superficial feet 

1 gallon of paint will cover on wood .... 376 to 625 superficial feet 

1 gallon of paint will cover on well-painted sur- 
face or iron 600 superficial feet 

1 gallon of tar will cover on first coat ... 90 superficial feet 

1 gallon of tar will cover on second coat . . 160 superficial feet 

EXAMPLES 

1. How many gallons of paint will it take to paint a fence 
6' high and 5(y long, if one gallon of paint is required for 
every 350 sq. ft.? 

2. What will be the cost of varnishing a floor 22' long and 
16' wide, if it tak^s a pint of varnish for every four square 
yards of flooring and the varnish costs $2.65 per gallon ? 

3. What will it cost to paint a ceiling 36' by 29' at 21 cents 
per square yard ? 

4. What will be the cost of painting a house which is 52' 
long, 31' wide, 21' high, if it takes one gallon of paint to cover 
300 sq. ft. and the paint costs $ 1.65 per gallon ? (House has 
a flat roof.) 

Papering 

Wall paper is 18" wide and may be bought in single rolls 
8 yards long or double rolls 16 yards long. When you get a 
price on paper, be sure that you know whether it is by the 
single or double roll. It is usually more economical to buy a 
double roll. There is considerable waste in cutting and match- 
ing paper, hence it is difficult to estimate the exact amount. 



CONSTRUCTION OF A HOUSE 143 

A fraction of a roll is not sold, — there are various rules pro- 
vided. The border, called frieze, is usually sold by the yard. 

Find the perimeter of the room in feet, and divide this by 
the width of the paper (which is 18" or 1^'). The quotient 
obtained equals the number of strips of paper required. Then 
divide the length of the roll by the height of the room in order 
to obtain the number of strips in the roll. The number of 
rolls required is found by dividing the strips in the room by the 
strips in the roll. 

Another rule is : Find the perimeter of the room in yards, 
multiply that by 2, and you have the number of strips. Find 
the length of each strip. How many whole strips can you cut 
from a double roll ? How many rolls will it take ? To allow 
for doors and windows deduct 1 yard from the perimeter for 
each window and each door. 

EXAMPLES 

1. A paper hanger is asked to paper a square room 18' by 
18' with a door and three windows. The door is 3' by 7' and 
tht windows 2' by 4'. How many double rolls of paper will 
he use ? (Consider all rooms 9' high.) 

2. How much paper will be required to paper a room 18' 
by 14'? 

3. How much paper will be required to paper a room 
18' 6" by 16' 4" with 2 doors and 2 windows ? 

4. How much will it cost to paper a room 19' 6" by 
16' 4" with 2 doors and 2 windows. The paper costs 49^ 
a roll to place it on the wall. 

Taxes 

Find out where the money comes from to support the 
schools, police, library, etc. in your city or town. How is it 
obtained ? What is real estate ? What is personal property ? 
What is a poll tax ? A tax is the sum of money assessed on 
persons and property to defray the expenses of the community. 



144 VOCATIONAL MATHEMATICS FOR GIRLS 

* 

The tax rate is usually expressed as so many dollars per 
thousand of valuation, generally between $10 and $20. In 
some places it is expressed as a certain number of mills on $ 1 
or cents on $ 100. 

The tax rate, or the amount on each thousand dollars of 
property, is determined by dividing the whole tax by the num- 
ber of thousand dollars of taxable property in the community. 
To illustrate : 

In a certain community the whole tax is $1,942,409.73. 
The taxable property is $ 97,945,162.00. 

$ 1,942,409.73 ^..qoo 
97,945 =^^^-^- 

EXAMPLES 

1. If the tax rate is $ 21.85, what are the taxes paid by a 
family of women owning property worth $ 16,000 ? 

2. What is the tax on $ 34,697 in your town or city ? 

3. A man owns real estate worth $ 84,313, and has personal 
property worth $ 16,584. What is his tax bill, if the tax rate 
is $ 1.75 per hundred and a poll tax is $ 2 ? 

4. A dwelling house is valued at $8500 and the tax rate 
is $ 17.52 per thousand. What is the tax ? 

5. What is the tax on a house valued at $ 3500, if the tax 
rate is $ 23.45 ? 

6. The taxable property of a city is $ 97,945,162.00 ; and the 
expenses (taxes) necessary to run the city are $ 1,900,136.14. 
Obtain the tax rate. 

United States Revenue 

The town or city derives revenue from taxes levied on real 
and personal property. The county and state derive part of 
their revenue from a tax imposed upon the towns and cities. 
The United States government derives a great part of its rev- 



CONSTRUCTION OF A HOUSE 145 

enue from a tax placed on tobacco and liquor sold within its 
boundaries and from a tax, called customs duties, imposed upon 
articles imported from other countries. 

Some articles are admitted into the country free; these are said to 
be on the free list. The others are subject to one or both of the follow- 
ing duties : a duty placed on the weight or quantity of an article without 
regard to value (called specific duty), or a duty based upon the value of 
the article (expressed in per cent and called ad valorem duty). 

When goods are received into this country, they are examined by an 
officer (called a customs officer). The goods are accompanied by a 
written statement of the quantity and value (called manifest or invoice). 

Sometimes the goods are liquid, and in this case the weight of the bar- 
rel (called tare) must be subtracted from the total weight to obtain the 
net weight on which duty is imposed. 

In case bottles are broken and liquids have escaped, due allowance 
must be made before imposing duty. This is called leakage or breakage, 

EXAMPLES 

1. What is the duty on bronze worth % 8760 Sit^5%? 

2. What is the duty on goods valued at $ 3115 at 35 % ? 

3. What is the duty on 3843 sq. ft. of plate glass, duty 
$ 0.09 per square foot ? 

4. What is the duty on jewelry valued at $ 8376 at 40 % ? 

5. What is the duty on cotton handkerchiefs valued at 
$ 834 at 45 % ? 

6. What is the duty on woolen knit goods valued at $ 1643, 
41 cts. per pound plus 50 % ? 

7. What is the duty on rugs (Brussels), 120 yards, 27" wide, 
invoiced at $ 1.80 a yard, at 29 cts. per square yard and 45 % 
ad valorem ? 



CHAPTER VII 

COST OF FURNISHING A HOUSE 

When about to furnish a house, one of the first things to 
consider is the amount of money to be devoted to the purpose. 
This amount should depend on the income. A person with 
a salary of $ 1000 a year should have saved at least $ 250 
toward the equipment of his home before starting house- 
keeping. This is sufficient to purchase the essentials of a 
simply furnished apartment or small house. 

After one has lived in the house for a short time, it will be easy 
to study the possibilities and necessities of each room, and as time, 
opportunity, and money permit, one can add such other things as are 
needed. In this way the purchase of undesirable and inharmonious 
articles may be avoided. 

There are many different styles and grades of furniture. The cost 
depends upon the kind of wood used, and the care with which it is put 
together and finished. The most inexpensive furniture is not the 
cheapest in the end. It is made of inferior wood and with so little care 
that it is neither durable nor attractive. The medium grades are gen- 
erally made of birch, oak, or willow, are durable, and may be found 
in styles that are permanently satisfactory. The best grades are made of 
mahogany and other expensive woods, and those whose income consists 
only of wages or a salary cannot usually afford to buy more than a few 
pieces of this kind. 

Furniture that is well made, of good material, and free from striking 
peculiarities of design and of decoration is chosen by all people of good 
taste and good judgment. 

Furnishing the Hall 

The only furniture necessary for the vestibule is a rack for umbrellas. 
The walls should be painted with oil paint in some warm color, and the 
floor should be tiled or covered with inlaid linoleum in tile or mosaic 

146 



COST OF FURNISHING A HOUSE 



147 



design. If the vestibule serves also as the only hall, it should contain a 
rug, a small table or chair, and a mirror. ^ A panel of filet lace is suitable 
to use across the glass in the front door. 

Through the front door one gets one's first impression of the occupants 
of the house. The furnishings of the hall should therefore be carefully 
chosen. It is a passageway rather than a room, and requires very little 
furniture. The walls may be done in a landscape paper, if one wishes to 
make the room appear larger, or in plain colonial yellow, if a bright effect 
is desired. If the size of the hall will permit, it is best to furnish it as a 
reception room; it may be made an attractive meeting place for the 
family and friends ; but if it is one of the narrow passages so often found 
in city houses, one must be content with the regulation hall stand, or a 
mirror and a narrow table, and possibly one chair. 

Price List of Hall Furniture 



• 


g H M 

Boo 

b 39 ij 


£ t^ 


S M 


CO M 


« ^ 


J, 


H 




§5 

2o 

CD 


0^3 


Design 

IN Oa 

Inamel 


Design 
inBba 


1^ 


B3 




^ ^K 


Q 


^ S 


ew 


a 


K 


u 




!S «^ o 
2 -^ H 
io * 

H -4 


LONIAL 
PBODUCB 

Bieou 




» 9 S 
2 25 


LONIAL 

PRODUCE 

LHOGANT 


H < 

is 


1 

•J 






o H oa 


o wT 


53 1 




it 


^ 


Umbrella rack . 


.$ 1.25 


^.00 


^7.25 


$8.50 


$10.00 


$5.00 


$7.50 


Table .... 


3.75 


6.75 


8.25 


9.76 


20.00 


10.00 


87.50 


Mirror . . . 


3.00 


3.00 


3.40 


3.75 


30.00 


7.50 




Straight chair . 


2.75 


4.50 


6.50 


6.60 


25.00 


6.60 


8.00 


Chest .... 


13.50 


13.50 


16.60 


19.50 


60.00 


40.00 




Sofa .... 










50.00 


85.00 


16.00 


Tall clock . . 


60.00 


60.00 






160.00 




75.00 


Settle .... 


18.00 


18.00 


22.50 


27.00 


32.00 


82.00 


21.00 


Telephone stand 


6.75 


6.75 


8.25 


9.75 


10.50 


5.50 


15.00 


Clothes rack 


3.50 


3.50 


4.15 


4.90 


5.00 


7.00 


8.25 



EXAMPLES 

1. What is the complete cost of furnishing a hall with 
willow furniture ? 



148 VOCATIONAL MATHEMATICS FOR GIRLS 

2. Compare the cost of furnishing a hall with mahogany 
or birch. 

3. If a family receives an income of $1400 a year and 
lives in a single cottage house, what kind of furniture should 
be selected? What should the cost not exceed for the hall 
furniture ? 

4. A hall was furnished with the following articles. What 
did it cost ? What kind of furniture was probably purchased ? 

Seat, $ 11.85 Rug, $ 0.86 

Mirror, $ 2.15 China umbrella stand, $ 2.10 

Table, $ 2.20 Table cover (one yard of felt), $ 1. 15 

Two chairs, ^ 7.40 Pole, $ 2.20 

With hardwood or stained floors the furnishing and care of a house are 
much simplified. If one must have carpets, the colors should be neutral. 
The best quality of Canton or Japanese matting is satisfactory ; it is 
a yard wide and costs fifty cents a yard. Next to matting, the most sani- 
tary and economical carpet is good body Brussels. It wears well, and the 
dust does not get under it. A cheap, loosely woven matting or woolen 
carpet is always unsatisfactory. 

Floor Coverings 

In selecting floor coverings there are several important considerations. 
The design and quality should be governed by the treatment the rug will 
necessarily have. 

Hall 

A hall rug or carpet will receive hard wear ; therefore, the quality 
should be good. A small all-over symmetrical design in two tones of one 
color or in several harmonizing colors will show dust and wear less than 
a plain surface would do. 

Rag rug, machine made, 8 by 6 feet $2.18 

Hand- woven rag rug, 3 by 6 feet 7.50 

Scotch wool rug, 3 by 6 feet 4.00 

Hand-woven wool rug, 3 by 6 feet 6.00 

East India drugget, 3 by 6 feet 8.00 

Saxony, 3 by 6 feet 9.00 

Brussels rug, 8 by 6 feet 9.00 

Oriental rug, 8 by 6 feet 85.00 



COST OF FURNISHING A HOUSE 149 

' Living Boom 

In a living room the floor covering will be worn all over equally. 
Since there is always a variety of colors and forms in a living room, it is 
well to keep the floor covering as plain as possible. A rug with a plain 
center and a darker border of the some color is excellent in this room, 
particularly if the walls or hangings are figured. If they are plain, 
the rug or carpet may have a small, indefinite figure. If several domestic 
rugs are used in the same room, they should be exactly alike in design and 
color. If small Oriental rugs are used, they will, of course, differ in 
design, but they should be as nearly as possible in the same tone. 

Good Living-room Bugs 

Crex or grass rug, 9 by 12 feet $8.60 

Rag rugs, 9 by 12 feet $ 10.00 to 46.00 

Scotch wool rug, 9 by 12 feet $ 14.60 to 26.00 

Brussels, 9 by 12 feet 32.76 

Hand-woYen wool rug, 9 by 12 feet 36.00 

East India drugget, 9 by 12 feet 43.00 

Saxony, 9 by 12 feet 60.00 

Oriental, 9 by 12 feet 200.00 up 

Dining Boom 

A dining-room rug gets very hard wear in spots. It should, therefore, 
be selected in as good quality as one can afford. It is not well to have a 
perfectly plain rug in a dining room, as a plain surface shows crumbs and 
spots too readily. There is no objection to having a dining-room floor 
quite bare, if the floor is well finished. Inlaid linoleum also makes an 
excellent floor covering for a dining room that receives very hard usage. 

The best coverings for this room are : 

Crex ingrain rug, 9 by 12 feet ....... $8.60 

Rag rug, 9 by 12 feet $ 10.00 to 46.00 

Brussels, 9 by 12 feet 32.76 

East India drugget, 9 by 12 feet 36.00 

Saxony, 9 by 12 feet 60.00 

Oriental, 9 by 12 feet 200.00 up 

Bedroom and Sewing Room 

On account of the lint which accumulates in bedrooms, it is a good plan 
to keep the space under the beds bare, so that it may be dusted every 
day. Small rugs laid where most needed are more hygienic in sleeping 



150 VOCATIONAL MATHEMATICS FOR GIRLS 

rooms than are large rugs and carpets. Plain Chinese matting makes a 
clean floor covering when the boards are not in good condition. Although 
it is in good taste to use a carpet or one large rug in a bedroom, the 
preference lies among the foilowing : 

Small rag rugs, 8 by 6 feet $ 1.76 

Oval braided rag rugs, 3 by 6 feet 2.50 

East India drugget, 3 by 6 feet 8.00 

Saxony, 3 by 6 feet 8.00 

Oriental, 3 by 6 feet 36.00 

EXAMPLES 

1. A family has an income of $ 1400. They buy a Brussels 
rug 3' X 6' for $ 9. Are they extravagant ? 

2. How much cheaper is a crex rug, 9 by 12 feet, than a 
Brussels the same size ? What per cent cheaper ? 

3. A dining-room rug is purchased for $ 49.75. What kind 
of a rug is it ? Is it suitable for a family with an income of 
$2500? 

4. An oval braided rag rug 3' x 6' costs $ 2.50 and will last 
twice as long as a small rag rug that costs $ 1.75 for the bed- 
room. Which is more economical to purchase ? How much 
more economical is it? 

The Living Room 

In houses or apartments of but five or six rooms there is 
usually but one living room. This room should represent the 
tastes which the members of the family have in common. The 
first requisite of such a room is that it should be restful. It 
is, therefore, advisable to use a wall covering that is plain in 
effect. Tan is good in a room that is inclined to be dark ; 
gray-green or gray itself in a very bright living room. One 
large rug in two tones of one color, preferably the same color 
as the walls, is better than a figured rug for this room. 

Chairs are an important part of the furnishing of a living 
room. It is well to have comfortable armchairs, upholstered 



COST OF FURNISHING A HOUSE 151 

in plain material, or willow chairs with cushions of chintz, if 
this material is used aa curtains. A roomy table with a good 
reading lamp ia essential, while open bookshelves, a writing 
desk or table, a sofa, a sewing table, and a piano are all appro- 
priate furnishings for this room. 



A HARUONlOUSLr FUBNIBHKD LlYING ROOU 

The curtains may be of figured materials, such as chintz or 
cretonne. Plain scrim or net curtains may be used over cur- 
tains of plain-colored material or of chintz simply to give the 
necessary warmth and color to the sides of the room. Valances 
are used to reduce the apparent height of a window and to give 
a low cozy look to the room. Plants are always appropriate to 
use in sunny windows, and pictures of common interest, framed 
in polished wood or dull gilt frames, help to make the living 
room attractive. Use very little bric-a-brac. Nothing which 
does not actually contribute to the beauty of the room should 
be allowed to find a place there. 



162 VOCATIONAL MATHEMATICS FOR GIRLS 



Price List of Living-room Furniture 



Table . . 
Chair . . 
Sofa . . . 
Armchair . 
Desk chair 
Desk . . 
Bookcase . 
Sewing table 
Tea table . 
Footstool . 
Wood box or rack 
Magazine stand . 
Piano .... 
Music cabinet 







« ^ J 


o3 


E? M >« 


fi^ 


0£St 


£05 








S ^ 




J 5? as 


•J 1 Se; 


►J 2 » 


5 ■< « 


LONIA 

PEODl 

BiRC 


ill 


-^ g «< 


cSScS ' 


n tf 
0«0 


a^a 


$4.50 


$15.00 


$17.00 


$50.00 


17.00 


22.50 


25.00 


45.00 
65.00 




20.00 




38.00 


2.75 


6.75 


7.75 


15.00 


0.75 


19.60 


21.75 


90.00 


9.00 


9.00 


11.25 


100.00 


5.00 


5.00 


6.00 


17.00 


1.50 


1.50 


2.00 


35.00 


2.25 


3.75 


3.00 


6.00 




5.00 


• 


5.00 


6.00 


6.75 


8.25 


10.00 


200.00 


250.00 




450.00 


6.75 


6.75 


8.26 


28.00 . 



I 

to 








Hi 


$35.00 


$59.00 


30.60 


50.00 


68.00 


100.00 


82.00 


65.00 


4.75 


15.00 


28.00 


90.00 


25.00 


100.00 


18.50 




12.00 




4.50 


6.00 


6.00 


6.00 


8.50 


8.50 


450.00 




10.00 





S 
S 



$12.00 

12.75 

23.50 

9.76 

8.25 

37.50 

13.50 

13.50 

7.25 

6.25 

3.50 

12.76 



^'^^^ICoal, 17.00 Wood or coal 



$16.00 Franklin grate or andirons, 
25.50 wood or coal $35.00 



EXAMPLES 

1. How much more will it cost to furnish a living room with 
library furniture than with willow furniture ? 

2. How much more will it cost to furnish a living room with 
hand-made oak furniture than with colonial designs in oak ? 

3. A living room was furnished with the following furni- 
ture. Ascertain from the price list what kind of furniture it is. 

Large round table and small Curtains and shades for three 



table, $7.95 
Six chairs and couch, $ 51.15 
Bookcase or shelves, $ 9.85 

What is the cost ? 



windows, $6.15 
Rug and draperies, $ 34. 15 
Incidentals, $ 24.65 



COST OP FURNISHING A HOUSE 153 

The Bedroom 

When one stops to think that about one-third of one's life k 

spent in aleep, it is easy to understand that the first requisite 

in the fumiBhing of the bedroom is that it be fresh and clean. 



A COHFURTABLB BeDBOOM 

UnlesB the room must be used as a study or sitting room in 
the daytime, the amount of furniture should be reduced aa 
much as possible. The necessary pieces are a bed, a dressing 
case which should be generous in drawers and mirror, a wash- 
stand, a toilet set, towel-rack, one easychair and one plain one, 
a small table, a rug, and window shades. If space and money 
permit, a couch is desirable. Naturally, a writing desk, book- 
ahelveSj and pictures all add to the attractiveness of such a 
room. If one cannot have bare floors, the next best thing is 
good matting. A woolen carpet is not desirable for a sleeping 
room. All draperies should be of materials that will hold 
neither dust nor odor. 



154 VOCATIONAL MATHEMATICS FOR GIRLS 

The bed is the most important article in the room. The 
springs and mattress should be firm enough to support all parts 
of the body when it is in a horizontal position. 

The walls should be light in color and the woodwork white 
if possible. The furniture also may be white, although dull- 
finished mahogany in colonial designs, with small rugs on 
the floor, makes a charming bedroom. One set of draw cur- 
tains, of figured chintz if the walls are plain, and of plain-colored 
material if the walls have a small figure, is enough for each 
window. 

The furnishings of a young girl's bedroom should be carried 
out in her favorite color, and to the usual bedroom furniture 
should be added a desk, lamp, worktable, and bookshelves. 

The bedroom for a growing boy should be his own sitting 
room and study as well ; a place where he can entertain his 
friends, do his studying, and develop his hobbies. The walls, 
hangings, couch cover, etc., should be very plain, as a boy 
usually has a collection of trophies which need' the plainest 
sort of a background in order to prevent the room from looking 
cluttered. Instead of the usual bed he should have an iron- 
framed couch, which in the daytime may be made up with a 
plain dark cover with cushions, to be used as a couch. A chif- 
fonier, an armchair, bookshelves, writing table, and one or two 
small rugs will complete the furnishings of the boy's bedroom. 

EXAMPLES 

1. Sheets should be of ample length and breadth. The 
finished sheets should be nearly three yards long. How many 
inches long ? 

2. The supply of bedroom linen, blankets, and counterpanes 
for a small house is as follows : 

12 sheets @ $ 0.85 4 pairs blankets @ $8.00 

12 pillow cases @ $ .40 2 counterpanes @ $ 2.50 

24 towels @$ 0.50 

What is the total cost ? 



COST OP FURNISHING A HOUSE 



155 



Price List of Bedroom Furniture 





Ml 

2 -"l M 


Colonial Designs 
Kepboduced in Oak 

OB BiBCU 


1 
Colonial Designs 
Kepboduced in Oak 
— Gloss Enamel 


Colonial Designs 
Kepboduced in Oak 
— Kubbed Enamel 

1 


Colonial Designs 
Kepboduced in Keal 
Mahogany 


Hand-made Fubni- 
TUBE IN Oak 


H 

a 

s 
s 

.J 


Bed .... 


19.75 


.$16.50 


118.75 


$21.00 


$55.00 


$30.00 


$56.00 


Mattress . . 


3.35 


16.00 


16.00 


16.00 


36.00 


36.00 


36.00 




to 


to 


to 


to 










16.00 


25.00 


25.19 


25.00 








Box spring . . 


20.00 


20.00 


20.00 


20.00 


20.00 


20.00 


20.00 


Crib (iron) . . 


12.75 


12.75 


12.75 


12.75 


12.75 


12.75 




Crib mattress . 


3.75 


9.00 


9.00 


9.00 


9.00 


9.00 




Pillows (pair) . 


1.25 


2.10 


2.10 


2.10 


6.00 


6.25 


5.25 


Bureau . . . 


0.75 


22.50 


25.00 


27.60 


75.00 


50.00 


67.50 


Washstand 


1.50 


2.00 


2.75 


3.50 


6.00 
(enamel 
iron) 


10.00 




Dressing table 


9.00 


12.57 


14.25 


15.75 


55.00 


26.00 


48.00 


Chiffonier (no 


9.00 


12.00 


14.25 


16.'50 


100.00 


39.00 


60.00 


mirror) . . 










(high- 
boy) 






Chair . . . 


2.75 


4.50 


5.25 


6.00 


10.00 


6.50 


8.00 


Rocking chair . 


2.75 


6.75 


7.75 


8.75 


9.00 


6.50 


8.25 


Waist box . . 


Home- 
















made 


2.50 


3.50 


4.50 


20.00 


16.00 


4.50 


i^esK . • . . 


4.50 


9.75 


10.75 


11.76 


60.00 


20.00 


28.50 


Armchair . . 




6.75 


7.75 


8.75 


24.00 


8.00 


7.60 


Couch , . . 


6.00 

(iron 

frame) 


13.26 
(box) 






60.00 


50.00 


25.00 


Bookshelves . 


Home- 
















made 


9.00 


10.50 


12.00 


(built in) 


21.50 


13.50 


Cheval glass . 


11.25 


15.50 


16.50 


18.00 


50.00 


25.00 





qx^ / Gas, $5.00 Wood . . .$15.50 Franklin grate or andirons, 
DTOves <^ ^^^^^ ^jQQ ^^^ Qj. ^Q^j 25.50 wood or coal . $35.00 



156 VOCATIONAL MATHEMATICS FOR GIRLS 

3. If a person spends one-third of a life in a bedroom, how 
many hours a day are spent in the bedroom ? 

4. A bedroom is furnished with the following furniture : 

Enameled bedstead with springs, Dimity for draping bed , washstand 

97.50 and two windows, twenty-one 

A dressing case, $ 15.00 yards, $ 3.15 

A plain wooden table to be Enameled cloth for washstand, $.65 

used as washstand, $ 1.00 Two pillows, |4.00 

A small table $ 2.00 Toilet set, $ 3.00 

• Chair, $ 2.00 Shades for two windows, $ 1.00 

Mattress, $ 5.00 Towel rack, $ .75 
Bug, $3.00 

What is the total cost ? 

5. What will it cost to furnish a bedroom with simple cot- 
tage furniture as provided above ? 

6. What will it cost to furnish a bedroom with the good 
grade of oak furniture in gloss enamel ? What is the least 
income a family should have in order to buy this furniture ? 

7. What will it cost to furnish a bedroom with real mahog- 
any furniture ? What is*the least income one should have in 
order to buy this furniture ? 

The Dining Room 

The dining room does not require a great deal of furniture, 
but what there is should be of the most substantial kind. 
Mahogany and oak are the woods to be preferred. The table 
should be broad, stand well, with the legs so placed that they 
will not interfere with the comfort of any one seated at the 
table. The chairs should be well made, with broad, deep 
seats and high, straight backs. Unless one can afford the 
right kind of a sideboard it is better to purchase a sideboard 
table in simple design. A piece of Japanese matting in the 
center of the dining room floor is quite satisfactory when the 
floor is stained. 



COST OF FURNISHING A HOUSE 157 

The room in which the family assemblea several times each 
day to enjoy its meals together should be the most cheerful 
room in the house. 



An Attbactivb Dinihq Roou 

Because there ia bo much attractive bhie-and-nbite china in use, 
lUAUj peraons want dining rooms with blue walls. Tbie is usually a mis- 
take, as tilue used in large quantitiea absorbs the light and makes a room 
gloomy, particularly on dark days and at night. By using colonial yel- 
low on. the walla, with hangings, rug, and decorative china in blue and 
white, one has an almost ideal arrangement. There are many charming 
landscape and foliage papers on the market which, used without pictures 
against them, but with bulbs or plants blooming on the windowsills and 
with hangings of plain, semi transparent, colored material make most 
delightful rooms. 

Plat« rails or racks reduce the apparent height of an oyer-high ceiling. 
It is better to use a rimple flat molding than to crowd a plate rail full of 
inharmonious objects. 

Ugly glass domes on lamps are tieing replaced by silk ones with deep 
silk fringe or, better still, the center light is abandoned iu faror of side 
wall natures in all of the rooms. Candles, prettily shaded, are used on 
the table at night, with a jar of flowers or fruit ai 



158 VOCATIONAL JVIATHEMATICS FOR GIRLS 

EXAMPLES 

1. What will the following cottage dining-room furniture 
cost ? (Include the items given in the price list below.) 

2. What will the following oak dining-room furniture cost ? 

3. What will the following real mahogany dining-room fur- 
niture cost ? 

Price List of Dining-room Furniture 



Table . . 
Chair . . 
Armchair . 
Serving table 
Buffet . . 
China closet 
Serving table 

wheels . 
Screen . . 



High chair 



on 



HUM 


£ « 


S M 


£ M 


00 ,j 




MOO 


^ < 


^ <« 


(B ■< >3 


£ -< 


^ 


RNITU 
BiR 

r Col 


20 


20u 


2o« 


O H 




to 2 as 


fi 


A S 


qH 





M 


"MP 


M 

►J P M 

3 u a 
- o 2 




:^toS 

^ Q « 


J O C 

i§5 


5® 


2 *^ w 
Q SCO 


OJS (A 
ox o 


Colon 
Repro 
— Glo 


Colon 
Kbfro 
— Rub 


Colon 
Repro 
Mauoc 


Hand- 

TURE 1 


$9.00 


$30.00 


$10.50 


112.00 


$85.00 


$21.00 


2.76 


4.50 


5.50 


6.50 


10.00 


6.50 


2.75 


6.76 


7.75 


8.75 


15.00 


10.00 


8.26 


9.00 


10.50 


12.76 


35.00 


18.00 


18.00 


27.50 


21.00 


24.00 


126.00 


34.00 


15.00 


30.00 


34.50 


39.00 


60.00 


46.00 


16.75 


16.75 


30.50 


34.00 


27.00 


27.00 


3.76 


5.00 


4.50 


5.25 


25.00 


20.00 


2.50 


2.50 


4.15 


5.50 


10.00 


9.00 



S3 



t3 

S 

pi 

M 



$16.00 
8.25 

28.00 
82.50 



24.00 



8.00 



Sfnvfts/^^' $5.00 Wood. . .$15.50 Franklin grate or andirons, 
\ Coal, 17.00 Wood or coal 25.00 wood or coal . . $36.00 

4. What will it cost to furnish a home on a moderate scale 
with china of the following amounts and kinds : 

J dozen soup plates (to be used for cereals also) . . $2.36 

J dozen dinner plates 2.26 

1 dozen lunch plates (used also for breakfast and for 

salads) 3.85 

} dozen dessert plates . 1.60 



COST OF FURNISHING A HOUSE 159 

) dozen bread-and-butter plates $0.70 

I dozen coffee cups and saucers 3.30 

i dozen tea cups and saucers 2.80 

^ dozen after-dinner coffee cups and saucers . . . 2.35 

1 teapot . 1.90 

1 coffee pot 2.00 

1 covered hot-milk jug or chocolate pot 2.60 

1 large cream pitcher 70 

1 small platter or chop platter 2.50 

3 odd plates for cheese, butter, etc 95 

Covered dish 2.80 

I dozen egg cups 1.60 

5. What will it cost to furnish a home on' a moderate scale 
with glass, colonial period, of the following amounts and 
kinds : 

} dozen tumblers f^OM 

i dozen sherbet glasses 35 

I dozen dessert plates . .* 1.25 

J dozen finger bowls 75 

Sugar bowl and cream pitcher 50 

Dish for lemons 60 

Dish for nuts 25 

Pitcher 60 

Candlesticks 65 

Vinegar and oil cruets 50 

Berry dish 25 

} dozen iced-tea glasses 76 

} dozen individual salt cellars .60 

6. What will it cost to furnish a home on a moderate scale 
with silver, pilgrim pattern, of the following amounts and 
kinds : 

1 dozen teaspoons $14.00 

} dozen dessert spoons (used for soup also) . . . 9.60 

4 tablespoons 9.60 

1 dozen dessert forks (used also for breakfast, lunch, 

salad, pie, fmit, etc.) 19.00 

I dozen dessert knives 11.00 



160 VOCATIONAL MATHEMATICS FOR GIRLS 

1 dozen table knives with steel blades and ivoroid 

handles $2.00 

Carving set to match steel knives 4.00 

J dozen table forks 12.00 

2 fancy spoons for jellies, bonbons, etc. ($ 1.60 each) 3.00 
2 fancy forks for olives, lemons, etc. (|1.60 each) . 3.00 

^ dozen after-dinner coffee spoons 5.00 

i dozen bouillon spoons 8.00 

} dozen butter spreaders 1.60 

1 gravy ladle 4.76 

Saltspoon .20 

Sugar tongs 2.26 

7. What will it cost to furnish a home on a moderate scale 
with silver-plated ware of the following amounts and kinds : 

Covered vegetable dish (cover may be used as a 

dish by removing handle) $10.00 

Platter 11.60 

Pitcher 12.00 

Coffeepot 12.60 

Toast rack 4.60 

Small tray 6.60 

Sandwich plate 6.00 

SUverbowl 9.00 

Egg steamer 8.00 

Bread or fruit tray 6.60 

Tea strainer 1.00 

Candlesticks, each 3.76 

Household Linen 

The quality of linen in every household should be the best that one 
can possibly afford. The breakfast runners and napkins are to be made 
by hand, of unbleached linen such as one buys for dish towels. With 
insets of imitation filet lace these are very attractive, durable, and easy 
to launder. 

1. What is the cost of supplying the following amount of 
table and bed linen for a couple with an average income of 
$ 1400, who are about to begin housekeeping ? 



COST OF FURNISHING A HOUSE 161 

Table Linen 

2 dozen 22-inch napkins, at $3.00 a dozen. 

2 dozen 12-inch luncheon napkins, at $4.50 a dozen. 

(Luncheon napkins at $1.00 a dozen if made by hand of coarse linen.) 
2 two-yard square tablecloths, at $1.25 a yard. 
Two-yard square asbestos or cotton flannel pad for table, at $ 1.00. 
J dozen square tea cloths, $12.00. 
i dozen table runners for breakfast, at $2.40. 
1 dozen white fringed napkins, at $1.20. 
4 tray covers, at 65 cts. 
1 dozen finger-bowl doilies, at $3.00. 
1 dozen plate doilies, at $3.00. 

Bed Linen 

4 sheets (extra long) for each bed, at $ 1.10. 
4 pillow cases for each pillow, at 20 cts. 

1 mattress protector for each bed, with one extra one in the house, 

at $1.50. 

2 spreads for each bed, at $ 2.50. 

1 down or lamb's-wool comforter for each bed, at $ 6. 

1 pair of blankets for each bed, with 2 extra pairs in the house, at $ 8. 

} dozen plain huckaback towels for each person, at 25 cts. 

3 bath towels for each person, at 30 cts. 

} dozen washcloths for each person, at 11 cts. 

1 bath mat in the bathroom, 2 in reserve, at $ 1.50. 

The Sewing Room 

Even in a small house there is sometimes an extra room which may be 
fitted up as a sewing room in such a way as to be very convenient and 
practical, and at the same time so attractive as to serve occasionally as an 
extra bedroom. This room should be kept as light as possible and should 
be so furnished that it may easily be kept clean. 

EXAMPLE 

1. What will it cost to furnish a sewing room with the fol- 
lowing articles ? 

Sewing machine with flat top to be Used as a dressing table . . $ 20.00 

Chair 1.25 

Box couch 13.25 

Chiffonier 9.00 



162 VOCATIONAL MATHEMATICS FOR GIRLS 

Mirror againat a door 811.25 

Low rocking-chair without arms l.&O 

Cutting table, box underneatli ; tilt top to be used 6.76 

Clothes tree 3.88 

Tbe Kitchen 
The room in which the average housekeeper spenda the 
greater part of her time ia usually the least attraetive room 
in the house, whereas it should be made — and we learn by 
visiting foreign kitchena that it may be made — a picturesque 
setting for one of the finest arts — the art of cookery. 



A Convenient EiTcaEN 

The woodwork should be light in color, the walls should be painted 
with oil paint, or covered with washable material, this also in a light 
color. A limited number of well-made, carefutt; selected utensils will 
be found more useful than a large supply purchased without due con- 
sideration as to their real valne and the need of them. Of course, the 
style of living and the size of the family must to aome extent control the 
number, size, and kind of utensils that are required in each kitehen. As 
in all the other fiirnishingB, the beginner will do well to purchase only 
the essential articles until time demonstrates the need of otbeis. 



COST OF FURNISHING A HOUSE 



163 



EXAMPLES 

1. What will it cost to furnish your kitchen ? ^ 

Stoves — Gas $2.60, $10.00, ^30.00 

Blue-flame kerosene 10.25 

Coal, wood, gas 86.00 

Coal and wood 49.75 

Small electric 33.00 

Table . . . $2.10; $9.00 (drop leaf) ; $11.25 (white enamel on steel) 

Chair $1.87, $6.75 

Ice chest $7.00, $15.00, $40.00 (white enamel) 

Kitchen cabinet $28.00, $29.00 (white enamel on steel) 

Linoleum . . . 60c. square yard, printed ; $ 1.60 square yard, inlaid 



2. What will the following 



$0.85 
.35 



Small-sized ironing board 
Small glass washboard 
Clothesline and pins . 
2 irons, holder and stand 
2-gallon kerosene can 
Small bread board 
Hack for dish towels 
6 large canisters . 
Wooden salt box . 
1 iron skillet . . 

1 double boiler . . 
Dish drainer . . 

2 dish mops . . . 
Wire bottle washer 
Small rolling pin . 
Chopping machine 
Large saucepan 

3 graduated copper, enam- 
eled or nickel handled 
dishes 50 

2 covered earthenware or 

enameled casseroles . . 1.50 
2 pie plates enameled . . .20 
Alarm clock 1.00 



.59 
.70 
.45 
.15 
.10 
.60 
.10 
.30 

1.00 
.25 
.10 
.10 
.10 

1.10 
.30 



small kitchen furnishings cost ? 

Small covered garbage pail . .35 

Scrubbing brush 20 

Broom and brushes ... .60 

1 quart ice-cream freezer . 1.75 

Roller for towel 10 

Bread box 50 

4 small canisters 40 

2 sheet-iron pans to use as 
roasting pans 20 

Dishpan (fiber) ^ . . . .50 

Plate scraper 15 

Soap shaker 10 

Vegetable brush 05 

Muffin tins 25 

Granite soup kettle ... .45 

3 graduated small saucepans .30 

Glass butter jar 35 

6 popover or custard cups . .30 

Soap dish 25 

Knives, forks, egg beater, 

lemon squeezer, etc. . . 5.50 
Sink strainer, brush, and 

shovel 50 

Galvanized-iron scrub pail . .30 



^ Consider income of family and size of kitchen. 



164 VOCATIONAL MATHEMATICS FOR GIRLS 



SXAMPLES IN LAYING OUT FURNITURE 

Considerable practice should be given in laying out furniture according 
to scale. 

1. A bedroom 12' x 10' 6" faces the south, and has 2 win- 
dows, 3' 6" wide, 1 window, 3' 6", two feet from corner of west 
sidej and a door 3' wide two feet from east wall. This room 
is to contain the following furniture : 



1 bed, 6' 6'' X 4' 
1 dresser, 3' x 1'6" 





, p^' , 


s 


j'-*~ 


,»• 




^ 


D 


1 


>• 






C 




' 


£ 






\<^ 







bJJ t 



-/a- 



J9 

Solution 



1 dining table, 5' in diameter 
1 buffet, 4' X 2' 



1 table, 2' 6" x 3' 

2 chairs, 1' 6" x 2' 

Draw a plan showing the 
most artistic arrangement of 
furniture. Scale y = 1'. 

2. A dining room 15' X 18' 
faces the east, and has two 
windows 3' 6" wide on the 
east side, 2 windows 3' 6" on 
the north side, folding doors 6 
wide in the center, on the 
south side. Draw a plan and 
place the following furniture in 
it in the most artistic manner : 

6 chairs, 2' x 1' 6" 
Scale, 1" = 1' 



3. A living room 15' x 18' faces the north and has 2 win- 
dows 3' 6" wide on the north side, 2 windows 3' 6" on the 
west side, and folding doors on the south side. Draw a plan 
and place the following furniture in the most artistic manner : 



1 settee 

1 table 

1 desk and chair 



2 easy-chairs 
2 rockers 
Scale \" = V 



4. A kitchen 12' x 10' 6" faces the south and has 2 windows 
3' 6" wide on the south side, 1 on the west side, two feet 



COST OF FURNISHING A HOUSE 165 

from the north comer, a door 3' wide, two feet from the north- 
east comer that leads into the dining room. Draw a plan and 
place the furniture in proper places : 

1 kitchen range 1 table 

1 sink 2 chairs 

• 2 set tubs Scale f' = l' 

^ REVIEW EXAMPLES 

1. A living room was fitted out with the furniture in the list 
below. What kind of furniture is it ? What is the cost ? 

Large round table and small Curtains and shades for three 

table, $8.00 windows, $ 6.30 

Six chairs and couch, $ 60.00 Rug and draperies, ^ 84.00 

Bookcase or shelves, $ 10.00 Incidentals, $25.00 

2. A hall was furnished with the following articles. What 
was the total cost ? What kind of furniture was used ? 

Seat, $ 12.00 Rug, $ 10.00 

Mirror, $ 2.00 Umbrella stand, $ 2.00 

Table, 1 2.00 Table cover, $ 1.00 

Two chairs, ij^ 7.50 Pole, ^ 3.00 

3. A family of seven — three grown people and four chil- 
dren — lived in a southern city on $ 600 a year. The monthly 
expense was as follows : 

House rent, $ 12.00 Bread, $3.50 

Groceries, k 12.00 Beef, $3.60 

Washing, $5.00 Vegetables, $3.00 

What is the balance from the monthly income of $ 60 for 
clothing and fuel ? 

4. What is the cost of the following kitchen furniture ? 

1 kitchen chair, $ 1.25 1 broom, 50 cents 

1 table, $ 1.50 Kitchen utensils, $8.50 



166 VOCATIONAL MATHEMATICS FOR GIRLS 



5. What is the cost of the following living-room furniture ? 
How much income should a family receive to buy this furniture ? 



Overstuffed chair, $ 12.60 
2 willow chairs, $ 6 each 
1 willow stool, $4.26 
1 rag rug, $ 9.60 
1 newspaper basket, $2.26 
12 yards of cretonne, 36 cents a 
yard 



1 green pottery lamp bowl, f 3.00 
1 wire shade frame, 60 cents 
7 yards of linen, at 60 cents a yd. 
10 yards of cotton fringe, at 6 

cents a yd. 
6 yards of net, at 26 cents a yd. 
Table, 48 by 30 inches, $ 7.00 



6. What is the cost of the following bedroom furniture? 
How much income should a family have to buy this furniture ? 



1 bed spring, $ 3.60 

1 single cotton mattress, $4.26 

1 chiffonier, $6.50 

1 dressing Uble, $2.26 

1 mirror, $2.76 

1 armchair, $4.00 

1 rag rug, $3.26 

2 pillows, 76 cents each 



1 bed pillow, $ 1.00 

10 yards of white Swiss, at 26 cento 

a yd. 
8 yards of pink linen, at 60 cento 

a yd. 
1 comfortable, $ 4.26 
Sheeto and blanketo for one bed, 

$6.00 



3 yards of cretonne, at 36 cento a yd. 

7. What is the cost of the following bedroom furniture ? 
How much income should a family have to warrant buying 
this furniture ? 



2 white iron beds, at $ 4.26 each 
2 single springs, at $ 2.60 each 
2 cotton mattresses, at $4.26 

each. 
2 bed pillows, at $ 1.00 each 
1 dressing table, $ 6.60 
1 white desk, $6.76 
1 chiffonier, $6.60 
1 dressing-table mirror, $ 3.26 
1 chiffonier mirror, $ 1.60 
1 rag rug, $3.26 

I wastepaper basket, .60 

II yards of cretonne, at 36 cento 
a yd. 



6 yards of yellow sateen, at 26 

cento a yd. 
2 comfortables, at $ 4.26 each 
10 yards of cream sateen, at 26 

cento a yd. 
16 yards of cotton fringe, at 6 cento 

a yd. 
1 willow chair, $ 6.00 
1 cushion, 76 cents 
4 yards of net, at 26 cento a yd. 
Sheeto and blanketo for two beds, 

$12.00 
1 dressing table chair, $4.60 



HEAT AND LIGHT 



167 



8. What is the cost of the following dining-room furniture ? 
What income should one receive to buy this furniture ? 



6 dining-room chairs, $ 4.50 

1 dining table, $6.75 

1 serving table, $ 6.25 

1 rag rug, $ 0.50 

1 set of dishes, $ 9.75 



10 yards of cretonne, at 35 cents a yd. 
One wire shade frame, 50 cents 
Table linen, $8.00 
Silverware, $7.50 
1 willow tray, $3.25 



HEAT AND LIGHT 

Value of Coal to Produce Heat 

Several different kinds of coal are used for fuel. Some grades of the 
same coal give off more heat in burning than others. The heating value 
of a coal may be determined in three ways : (1) by chemical analysis to 
determine the amount of carbon ; (2) by burning a definite amount in a 
calorimeter (a vessel immersed in water) and noting the rise in tempera- 
ture of the water ; (3) by actual trial in a stove or under a steam boiler. 
The first two methods give a theoretical value ; the third gives the real 
result under the actual conditions of draft, heating surface, combustion, 
etc. 

The coal generally used for household purposes in the Eastern states 
comes from the anthracite fields of Pennsylvania. This coal, as shipped 
from the mines, is divided into several different grades according to size. 
The standard screening sizes of one of the leading coal-mining districts are 
as follows : 



Broken, through 4 J" round 
Egg, through 2f" square 
Stove, through 2" square 
Nut, through If" square 



Pea, through }" square 
Buckwheat, through i" square 
Rice, through f " round 
Barley, through J" round 



The last three sizes given above are too small for household use and 
are usually purchased for generating steam in large power-plant boilers. 

Coke is used to some extent in localities where it can be obtained at a 
reasonable price in sizes suitable for domestic purposes. The grades of 
coke generally used for this purpose are known as nut and pea. The use 
of coke in the household has one principal objection. It bums up quickly 
and the fires, therefore, require more attention. This is due to the fact 
that a given volume of coke weighs less and therefore contains less heat 
than other fuel occupying the same space in the stove or furnace. 



168 VOCATIONAL MATHEMATICS FOR GIRLS 

The chief qualities which determine the value of domestic coal are its 
percentage of ash and its behavior when burned. Coal may contain an 
excessive amount of impurities such as stone and slate, which may be easily 
observed by inspection of the supply. The quality of domestic coke 
depends entirely upon the grade of coal from which it has been made, 
and may vary as much as 100 ^ in the amount of impurities contained. 

Aside from the chemical characteristics of domestic coal, the most im- 
portant factor to consider in selecting fuel for a given purpose is the size 
which will best suit the range or heater. This depends on the amount 
of grate surface, the size of the fire-box, and the amount of draft. 

EXAMPLES 

1. Hard coal of good quality has at least 90 % of carbon. 
How much carbon in 9 tons of hard coal ? 

2. A common coal hod holds 30 pounds of coal. How many 
hods in a ton ? 

3. If coal sells for $8.25 in June and for $ 9.00 in January, 
what per cent is gained by buying it in Jime rather than in 
January ? When is the most economical time to buy coal ? 

4. The housewife buys kerosene by the gallon. If the price 
per gallon is 13 cts. and live gallons cost 6b cts., what is the per 
cent gained by buying in 6-gallon can lots ? 

5. If kerosene sells for $ 4.60 a bg^rrel, what is the price per 
gallon by the barrel? What per cett is gained over single 
gallons at 13 cts. retail ? What is the most economical way 
to buy kerosene ? (A barrel contains 42 gallons.) 

How to Read a Gas Meter ^ 

1. Each division on the right-hand circle denotes 100 feet; 
on the center circle 1000 feet; and on the left-hand circle 

10,000 feet. Read from left- 
hand dial to right, always tak- 
ing the figures which the hands 
have passed, viz. : The above 
dials register 3, 4, 6, adding 

^ Gas is measured in cubic feet. 




HEAT AND LIGHT 1^9 

two ciphers for the hundreds, making 34,600 feet registered. 
To ascertain the amount of gas used in a given time, deduct 
the previous register from the present, viz. : 

Register by above dials 34,600 

Register by previous statement 18,200 

Given number of feet registered 16,400 

16,400 feet @ 90 cts. per 1000 costs what amount ^ 

2. If a gas meter at the pre- .^^^^^\^ ^^^^*^^ J^^^T^ 
vious reading registered 82,700 ^?^\^^^''^^^ 

feet, and to-day the dials read W ^ ysA^v \ Aa^V \ /3/ 
as follows, ^^^^3^^ ^^^^^^^ X!l3j>^ 

what is the cost of the gas at 95 cts. per 1000? 

3. What is the cost of the gas used during the month from 
the reading on this meter, if ^-,hoos^^ o'******'*^ i^^^r^ 
the previous reading was 6100 /x^\\ //^~\\ Z/^^\\ 
feet ? The rate is $ 1.00 per r(\ jYf • [Tfj^ Yj 
1000 cu. ft. less ten per cent, \^--jr''^\k''^^ 

if paid before the 12th of the ^-^2.-^ ^^--i-^^ 

month. Give two answers. si^p^^^ ^^^^S^d n?^^^5^^ 

4. What is the cost of gas pf^^Y\rf ^r\r/>^ ^^ 
registered by this meter at wl yTvV ^>7 \ V yv 
85 cts. per 1000 cu. ft.^ ^^is:^ x^l^^ ^k:3^ 

How to Read an Electric Meter 

(See the subject of the electricity in the Appendix) 

There are three terms used in connection with electricity 
which it is important to understand; namely, the volt, the 
ampere, and the watt or kilowatt. 

(1) The volt is the unit of Electromotive Force or electrical 
pressure. It is the pressure necessary to force a current of 
one ampere through a resistance of one ohm, 

(2) The imit of electric current strength is the ampere. It 



170 VOCATIONAL MATHEMATICS FOR GIRLS 

is the amount of current flowing through a resistance of one 
ohm under a pressure of one volt. 

(3) The watt is the unit of electrical power ; it is the prod- 
uct of volts (of electromotive force) and current (amperes) in 
the circuit, when their values are respectively one volt and 
one ampere. That is to say, if we have an electrical device 
operated at 3 amperes, on a line voltage of 115 volts, the 
amount of current consumed is equal to 116 X 3 = 346 watts, 
which, if operated continuously for one hour, will register on 
the electric meter as 345 watt hours, or .345 kilowatt hours 
(a kilowatt hour being equal to 1000 watt hours). 

All electrically operated devices are stamped with the ampere and 
voltage rating. This stamping may be found on the name-plate or bottom 
of the device. By multiplying the voltage of the circuit upon which the 
device is to be operated by the amperes as found stamped on the device, 
we can quickly determine the wattage consumption of the latter, as ex- 
plained under the definition of the watt, and as shown above. The line 
voltage which is most extensively supplied by Electric Lighting com- 
panies in this country is 115 volts, and where this voltage is in operation, 
the devices are stamped for voltage thus : V. 110-126. This means 
that the device may be used on a circuit where the voltage does not drop 
below 110 volts or rise above 126 volts. By operating a device with the 
above stamping on a circuit of 106 volts the life of the device would be 
very much longer, but the results desired from it would be secured much 
more slowly. Again, if the same device were used on a circuit oper- 
ating at 130 volts, the life of the device would be very short, although the 
results desired from it would be brought about much more quickly. Be- 
fore attempting to operate an electrically heated or lighted device, if in 
doubt about the voltage of the circuit, it is best to call upon the Electric 
Company with which you are doing business and ask the voltage of their 
lines. 

Incandescent electric lamps, while known to the average user as 
lamps of a certain "candle-power,'* are all labeled with their proper 
wattage consumption. Mazda lamps, suitable for household use and 
obtainable at all lighting companies, are made in 16, 26, 40, 60, and 100 
watt sizes. For commercial use, lamps of 1000 watts and known as the 
nitrogen-filled lamps are on the market. Nitrogen lamps are made in 
sizes of 200 watts and upwards. 



HEAT AND LIGHT 171 

The rate by which current coDsumed for lighting and small heating is 
figured in some cities is known as the <* sliding scale rate,^* and current 
is charged for each month, as follows : 

The first 200 kw. hrs. used @ 10^ per kilowatt hour. 
The next 300 kw. hrs. used @ 8^ per kilowatt hour. 
The next 600 kw. hrs. used @ 7 f per kilowatt hour. 
The next 1000 kw. hrs. used @ 6 ^ per kilowatt hour. 
The next 3000 kw. hrs. used @ 6 ^ per kilowatt hour. 
All over 6000 kw. hrs. used @ 4 ^ per kilowatt hour. 

Less 6% discount, if bill is paid within 16 days from date of issue. 

Under the sliding-scale rate the more electricity that is consumed, the 
cheaper it becomes. But it is also readily seen that the customer who 
uses a large amount of electricity pays in exactly the same way as the 
small consumer pays for his consumption. 

If a person uses less than 200 kw. hrs. per month, he pays for his con- 
sumption at the rate of 10 ^ per kilowatt hour ; if he uses 201 kw. hrs. of 
electricity per month, he pays for his first 200 kw. hrs. at the first step, 
namely 10 ^, and for the remaining 1 kw. hr. he pays 8 ^ per kilowatt 
hour. 

If a meter reads ** 1000 kw. hrs.,'* the bill is not figured at 6^ direct, 
but must be figured step by step as shown in the examples below. 

For convenience in figuring, the amount of power used by various 
electrically operated devices is given in the following table. By figuring 
the cost of each per hour, it will be seen that these electric servants work 
very cheaply. 



Appabatdb 


"Watts used 


What 

FEB 


18 Cost 

HOUB* 


(a) Disk stove 


200 • 




? 


(6) 61b. iron 


440 




? 


(c) A'ir heater, small 


1000 




? 


(d) Toaster-stove 


600 




? 


(e) Heating pad 


66 




? 


(/) Sewing-machine motor 


60 (average) 




? 


(gr) 26 watt (16 c p.) lamp 


26 




? 


(h) Chafing dish 


600 




? 


(i) Washing-machine motor 


200 (average) 




f 



Example. — Suppose a customer in one month used 6120 
kilowatt hours of electricity, what is the amount of his bill 

^ Based on 10 cents per kilowatt hour. 



172 VOCATIONAL MATHEMATICS FOR GIRLS 

with 5 % deducted if the bill is paid within the discount 
period of 15 days from date of issue ? 



Solution. — 


6120 kw. hrs. = 


total amount used. 


First 


200kw. hrs. @10)^ = 
6920 


$ 20.00 


Next 


800 kw. hrs. @ 8^ = 
6620 


24.00 


Next 


600 kw. hrs. @ 7 ^ = 
6120 


36.00 


Next 


1000 kw. hrs. @ 6^ = 
4120 


60.00 


Next 


8000 kw. hrs. @ 5^ = 


160.00 



We have now figured for 6000 kw. hrs., and as our rate states that all 
over 6000 kw. hrs., is figured at 4 ^ per kilowatt hours, we have 

> 

1120kw. hrs. @ 4j^ = | 44.80 

$383.80 = gross bill 

Assuming that the bill is paid within the given discount period, we 
deduct 6% from the 

gross bill, which equals $ 16.69 

$317.11 = net bill 

EXAMPLES 

1. A customer uses in one month 300 kw. hr. of electricity. 
What is the amount of his bill if 5 % is deducted for payment 
within 15 days ? 

2. What is the amount of bill, with 5 % deducted, for 15 
kw. hr. of electricity ? 

An electric meter is read in the same way that a gas meter is read. 
In deciding the reading of a pointer, the pointer before it (to the right) 
must be consulted. Unless the pointer to the right has reached or passed 
zero, or, in other words, completed a revolution, the other has not com- 
pleted the division upon which it may appear to rest. Figure 1 reads 
11 kw. hrs., as the pointer to the extreme right has made one complete 
revolution, thus advancing the second pointer to the first digit and has 
itself passed the first digit on its dial. 



HEAT AND LIGHT 



173 




Fig. 1. — Reading 11 kw. hrs. 



KpiOOO 



1.000 



too 



10 




KIL0WATT-t40URS 



Fig. 2. — What is the Reading? 



10,000 




KILOWATT- HOUKfi 



Fig. 3. — Reading 424 kw. hrs. 



laooo 



1.000 



100 



10 




KILO WATT- HOilBS 



Fig. 4. — What is the Reading? 



laooo 




KILOWATT-MOUPS 



Fig. 6. — What is the Reading ? 



174 VOCATIONAL MATHEMATICS FOR GIRLS 

1. What is the cost of electricity in Eig. 1, using the rates 
on page 171 ? 

2. What is the cost of electricity in Fig. 2, using the rates 
on page 171, with the discount ? 

3. What is the cost of electricity in Fig. 3, using the rates 
on page 171, with the discount ? 

EXAMPLES 

1. What is the cost of maintaining ten 25-watt Mazda lamps, 
burning 30 hours at 10 cents per kw. hr. ? 

2. What will it cost to run a sewing machine by a motor 
(50 watts) for 15 hours at 9 cents per kw. hr. ? 

3. A 6-lb. electric flatiron is marked 110 V. and 4 amperes. 
What will it cost to use the iron for 20 hours at 8 cents per 
kw. hr. ? 

4. An electric washing machine is marked 110 V. and 
2 amperes. What will it cost to run it 15 hours at 8^ cents 
per kw. hr. ? 

5. An electric toaster stove is marked 115 volts and 3^ am- 
peres. What will it cost to run it for a month (thirty break- 
fasts) 15 hours at 8f cents per kw. hr. ? If a discount of 
5 % is allowed for prompt payment, what is the net amount 
of the bill ? 

Methods of Heating 

Houses are heated by hot air, hot water, or steam. In the 
hot-water system of heating, hot water passes through coils 
of pipes from the heater in the basement to radiators in the 
rooms. The water is heated in the boiler, and the portion of 
the fluid heated expands and is pushed upward by the adjacent 
colder water. A vertical circulation of the water is set up 
and the hot water passes from the boiler to the radiators and 
gives off its heat to the radiators, which in turn give it off to 
the surrounding air in the room. The convection currents 



HEAT AND LIGHT 



175 



carry heat through the room and at the same time provide for 
ventilation. 

In the hot-air method the heat passes from the furnace 
through openings in the floor called registers. This method 
frequently fails to heat 
a house uniformly be- 
cause there is no way for 
the air in certain rooms 
to escape so as to per- 
mit fresh and heated 
air to enter. 

Steam heating consists 

in allowing steam from 

a boiler in the basement 

to circulate through coils 

or radiators. The steam 

gives off its heat to the xx * tt 

° , . , . Hot Aib Heating System 

radiators, which in turn 

give it off to the surrounding air. 




Room-heating Calculations 




Hot Water Heating System 



In order to insure comfort 
and health, every housewife 
should be able to select an 
efficient room-heating appli- 
ance, or be able to tell whether 
the existing heating appara- 
tus is performing the required 
service in the most econom- 
ical manner. In order to do 
this, it is necessary to know 
how to determine the re- 
quirements for individual 
room heating. 



176 VOCATIONAL MATHEMATICS FOR GIRLS 

For Steam Heating 

Allow 1 sq. ft. of radiator surface for each 
80 cu. ft. of volume of room. 
13 sq. ft. of exposed wall surface. 
3 sq. ft. of exposed glass surface (single window). 
6 sq. ft. of exposed glass surface (double window). 

For Hot-water Heating 

Add 60 per cent to the amount of radiator surface obtained by the 
above calculation. 

For Oas Heaters having no Flue Connection 
Allow 1 cu. ft. of gas per hour for each 
215 cu. ft. of volume of room. 
36 sq. ft. of exposed wall surface. 
9 sq. ft. of exposed glass surface (single window). 
18 sq. ft. of exposed glass surface (double window). 

The results obtained must be further increased by one or more of the 
following factors if the corresponding conditions are present. 

Northern exposure 1.8 

Eastern or western exposure 1.2 

Poor frame construction 2.5 

Fair frame 2.0 

Good frame or 12-inch brick 1.2 

Room heated in day time only 1.1 

Room heated only occasionally 1.3-1.4 

Cold cellar below or attic above . . . . . 1.1 

Example. — How much radiating surface, for steam heating, 
is necessary to heat a bathroom containing 485 cu. ft. ? The 
bathroom is on the north side of the house. 

y^ = 6^ sq. ft. of radiating surface 
6^ X 1.3 = IJ X i* = 7itt sq. ft. 
eVs + 7Hi = 6^^ + 7 Hi = 13iH sq. ft. or approx. 14 sq. ft. Ana, 

EXAMPLES 

1. How much radiating surface, for steam heating, is re- 
quired for a bathroom 12' x 6' x 10' on an eastern exposure ? 

2. How much radiating surface, for hot-water heating, is 
required for the bathroom in example 1 ? 



COST OP FURNISHING A HOUSE 177 

3. How large a gas heater should be used for heating the 
bathroom in example 1 ? 

4. (a) How much radiating surface is required for steam 
heating, in a living room 18' x 16^' x 10', with three single 
windows 2' x 5^' ? The room is exposed to the north. 

(b) How much radiating surface for hot-water heating ? 

(c) How much gas should be provided to heat the room in 
example (a) ? 

5. (a) How much radiating surface is required for steam 
heating a bedroom 19' x 17' x 11' with two single windows 
2' X 5^' ? The house is of poor frame construction. 

(b) How much radiating surface for hot-water heating ? 

(c) How much gas should be provided to heat room in 
example (a) ? 



CHAPTER VIII 
THRIFT AND INVESTMENT 

It is not only necessary to increase your earning capacity, but 
also to develop systematically and regularly the saving habit. 
A dollar saved is much more than two dollars earned. For a 
dollar put at interest is a faithful friend, earning twenty-four 
hours a day, while a spent dollar is like a lost friend — gone 
forever. Histories of successful men show that fortune's 
ladder rests on a foundation of small savings ; it rises higher 
and higher by the added power of interest. The secret of 
success lies in regularly setting aside a fixed portion of one's 
earnings, for instance 10 % ; better still, 10 % for a definite 
object, such as a home or a competency. 

In every community one will find various agencies by which 
savings can be systematically encouraged and most success- 
fully promoted. These institutions promote habits of thrift, 
encourage people to become prudent and wise in the use of 
money and time. They help people to buy or build homes for 
themselves or to accumulate a fund for use in an emergency or 
for maintenance in old age. 

Banks 

Working people should save part of their earnings in order to have 
something for old age, or for a time of sickness, when they are unable to 
work. This money is deposited in banks — savings, National, cooper- 
ative, and trust companies. 

National Banks 

National banks pay no interest on small deposits, but give the depositor 
a check book, which is a great convenience in business. National banks 
require that a fixed sum should be left on deposit, $ 100 or more, and 
some of them charge a certain amount each month for taking care of the 
money. 

178 



THRIFT AND ESTVESTMENT 179 

Trust Companies 

Trast companies receive money on deposit and allow a customer to 
draw it out by means of a check. They usually pay a small interest on 
deposits that maintain a balance over $ 500. 

CoQperative Banks 

When a person takes out shares in a cobperative bank, he pledges him- 
self to deposit a fixed amount each month. If he deposits $5, he is said 
to have live shares. No person is permitted to have more than twenty- 
five shares. The rate of interest is much higher than in other banks, and 
when the shares mature, which is usually at the end of about eleven 
years, all the money must be taken out. Many people build their home 
through the cooperative bank, for, like every other bank, it lends money. 
When a person borrows money from a cooperative bank, he has to give a 
mortgage on real estate as security, and must pay back a certain amount 
each month. 

Savings Banks 

The most common form of banking is that carried on by the Savings 
Bank. People place their money in a savings bank for safe keeping and 
for interest. The bank makes its money by lending at a higher interest 
than it pays its depositors. There is a fixed date in each bank when 
money deposited begins to draw interest. Some banks pay quarterly and 
some semi-annually. At different times banks pay different rates of 
interest ; and often in the same community there are different rates of in- 
terest paid by different banks. 

Every bank is obliged to open its books for inspection by special 
officers who are appointed for that work. If these men did their work 
carefully and often enough, there would be almost no chance of loss in 
putting money in a bank. Banks fail when they lend money to too many 
people who are unable to pay it back. 

EXAMPLES 

(Review interest on page 60) 

1. I place $ 400 in a savings bank that pays 4 % on Jan. 1, 
1916. Money goes on interest April 1 and at each successive 
quarter. How much money have I to my credit at the begin- 
ning of the third quarter ? 

2. A man with a small business places his savings, $ 1683, 



180 VOCATIONAL MATHEMATICS FOR GIRLS 

■ 

in a trust company so lie can pay his bills by check. The 
bank pays 2 % for all deposits over $ 500. He draws checks 
for $ 430 and $ 215 within a few days. At the end of a 
month he will receive how much interest ? 

3. Practically 10 % of the entire population of the United 
States, including children, have savings-bank accounts. If* the 
population is 92,818,726, how many people have savings bank 
deposits ? 

4. On April 1, 1910, a woman deposited $ 513 in a savings 
bank which pays 4 ^ interest. Interest begins April 1 and at 
each succeeding quarter. Dividends are declared Jan. 1 and 
July 1. What is the total amount of her deposit at the present 
date ? 

The savings bank is not adapted to the needs of those ^ith large sums 
to place at interest. It is a place where small sums may be deposited 
with absolute safety, earn a modest amount, and be used by the depositor 
at short notice. The savings bank lends money on mortgages and re- 
ceives about 6 ^0, It pays its depositor either 3J % or 4 %. The differ- 
ence goes to pay expenses and to provide a surplus fund to protect 
depositors. 

The question may be asked, " Why cannot the ordinary depositor lend 
his money on mortgages and receive 5 % ? " He can, if he is willing to 
assume the risk. When you receive 4 % interest, you are paying 1 9^ to 
1^ % in return for absolute safety and freedom from the necessity of 
selecting securities. 

Mortgages 

A mortgage is the pledging of property as a secuilty for a debt. Mr. 
Allen owns a farm and wants some money to buy cattle for it. He goes 
to Mr. Jones and borrows $ 1000 from him, and Mr. Jones requires him 
to give as surety a mortgage on his farm. That is, Mr. Allen agrees that 
if he does not pay back the f 1000, the farm, or such part as is necessary 
to cover the debt, shall belong to Mr. Jones. 

Under present law, if a man wishes to foreclose a mortgage, — that is, 
compel its payment when due, — he cannot take the property, but it must 
be sold at public auction. From the money received at the sale the man 
who holds the mortgage receives his full amount, and anything that is 
left belongs to the man who owned the property. 



THRIFT AND INVESTMENT 181 

Notes 

A promissory note is a paper signed by the borrower promising to 
repay borrowed money. Notes should state value received, date, the 
amount borrowed (called the face), the rate, to whom payable, and 
the time and place of payment. Notes are due at the expiration of 
the specified time. 

The rate of interest varies in different parts of the country. The 
United States has to pay about 2 %. Savings banks pay S^o or 4^o, 
Individuals borrowing on good security pay from 4^o to 6 %. 

In order to make the one who loans the money secure, the borrower, 
called the maker of the note, often has to get a friend to indorse or sign 
this note. The indorser must own some sort of property and if, at the 
end of six months or the time specified, the maker cannot pay the note, 
he is notified by written order, called a protest, and may, later, be called 
upon to repay the note. 

A man is asking a great deal when he asks another man to sign a note 
for him. Unless you have more money than you need, it is better busi- 
ness policy to refuse the favor. 

Always be sure that you know exactly what you are signing and that 
you know the responsibility attached. If you are a stenographer or a 
clerk in an office, you will often be called upon to witness a signature and 
then to sign your own name to prove that you have witnessed it. Always 
insist upon reading enough of the document to be sure that you know 
just what your signature means. 

EXAMPLES 

1. My house is worth $ 4000 and the bank holds a mortgage 
on it for one-half its value. They charge 5 % interest, which 
must be paid semi-annually. How much do I pay each time ? 

2. A bank holds a mortgage of $ 2500 on a house. The in- 
terest is 5 % payable semi:annually. How much is paid for 
interest at the end of three years ? 

3. A man buys property worth $ 3000. He gives a $ 2000 
mortgage and pays 5^ % interest. What will be the interest 
on the mortgage at the end of the year ? Suppose he does not 
pay the interest, how long can he hold the property ? 



182 VOCATIONAL MATHEMATICS FOR GIRLS 

Different Kinds of Promissory Notes 

$ Montgomery, Ala 191 

after date for value received promise 

to pay to the order of 



.Dollars 



a4> iWedjanicg National JSank* 
JVb Due 



A Common Note 



$ St, Paul, Minn 19 

after date for value received we jointly and 

severally promise to pay to the order of 



.Dollars 



a4> fHerijanicg National JSanfe. 
J^o Due 



Joint Note 

$ Fall RiYEB, Mass. 191 

after date for value received 

promise to pay to the order of The Mechanics National Bank of Fall River, 

Mass. Dollars, 

at said Bank, and interest for such further time as said principal sum or any 

part thereof shall remain unpaid at the rate of per cent per annum, 

having deposited with the said Mechanics National Bank, as General Col- 
lateral Security, for the payment of any of liahilities to said 

Bank due, or to become due, direct or indirect, joint or several, individual or 
firm, now or hereafter contracted or incurred, at the option of said Bank, 
the following property, viz. : 



and hereby authorize said Bank or its assigns to sell and transfer said 

property or any part thereof without notice, at public or private sale, at the 



THRIFT AND INVESTMENT 183 

option of said Bank or its assigns, on the non-payment of any of the liabili- 
ties aforesaid, and to apply the proceeds of said sale or sales, after deducting 
all the expenses thereof, interest, all costs and charges of enforcing this 
pledge and all damages, to the payment of any of the liabilities aforesaid, 

giving credit for any balanqe that may remain. Said Bank or its 

assigns shall at all times have the right to require the undersigned to deposit 
as general collateral security for the liabilities aforesaid, approved additional 

securities to an amount satisfactory to said Bank or its assigns, and 

hereby agree to deposit on demand (which may be made by notice in writing 

deposited in the post office and addressed to at last known 

residence or place of business) such additional collateral. Upon fail- 
ing to deposit such additional security, the liabilities aforesaid shall be deemed 
to be due and payable forthwith, anything hereinbefore or elsewhere ex- 
pressed to the contrary notwithstanding, and the holder or holders may 
immediately reimburse themselves by public or private sale of the security 
aforesaid ; and it is hereby agreed that said Bank or any of its officers, 
agents, or assigns may purchase said collateral or any part thereof at such 
sale. In case of any exchange of or addition to the above described collateral, 
the provisions hereof shall apply to said new or additional collateral. 



COLLATEBAL NOTE 

4. On Jan. 2, 1915, Mr. Lewis gave his note for $2400, 
payable on Feb. 27, with interest at 6 %. On Feb. 2, he paid 
$ 600. How much was due Mar. 2, 1915 ? 

Solution. — In the case of notes running for less than a year, exact 
days are counted ; from Jan. 2 to Feb. 2 is 31 days. 

Interest Jan. 2 to Feb. 2, 31 days, 

$12.00 for 30 days 

.40 for 1 day 
$ 12.40 31 days 

Amount due Feb. 2, $ 2400 + 12.40 = $ 2412.40. 

$ 2412.40 - 600 = $ 1812.40. 

Interest Feb. 2 to March 2, 28 days, 

$6.0413 20 days 

1.8124 6 days 

.6041 2 days 

$8.4678 or $8.46 

1812.40 

Amount due March 2, $ 1820.86 Ans. 



184 VOCATIONAL MATHEMATICS FOR GIRLS 

Money lenders may discount their notes at banks and thus obtain their 
money before the note comes due. But the banks, in return for this serv- 
ice, deduct from the full amount of the note interest at a legal rate on 
the full amount for such time as remains between the day of discount 
and the day when the note comes due. 

To illustrate : A man has a note for $ 600 due in three months at 6 9^ 
interest. At the end of a month he presents the note at a bank and 
returns the difference between the amount at maturity, $600, and the 
interest on $609 for two months, the remaining time, at legal rate 69^, 
$6.09 or $609 — 6.09 = $602.91. 

5. On June 1, 1914, Mr. Smith givea his note for $ 1200, 
payable on demand with interest at 6%. The following pay- 
ments are made on the note : Aug. 1, 1914, $ 140 ; Oct. 1, 1914, 
$ 100 ; Dec. 1, 1914, $ 100 ; and Feb. 1, 1914, $ 160. How 
much was due May 1, 1915 ? 

6. A merchant buys paper amounting to $ 945. He gives 
his note for this amount, payable in three months at 6 % . 
The paper dealer desires to turn the note into cash immedi- 
ately. He therefore discounts it at the bank for 6%. How 
much does he receive ? 

Stocks 

It often happens that one man or a group of men desire to engage in a 
business that requires more money than they alone are able or willing to 
invest in it. They obtain more money by organizing a stock company, 
in which they themselves buy as many shares as they choose, and then 
they induce others to pay for enough more shares to make up the capital 
that is needed or authorized for the business. 

A stock company consists of a number of persons, organized under a 
general law or by special charter, and empowered to transact business as 
a single individual. The capital stock of a company is the amount named 
in its charter. A share is one of the equal parts into which the capital 
stock of a company is divided (generally $ 100). 

The par value of a share of stock is its original or face value ; the 
market value of a share of stock is the price for which the share will sell 
in the market. The market values of leading stocks vary from day to 
day, and are quoted in the daily papers ; e.g. *' N. Y. C, 131 " means 
that the stock of the New York Central R. R. Co. is selling to-day at 
$ 131 a share. 



THRIFT AND INVESTMENT 185 

DiTidends are the net profits of a, stock company divided among the 
BtockholderH according lo llie amount of stock tbey own. 

Stock compantea often issue two kinda of stock, namely : preferred 
stoclc, wbich consists of a certain number of shares on wliicli dividends 
are paid at a fixed rate, and commOD stock, which consists of the re- 
maining shares, among wbich are apportioned whatever protiU there are 
remaining after payment of the required dividends on the preferred stock. 



Cbrtificatb of Stock 

Stocks are generally bought and sold by brokers, who act as agents 
for the owners of the stock. Broken receive as their compensation a 
certain per cent of the par value of the stock bongbt Qr sold. This Is 
called brokerage. The usual brokerage is } ^ of the par value ; e.g. if a 
broker sells 10 shares of stock for me, his brokerage is ) 9b of 1 1000, or 
1 1.26. 

Example. — What is the cost of 20 shares of No. Butte 30J ? 

*30i + J i 1 = f 30t, cost of 1 share. 
(30} x20 = i000+ $12^ = $012.60, total cost. 

1 1 of 1 % of 8 100 = I of $ 1, broker's charge pet share. 



186 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

1. The par value of a certain stock is $100. It is 
quoted on the market at $87^.. What is the difference in 
price per share between the market value and the par 
value ? 

2. What is the cost of 40 shares of Copper Range at 53 ? 

3. What is the cost of 53 shares of Calumet and Hecla 
at 680 ? 

4. I have 50 shares of Anaconda. How much shall I re- 
ceive if I sell at 66^ ? 

5. I buy 60 shares of Anaconda at 66^. It pays a quarterly 
dividend of $ 1.50. What interest am . I receiving on my 
money ? 

Bonds 

Corporations and national, state, county, and town govjBmments often 
need to borrow money in order to meet extraordinary expenditures. 
When a corporation wishes to borrow a large sum of money for several 
years, it usually mortgages its property to a person or bank called a trustee. 
The amount of the mortgage is divided into parts called bonds, and these 
are sold to investors. The interest on the bonds is at a fixed I'ate and is 
generally payable semi-annually. Shares of stock represent the property 
of a corporation, while bonds represent debts of the corporation ; stock- 
holders are owners of the property of the corporation, while bondholders 
are its creditors. 

Bonds of large corporations whose earnings are fairly stable and regu- 
lar, like steam railroads, street railways, and electric power and gas 
plants, whose property must be employed for public necessities regardless 
of the ability of the managers, are usually good investments. Well-secured 
bonds are safer than stocks, as the interest on the bonds must be paid re- 
gardless of the condition of the business. 

For the widow who is obliged to live on the income from a moderate 
amount of capital, it is better to invest in bonds and farm mortgages than 
in stock. 



THRIFT AND INVESTMENT 187 



A Sample Bond 



188 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

1. A man put $ 200 in the Postal Savings Bank and received 
2 ^0 interest. What would have been the difference in his 
income for a year if he had taken it to a savings bank that 
paid 3| % ? 

2. A widow had a principal of $ 18,000. She placed it in a 
group of savings banks that paid 3f %. The next year she 
purchased farm mortgages and secured h\ ^o* What was the 
difference in her income for the two years ? 

3. Two sons were left % 15,000 each. One placed it in first- 
class bonds paying 5^ %. The other placed it in savings banks 
and averaged 4^%. What was the difference in income per 
year ? 

Fire Insurance 

Household furniture, books, apparel^ etc., can be insured at a low rate. 
While it will not make a man less careful in protecting his home from fire, 
it will make him more comfortable in the thought that if fire should come, 
the family will not be left without the means of clothing themselves and 
refurnishing the house. One of the first duties then, after the home is 
established, is to secure insurance. 

Insurance companies issue a policy for 1, 3, or 5 years. There is an 
advantage in buying a policy for more than one year, for on the 3- or 6- 
year policy there is a saving of about 20 9^ in premiums. Rules of per- 
centage apply to problems in insurance. 

Example. — A house worth $8400 is insured for its full 
value at 28 cents per $ 100. What is the cost of premium ? 

Solution. 

$ 8400 is the value of the policy or base. 

28 cents is the rate of premium or rate. 

The premium or interest is the amount to be found. 

84 X $0.28 = $23.52, premium. 

EXAMPLES 

1. Find the insurance upon a dwelling house valued at 
$ 3800 at $ 2.80 per $ 1000 if the policy is on 80 % of the value 
of the house. 



THRIFT AND INVESTMENT 189 

2. Mr. Jones takes out $ 800 insurance on his automobile at 
2 fo' What is the cost of the premium ? 

3. The furniture in one tenement of a three-family house is 
valued at $ 1000. What premium is paid, if it is insured at 
the rate of 1 % for 5 years ? 

4. If the premium on the same furniture in a two-family 
house in a different city is $ 7.50, what is the rate, expressed 
in per cent ? 

Life Insurance 

Every indostrious and thrifty person lays aside it certain amount 
regularly for old age or future necessities, or in case of death to provide 
sufficient amount for the support of the family. This is usually done by 
taking out life insurance from a corporation called an insurance company. 
This corporation is obliged to obtain a charter from the state, and is 
regularly inspected by a proper state oflBcer. 

The poliqf or contract which id made by the company with the member, 
fixing the amount to be paid in the event of his death, is called a life 
insurance policy, and the person to whom the amount is payable is 
termed the beneficiary. The contribution to be made by the member to 
the common fund, as stipulated in the policy, is termed the pr^mtttm, and 
is usually payable in yearly, half-yearly, or quarterly installments. 

There are different kinds of insurance policies : the simplest is the 
ordinary life policy. Before entering into a contract of this, kind, it 
is necessary to fix the amount of the premium, which must be large 
enough to enable the company to meet the necessary expense of conduct- 
ing the businesd and to accumulate a fund sufficient to pay the amount of 
the policy when the latter matures by the death of the insured. 

Making the Premium. — If it were known to a certainty just how long 
the policy holder would live, anyone could compute the amount of the 
necessary premium. Let us suppose, for illustration, that the face of the 
policy is $ 1000, and that the policyholder will live just twenty years. Let 
us assume that the business is conducted without expense, and that the 
premiums are all to be invested at interest from date of payment. We 
do not know to a certainty what rate of interest can be earned during the 
whole period, and we shall therefore assume one that we can safely 
depend upon, say three per cent. A yearly payment of .$86.13 invested 
at three per cent compound interest will amount to $ 1000 in twenty 
years. 



190 VOCATIONAL MATHEMATICS FOR GIRLS 

JVo.j218649^ $5000 

Sftje "^ovth Mvcv ^ntnvd %iU %nsnvvcntt 

In Consideration of the application for this Policy, a copy of which 
is attached hereto and made a part hereof, and in further consideration of 
the payment of 

^m j^utilyreH Ctytrtg^giflbt^^^^-^^^^-^^-v^N^^^^^s Dollars 

100 ' 

the receipt whereof is hereby acknowledged, and of the_™55?Lpayment 
of a like simi to the said Company, on or before the irtrgt ^^.y of 
_5555?3_in every year during the continuance of this Policy, promises 

to pay at its of&ce in Milwaukee, Wisconsin, unto Itlarg wot 

~ , Beneficiar__J__, 



. CTliCe of 3ot;n IBoe ^hf. Insured, of 

JBeg fHotneg in the State of ^^^^ 

subject to tf|g rtg!|t of ttje ffneureH, tyerefeg resnrbeH, t0 diange ttye ISeneficiatg 
or iSntefictgrteg the sum nf .^tbg grtjottganH Dniiara, 

upon receipt and approval of proof of the death of said Insured while this 
Policy is in full force, the balance of the year's premium, if any, and any 
other indebtedness on account of this Policy being first deducted there- 
from; provided, however, that if no Beneficiary shall survive the said 
Insured, then such payment shall be made to the executors, administra- 
tors or assigns of the said Insured. 

In Witness Whereof, THE NORTH STAR MUTUAL LIFE INSURANCE 
COMPANY, at its office in Milwaukee, Wisconsin, has by its President and 

Secretary, executed this contract, this £ll^ ^day of ^Tanuary ^^^ 

thousand nine hundred and sixteen. 

S. A. Hawkins, Secretary. L. H. Perkins, President. 

Ordinary Life Insurance Policy 



THRIFT AND INVESTMENT 191 

If it were certain that the policyholder would live just twenty years, 
and that his premiums would earn just three per cent interest, and that 
the business could be conducted without expense, the necessary premium 
would be $36.13. But there are certain other contingencies that should 
be provided for; such as, for example, a loss of invested funds, or a 
failure to earn the full amount of three per cent interest. 

To meet these expenses and contingencies something should be added 
to the premium. Let us estimate as sufficient for this purpose the sum of 
$7. This v^U make the gross yearly premium $43.13, the original pay- 
ment ($36.13) being the net premium, while the amount added thereto 
for expenses, etc. ($7.00), is termed the loading. 

The net premium is the amount which is mathematically necessary 
for the creation of a fund sufficient to enable the company to pay the 
policy in full at maturity. The loading is the amount added to the net 
premium to provide for expenses and contingencies. The net premium 
and loading combined make up the gross premium^ or the total amount to 
be paid each year by the insured. 

Mortality Tables. — Although it is impossible, as in the illustration 
given above, to predict in advance the length of any individual life, there 
is a law governing the mortality of the race by which we may determine 
the average lifetime of a large number of persons of a given age. We 
cannot predict in what year the particular individual will die, but we may 
determine with approximate accuracy how many out of a given number 
will die at any specified age. By means of this law it becomes possible to 
compute the premium that should be charged at any given age with 
almost as much exactness as in the example given, in which the length of 
life remaining to the individual was assumed to be just twenty years. 

Let us suppose, for example, that observations cover a period of time 
sufficient to include the history of 100,000 lives. Of these, you will find a 
certain number dying at the age of thirty, a larger number at the age of 
forty, and so on at the various ages, the extreme limit of life reached 
being in the neighborhood of one hundred years. The mortuary records 
of other groups of 100,000, living where conditions are practically the 
same, would give approximately the same results — the same number of 
deaths at each age in 100,000 bom. The variation would not be great, 
and the larger the number of lives under observation, the nearer the 
number of deaths at the several ages by the several records would ap- 
proach to uniformity. 

In this manner mortality tables have been constructed which show how 
many in any large number of persons bom, or starting at a certain age, 
will live to age thirty, how many to age forty, how many to any other 



192 VOCATIONAL MATHEMATICS FOR GIRLS 

age, and likewise the number that will die at each age, with the average 
lifetime remaining to those still alive. The insurance companies from 
these tables construct tables of premiums, varying according to the amount 
and kind of insurance and the age at which the policy is taken out. 

Kinds of Policies. — An endowment policy is essentially for persons who 
must force themselves to save. It is ah expensive form of insurance, but 
one that affords the young man or woman an incentive for saving, and 
that matures at a time when the individual has, as a result of long 
experience, better opportunities to make profitable investments. This 
policy also has a larger loan value than any other, and this sometimes be- 
comes an advantage to the young person. However, the chief advantage 
of the endowment policy is its incentive to save. 

A limited payment policy^ such as the fvoenty-payment life, appeals 
most directly to those who desire to pay for life insurance only within the 
productive period of their life. This policy should attract the young man 
who is uncertain of an income after a given period, or who does not wish 
insurance premiums to be a burden upon him after middle life. Out of 
the relatively large and certain income of his early productive years he 
pays for his insurance. This policy also appeals to the man of middle 
age who has neglected to purchase life insurance but who wishes to buy 
it and pay for it before he becomes actually old. 

The Annuity 

An annuity is a specific sum of money to be paid yearly to some 
designated person. The one to whom the money is to be paid is termed 
the annuitant. If the payment is to be made every year until the annui- 
tant dies, it is termed a life annuity. For example, a life insurance 
company or other financial institution, in consideration of the payment 
to it of a specified amount, say $ 1000, will enter into a contract to pay 
a designated annuitant a stated sum, say $ 70, on a specified day in every 
year so long as the annuitant continues to live. The latter may live to 
draw his annuity for many years, until he has received in aggregate 
several times the original amount paid by him, or he may die after having 
collected but a single payment. In either case, the contract expires and 
the annuity terminates with the death of the annuitant. 

The amount of the yearly income or annuity which can be purchased 
with $ 1000 will depend, of course, upon the age of the annuitant That 
sum will buy a larger income for the man of seventy than for one of 
fifty-six, for the reason that the former has, on the average, a much 
shorter time yet to live. The net cost of an annuity, that is, the net 



THRIFT AND INVESTMENT 193 

amount to be paid in one sum, and which is termed the value of the 
annuity, is not a matter of estimate, but, like the life insurance premium, 
is determined by mathematical computation, based upon the mortality 
table. The process is quite as simple as the computation of the single 
premium. 

Many men who insure their lives choose a form of policy under which 
the beneficiary, instead of receiving the full amount of the insurance at 
the death of the insured, is paid an annuity for a period of years or 
throughout life. The amount of annuity paid in such cases is exactly 
equal to the amount that could be bought for a sum equal to the value of 
the policy when it falls due. 

EXAMPLES 

1. A young man at 26 years of age takes out a straight life 
policy of $ 1000, for which he pays $ 17.03 a year as long as 
he lives, and his estate receives $ 1000 at his death. If he 
dies at 46 years of age, how much has he paid in ? How much 
more than he has paid does his estate receive then ? 

2. Another young man at the same age takes out a twenty- 
payment life policy and pays $ 24.85 for twenty years. At 
the end of the twenty years, how much has he paid in ? Does 
he receive anything in return at the end of the twenty years ? 

3. Another form of insurance, called an endowment, is taken 
out by another young man at twenty-six years of age. He 
pays $ 41.94 a year. At the end of twenty years he receives 
$ 1000 from the insurance company. How much has he paid 
in ?. Where is the difference between these two amounts ? 

Exchange 

Bzchange is the process of making payment at a distant place without 
the risk and expense of sending money itself. Funds may be remitted 
from one place to another in the same country in six different ways : 
Postal money order, express money order, telegraphic money order, bank 
draft, check, and si^ht draft. 

The largest amount for which one can obtain a postal money order is 
$ 100. It is drawn up by the postmaster after an application has been 
duly made out. 

An express money order is similar to a postal money order, but may be 



194 VOCATIONAL MATHEMATICS FOR GIRLS 

drawn for any number of dollars at the same rate as the post office order. 
This is issued at express offices. 

A telegraphic money order is an order drawn by a telegraph agent at 
any office, instructing the agent at some other office to pay the person 
named in the message the sum specified. The rates are high, and in 
addition one must pay the actual cost of sending the telegram according 
to distance and number of words. 

A bank draft is an order written by one bank directing another bank 
to pay a specified sum of money to a third party. This order looks much 
like a check. 

A check is an order on a bank to pay the sum named and deduct the 
amount from the deposit of the person who signs the check. 

A sight dj'aft is an order on a debtor to pay to a bank the sum named 
by the creditor who signs the draft. 

Foreign exchange is a system for transmitting money to another country. 
By this means the people of different countries may pay their debts. 

The most common methods of foreign exchange for an ordinary 
traveler are letters of credit or travelers' cheques. 

A letter of credit is a circular letter issued by a banking house to a 
person who desires to travel abroad. The letter directs certain banks in 
foreign countries to furnish the traveler such sums as he may require up 
to the amount named in the letter. 

Fees For Money Orders 

Domestic Bates 

When payable in Bahamas, Bermuda, British Guiana, British Hon- 
duras, Canada, Canal Zone, Cuba, Martinique, Mexico, Newfoundland, 
The PJiilippine Islands, The United States Postal Agency at Shanghai 
(China), and certain islands in the West Indies, listed in the register of 
money order offices. 

For Orders from 

$00.01 to $2.50 Scents 

From $ 2.51 to $ 5 5 cents 

From $ 5.01 to $ 10 8 cents 

From $10.01 to $20 10 cents 

From $ 20.01 to $ 30 12 cents 

From $30.01 to $40 15 cents 

From $40.01 to $60 18 cents 

From $ 50.01 to $ 60 20 cents 

From $60.01 to $76 25 cents 

From $ 75.01 to $ 100 30 cents 



THRIFT AND INVESTMENT 195 

International Bates 

When payable in Asia, Austria, Belgium, Bolivia, Chile, Costa Rica, 
Denmark, Egypt, France, Germany, Great Britain and Ireland, Greece, 
Honduras, Hongkong, Hungary, Italy, Japan, Liberia, Luxemburg, 
Netherlands, New South Wales, New Zealand, Norway, Peru, Portugal, 
Queensland, Russia, Salvador, South Australia, Sweden, Switzerland, 
Tasmania, Union of South Africa, Uruguay, and Victoria. 

For Orders from 

$00.01 to 310 10 cents 

From S 10.01 to $20 20 cents 

From $20.01 to $30 30 cents 

From $30.01 to $40 40 cents 

From $40.01 to $50 60 cents 

From $60.01 to $60 60 cents 

From $ 60.01 to $ 70 70 cents 

From $70.01 to $80 80 cents 

From $80.01 to $90 90 cents 

From $90.01 to $100 • . • 1 dollar 

Rates for Honey Transferred by Telegraph 

The Western Union charges for the transfer of money by telegraph to 
its offices in the United Stales the following : 

First: For $ 25.00 or less 25 cents 

$ 25.01 to $ 60.00 36 cents 

$50.01 to $ 75.00 60 cents 

$ 75.01 to $ 100.00 85 cents 

For amounts above $ 100.00 add (to the $ 100.00 rate) 25 cents per hundred 
(or any part of $ 100.00) up to $ 3000.00. 

For amounts above $ 3000.00 add (to the $ 3000.00 rate) 20 cents per hundred 
(or any part of $ 100.00). 

Second : To the above charges are to be added the tolls for a fifteen word 
message from the office of deposit to the office of payment. 

Express rates are the same as postal rates. 

EXAMPLES 

1. A young woman in California desires to send $ 20 to her 
mother in Maine. What is the most economical way to send 
it, and what will it cost ? 

2. A young lady, traveling in this country, finds that she 



196 VOCATIONAL MATHEMATICS FOR GIRLS 

needs money immediately. What is the quickest and most 
economical way for her to obtain $ 275 from her brother who 
lives 1000. miles distant ? 

3. A merchant in Boston buys a bank draft of $ 3480 for 
Chicago. The bank charges | of 1 % for exchange. How 
much must he pay the bank ? 

4. A domestic in this country sends to her mother in Ireland 
5 pounds for a Christmas present. What will it cost her, if 
$ 4.865 = £ 1 ? A commission of ^ of 1 % is charged. 

Claims 

If a person traveling by boat, electric or steam railway is injured by an 
accident which is the fault of the company, it is bound to repair the finan* 
cial loss. The company is not responsible for the carelessness of passen- 
gers or for the action of the elements. When an accident occurs, the 
injured persons are interviewed by a claim agent, whom all large com- 
panies employ, and he offers to settle with you for a certain amount. If 
you are not satisfied with this amount, you may put in your claim and 
the case goes to court, where you may lose or win according to the decision 
of the jury. When a wreck occurs on a railroad, a claim agent and a 
doctor are brought to the scene as soon as possible. They take the name 
and address of each person in the accident and try to settle the case at 
once, because it is expensive to go to court and the newspaper notoriety 
injures the reputation of the company. If you are not seriously hurt, the 
claim agent tries to persuade you to sign a paper which relieves the Com- 
pany from any responsibility forever after. For instance, in a collision 
you seem to be only shaken up, not injured. The claim agent perhaps 
offers to pay you 1 26. You think that is an easy way to get $ 25, so you 
take it, but in turn you must sign a paper which states that the company 
has settled in full with you for any claim that you may have against it for 
that accident. Now it may prove later that you have an internal injury 
which you did not realize at the time, and that an operation costing $ 600 
is necessary. Can you compel the company to pay the bill ? People 
who are not hurt at all in an accident and to whom the claim agent offers 
nothing are also asked to sign a paper relieving the company from all 
responsibility. Do not sign such a paper. The company cannot compel 
you to, you gain nothing by it, and may lose much if it proves later that 
you are internally injured. 



THRIFT AND INVESTMENT 197 

EXAMPLES 

1. A woman was riding in an electric car that collided with 
another. She was cut with flying glass and was obliged to hire 
a servant for four weeks at $8. Doctor's bills amounted to 
$24.50, medicine, etc., $8.75. She settled at the time of the 
accident for $50. Did she lose or gain ? 

2. A man working in a mill was injured in an elevator acci- 
dent. The insurance company paid his wages and medical 
bills for 8 weeks at $13.50 per week. A year later he was out 
of work for three weeks for the same injury and did not receive 
any compensation. Would it have been better for him to have 
settled for $100 at the beginning ? 

3. A saleslady tripped on a staircase and sprained her ankle. 
She was out of work for two weeks and two days at $8.75 per 
week. Her medical supplies cost $9.75. She settled for $45. 
How much did she gain ? 



PART m — DRESSMAKING AND MILLINERY 

CHAPTER IX 
PROBLEMS IN DRESSMAKING 

The yardstick is much used for measuring cloth, carpets, 
and fabrics. The yardstick is divided into halves, quarters, 
and eighths. Dressmakers should know the fractional equiva- 
lents of yards in inches and the fractional equivalents of 
dollars in cents. 

It is wise to buy to the nearest eighth of a yard unless the 
cost per yard is so small that an eighth would cost as much as 
a quarter. 

EXAMPLES 

1. Give the equivalent in inches of the following : 
(a) 1 yd. 

W H yd. 

(c) H yd. 

(d) 2i yd. 

(e) 3f yd. 

2. A piece of cloth is 12 yd. long. How many pieces are 
needed for 16 aprons requiring 1^ yd. each ? 

3. A piece of lawn cloth is 28 yd. long. How many pieces 
are needed for 20 aprons requiring 1| yd. each ? 

4. Give the value in cents of the following fractions of a 
dollar : 



(/) 4| yd. 


(*) i yd. 


(9) H yd. 


(0 i yd. 


w n yd. 


(m) tV yd. 


(t) If yd. 


(n) ^Jjyd. 


U) i yd. 


(0) A yd. 



(«)il 


(«)il 


(0 A 


(m) ^^ 


(P) 1 


(/•)! 


(j)i 


(«) i\ 


Wi 


(9) i 


W i\ 


(o)i 


WH 


W A 


iO^ 


(Jp)i 



198 



ARITHMETIC FOR DRESSMAKERS 



199 



5. If 16" is cut from 1| yd. of cloth, how much remains ? 

6. If 1^ of a yard of lawn is cut from a piece 40 in. long, 
what part of a yard is left ? 

7. I bought 9| yd. of silk for a dress. If If yd. remained, 
how much was used ? 

« 

8. A towel is 33 inches long and and a dishcloth 13 inches. 

(a) Find the length of both. (Allow |^" for each hem.) 

(b) Find the number of yards used for both. 

(c) Find the number of inches used by a class of 24. 

(d) Find the number of yards used by a class of 24. 

(e) Find the cost per pupil at 6 cts. per yard. 

(J) Find the cost for a class of 24 at 6 cts. per yard. 

9. If it took 72 yards of material for a dishcloth and towel 
for two classes of 24 (48 in all), find the amount used by each 
pupil. 

10. Jf 45| yards of material were used for a class of 42, find 
the amount used by each pupil. 

11. (a) Reduce 75 inches to yards, {b) Find the number of 
inches in 3^ yards, (c) From 2f yards cut 40 inches. 



Tucks 

A tuck is a fold in the cloth 
for the purpose of shortening 
garments or for trimming or dec- 
oration. A tuck takes up twice 
its own depth ; that is, a 1" tuck 
takes up 2" of cloth. 

EXAMPLES 

1. Before tucking, a piece of 
goods was I yd. long ; after tuck- 
ing, it was f yd. long. How 
many y tucks were made ? 




Mbasurinq fob Tucks from 
Fold to Fold 



200 VOCATIONAL MATHEMATICS FOR GIRLS 

2. How mucli lawn is taken up in 3 groups of tucks, the 
first group containing 6 one-inch tucks, the second group 6 one- 
half-inch tucks, and the third group 12 one-eighth-inch tucks ? 

3. A piece of muslin 29 inches wide was tucked and when 
returned to the teacher was only 14 inches wide. How many 
\" tucks were made in it ? 

4. Before tucking, a piece of goods was f yd. long ; after 
tucking, it was ^ yd. long. How many ^" tucks were made ? 



Hem 




Hem Turned 



A hem on a piece of cloth is 
an edge turned over to form a 
border or finish. In making a 
hem an edge must always be 
turned to prevent fraying; ex- 
cept for very heavy or very 
loosely woven cloth this is usu- 
ally y. For an inch hem you 
would have to allow 1\", 



EXAMPLES 

1. I wish to put three y tucks in a skirt/ which is to be 40" 
long. How long must the skirt be cut to allow for the tucks 
and ^" hem ? 

2. My cloth for a ruffle is 10" deep. It is to have a ly 
hem, and five \" tucks. How long will it be when finished ? 

3. If. a girl can hem 2\ inches in five minutes, how long 
will she take to hem 2 yards ? 

4. At the rate of | of an inch per minute, how long will it 
take a girl to hem 2 yards ? 10 yards ? 

5. At the rate of 5|^ inches per ten minutes, how long will 
it take to hem 3^^ yards ? 



ARITHMETIC FOR DRESSMAKERS 201 

6. A girl can hem 3 inches in five minutes. How much in 
an hour ? 

7. How long will she take to hem 90 inches ? 

8. At 6 cents per hour, how much can she earn by hemming 
190 inches ? 

9. How long will it take a girl to hem 2\ yards if she can 
hem 5^ inches in ten minutes ? 

Ruffle 

A ruffle is a strip of cloth gathered in narrow folds on one 
edge and used for the trimming or decoration. Different pro- 
portions of material are allowed 
according to the use to which it 
is to be put. For the ordinary 
ruffle at the bottom of a skirt, 
drawers, apron, etc., allow once and 
a half. Once and a quarter is Rufplb 

enough to allow for trimming for 

a corset cover or for other places where only a scant ruffle is 
desirable. A plaiting requires three times the amount. 

EXAMPLES 

1. How much hamburg would you buy to make a ruffle for 
a petticoat which measures 3 yd. around, if once and a half 
the width is necessary for fullness ? 

2. How much lace 2^ inches wide would you buy to have 
plaited for sleeve finish, if the sleeve measures 8 inches around 
the wrist — allowing three times the amount for plaiting ? 

3. A skirt measuring S\ yd. around is to have two 5-inch 
ruffles of organdie flouncing. Allowing twice the width of 
skirt for lower ruffle, and once and three quarters for the 
upper one, how much flouncing would you buy, and what 
would be the cost at $ .87^ per yard for organdie ? 




202 VOCATIONAL MATHEMATICS FOR GIRLS 

4. How deep must a ruffle be cut to be 6" deep when 
finished, if there is to be a 1^" hem on the bottom and three 
^" tucks above the hem ? 

5. How deep a ruffle can be made from a strip of lawn 16" 
deep, if a 2" hem is on the bottom and above it three J" tucks ? 

6. How many yards of cloth 36" wide 
are needed for S^ yd. of ruffling which is 
to be cut 6" deep? 

7. How many widths for ruffling can be 

Ivpv^v-::^ cut from 4 yd. of lawn 36" wide, if the 
t^^Vp;;'^/-;;^^^ ^^^^ .g g„ finisiie^i^ ^j^^ i^ a |" hem 

and five y tucks ? 

Note. — Allowance must be made for joining a ruffle to a skirt, usu- 
ally i". 

8. How deep must a ruffle be cut to be 6" deep when 
finished, if there is to be a 1^" hem on the bottom, and 
five y tucks above the hem ? 

9. How many yards of ruffling are needed for a petticoat 
2 J yd. around the bottom ? 

EXAMPLES m FINDING COST OP MATERIALS 

1. What is the cost of hamburg and insertion for one pair 

of drawers ? 

32 in. around each leg. 

Hamburg at 16 cents a yard. 

Insertion at 15 cents a yard. 

2. What is the cost of hamburg and insertion for one pair 

of drawers ? 

36 in. around each leg. 

Hamburg at 18^ cents a yard. 

Insertion at 16} cents a yard. 

3. What is the cost of hamburg and insertion for a petticoat ? 

6 yd. around. 

Hamburg at 25 cents a yard. 

Insertion at 15 cents a yard. 



ARITHMETIC FOR DRESSMAKERS 203 

4. What is the cost of hamburg and insertion for a petti- 
coat? 

SJ yd. around. 

Hamburg at 27^ cents a yard. 
Insertion at 16} cents a yard. 

5. What is the cost of trimming for a corset cover ? 

38 in. around top. 

13 in. around armhole. 

Lace at 10 cents a yard. 

6. What is the cost of trimming for a corset cover ? 

41 in. around top. 

13} in. around armhole. 

Lace at 12} cents a yard. 

7. What is the cost of lace for neck and sleeves at 12}^ cents 

a yard ? 

Neck, 13 in., sleeves, 8 in. 

8. What is the cost of lace for neck and sleeves at 16 cents 

a yard ? 

Neck, 14 in., sleeves, 8} in. 

9. What is the cost of a petticoat requiring 2^ yd. long- 
cloth at 12 j^ cents a yard, and 2\ yd. hamburg at 16}^ cents 
a yard? 

10. What is the cost of a petticoat requiring 2f yd. long- 
cloth at 13} cents a yard, and 2^ yd. hamburg at 15^ cents a 
yard ? 

11. What is the cost of a nightdress requiring S^ yd. of 
cambric at 25 cents a yard and 3 skeins of D. M. C. em- 
broidery cotton which sells at 5 cents for 2 skeins, and 1}- yd. 
|-inch ribbon at 9 cents a yard ? 

12. What is the cost of the following material for a corset 

cover ? 

1} yd. longcloth at 15 cents a yard. 
2\ yd; hamburg at 8 cents a yard. 
6 buttons at 12} cents a dozen. 



204 VOCATIONAL MATHEMATICS FOR GIRLS 

13. What is the cost of the following material for a skirt ? 

7 yd. silk at 79 cents a yard. 
1} yd. lining at 35 cents a yard. 

14. What is the cost of the following material for a corset 

cover ? 

1} yd. longcloth at 16 cents a yard. 
2^ yd. hamburg at 8} cents a yard. 
4 buttons at 12^ cents a dozen. 

15. What is the cost of the following material for a corset 

cover ? 

1} yd. longcloth at 16| cents a yard. 
2} yd. hamburg at 25| cents a yard. 
2| yd. insertion at 19} cents a yard. 
4 buttons at 15 cents a dozen. 

16. What is the cost of the following material for a corset 

cover ? 

1} yd. longcloth at 14} cents a yard. 
1} yd. hamburg at 17} cents a yard. 

17. What is the cost of the following material for a skirt ? 

7} yd. silk at 83} cents a yard. 
1} yd. lining at 37} cents a yard. 

18. Find the cost of a corset cover that requires 

1 yd. cambric at 12} cents a yard, 
f yd. bias binding at 2 cents a yard. 
} doz. buttons at 12 cents a dozen. 
1} yd. lace at 10 cents a yard. 
} spool thread at 5 cents a spool. 

19. Find the cost of an apron that requires 

1 yd. lawn at 12} cents a yard. 
2} yd. lace at 10 cents a yard. 
} spool thread at 5 cents a spool. 



ARITHMETIC FOR DRESSMAKERS 205 

20. Find the cost of a nightgown containing 

3} yd. cambric at 12} cents a yard. 

2 yd. lace at 5 cents a yard. 

3 yd. ribbon at 3 cents a yard. 

i spool thread at 5 cents a spool. 

21. Find the cost of drawers containing 

2 yd. cambric at 12} cents a yard. 

1} yd. finishing braid at 5 cents a yard. 

1 spool thread at 5 cents a spool. 

2 buttons at 10 cents a dozen. 

22. What is the cost of a waist made of the following ? 

2f yd. shirting, 32 inches wide, at 23 cents a yard. 
Sewing cotton, buttons, and pattern, 25 cents. 

23. What is the cost of 7^ yd. chiffon faille, 36 inches wide, 
at $ 1.49 a yard ? 

24. How many yards of ruffling are needed for 1 dozen aprons 
if each apron is one yard wide and half the width of the apron 
is added for fullness ? 

25. How many pieces of lawn-36 inches wide are needed for 
the ruffle for one apron ? For eight aprons ? 

26. A skirt measures 2^ yards around the bottom. How 
much material is needed for ruffling if the material is one yard 
wide and ruffle is to be cut 7 inches wide ? 

27. How deep would you cut a cambric ruffle that when 
finished will measure 12^", including the hamburg edge which 
measures 4", two clusters of 6 tucks ^" deep, and allowing 1' 
for making? 

28. Find the cost of a poplin suit made of the following : 

Silk poplin, 40 inches wide : 5} yards, at $ 1.79 a yard. 
Satin facing for collar, revers, and cuffs, 21 inches wide : 1 yard, at 
11.26 a yard. 

Coat lining, 36 inches wide : 2J yards, at $ 1.60 a yard. 
Buttons, braid, sewing silk, two patterns, $ .64. 



206 VOCATIONAL MATHEMATICS FOR GlRLS 

Cloths of Different Widths 

There are in common use cloths of several different widths 
and at various prices. It is often important to know which is 
the most economical cloth to buy. This may be calculated by 
finding the cost per square yard, 36" by 36". To illustrate : 
which is less expensive, broadcloth 56" wide, at $2.25 per 
yard, or 50" wide, at $1.75 per yard ? 

?^JiM X 2.26 = 9 1.44^ per square yard. 
66 X 3^ 

^^^ X 1.76 = $ 1.26 per square yard. 



EXAMPLES 

Find the cost per square yard and the relative economy in 
purchasing : 

(a) Prunella, 46" wide, at $ 1.60 a yard. 
Prunella, 44'' wide, at $ 1.36 a yard. 

(6) Serge, 64'' wide, at $ 1.26 a yard. 
Poplin, 42" wide, at $ 1.00 a yard. 

(c) Serge, 42" wide, at 49 cents a yard. 
Serge, 37" wide, at 39 cents a yard. 

(d) Shepherd check, 64" wide, at $ 1.76 a yard. 
Shepherd check, 62" wide, at $ 1.60 a yard. 
Shepherd check, 42" wide, at $ 1.00 a yard. 

(e) Taffeta, 19" wide, at 89 cents a yard. 
TafEeta, 36" wide, at ^ 1.26 a yard. 

(/) Cashmere, 42" wide, at § 1.00 a yard. 
Nuns veiling 44" wide, at 76 cents a yard. 

(g) Cheviot, 67" wide, at $ 1.60 a yard. 
Diagonal, 64" wide, at ^2.00 a yard. 

(A) Messaline, 26 " wide, at 69 cents a yard. 
Messaline, 36 " wide, at $1.26 a yard. 



ARITHMETIC FOR DRESSMAKERS 207 

PROBLEMS IN TRADE DISCOUNT 

Illustrative Example. — A dressmaker bought $ 125 worth 
of material, receiving 6 % discount for cash. She sold the 
material for 20 % more than the original price. What was the 
gain? 

Solution. — $ 126.00 original price $126.00 

.06 7.50 

$ 7.50 discount $ 117.50 price paid for material. 

6 1^126 original cost $ 150.00 selling price 

$25 20 % gain 117.50 p rice paid 

$ 160 selling price $ 32.50 gain. Ans, 

EXAMPLES 

1. A dressmaker bought 25 yd. of hamburg at 50 cents per 
yard, receiving 6 % discount for cash. She then sold the ham- 
burg to her custonxers at 60 cents per yard. What was the 
price paid for hamburg, and what per cent did she make ? 

2. A dressmaker bought $ 325 worth of goods, receiving 6 % 
discount for cash. She sold the goods for 25 % more than the 
original price. What was the gain ? 

3. A milliner bought $200 worth of ribbons, velvets, and 
flowers, receiving 5 % discount for cash. She then sold the 
materials for 30 % more than the original price. What was 
the gain ? 

REVIEW EXAMPLES 

1. A dressmaker bought 30 yd. of silk at $ 1.25 per yard. 
She received a discount of 10 %. She sold the silk for $ 1.89 
per yard. How much did she gain on the 30 yards ? 

2. A merchant bought 50 yd. of lawn at 12^ cents a yard, 
and received a discount of 6 % for cash. How much did the 
lawn cost ? 

3. A piece of crinoline containing 45 yd. was bought for 
$ 18. It was made into dress models of 5 yd. each. What was 
the cost of the crinoline in each model ? 



208 VOCATIONAL MATHEMATICS FOR GIRLS 

4. A dressmaker bought $ 175 worth of silk, receiving 6 % 
discount for cash. She sold the silk for 25% more than the 
original price. What was the gain per cent ? 

5. A dressmaker bought 24| yd. of silk, at $ 1.10 per yard. 
From it she made three dresses, and had 13f yd. left. How 
much did the silk for one dress cost ? 

6. Find the cost of 36 yd. of Valenciennes lace at 7^ cents 
a yard, 12 yd. of insertion at 6J cents a yard, and 12 yd. of 
beading at 7 cents a yard. What is the net cost, when 2 % 
discount is given ? 

7. How many lingerie shirtwaists, each containing 2| yd., 
can be made from 49 yd, of batiste? What is the cost of 
material for one waist, if the whole piece cost $ 9.80, less 5 % 
discount ? 

8. A dressmaker bought 2^ yd. of crepe at 29 cents a yard, 
for a shirtwaist, 3 yd. of beading at 12^ cents a yard, 6 crochet 
buttons at 35 cents a dozen. What did the material for the 
waist cost ? 

9. A woman bought 9^ yd. of foulard silk, at $ 1.10 a yard, 
for a dress. If yd. of net at $ 1.50 a yard, and f yd. of plain 
silk at $ 1.25 a yard. What was the cost of material ? 

10. A dressmaker bought 50 yd. of taffeta silk for $ 45.00. 
She sold 8^ yd. to one customer for $ 1.25 a yard, 15^ yd. at 
$ 1.00 a yard to another customer, and the remainder at cost. 
What did she gain on the entire piece ? What was the gain 
per cent ? 

11. Two and one-half yards of cloth cost $ 2.75. What was 
the price per yard ? 

12. A dressmaker bought 50 yd. of handmade lace abroad 
and paid $ 75 for it. She paid 60 % duty on the lace and sold 
it at a gain of 33^ % . What was the selling price per yard ? 



ARITHMETIC FOR DRESSMAKERS 209 

13. A dressmaker bought 20 yd. of foulard silk at 90 cents 
a yard. She received 6 % discount. She sold it for lOJ % 
more than the original price. How much did she gain on the 
sale ? What per cent did she gain ? 

14. A dressmaker bought the following materials for a 
customer : 4^ yd, of broadcloth at % 2.75 a yard, 6^ yd. of silk 
at % 3 J5 a yard, 2\ yd. of trimming at $ 2.50 a yard. She 
received a dressmaker's discount of 6 %, and 5 % discount for 
cash payment. What did she pay for the materials? She 
charged the retail price for them. How much did she gain ? 
What per cent ? 

15. A dressmaker bought a 7^yd. remnant of broadcloth 
for $22.50. She sold 6 yd. to a customer at $3.50 a yard, but 
the remainder could not be sold. Did she gain or lose ? What 
per cent ? 

16. A dressmaker bought in France three 15-yd. pieces of 
dress silk at 25^ cents a yard. After paying 60% duty 
on them, she sold two pieces to one customer at 48 % gain, and 
the third piece to another customer at 35 % gain. What was 
the gain on the three pieces ? 

. 17. A dressmaker furnished the materials for a lingerie 
dress and charged $25 for it. For the materials she paid 
the following : 10 yd. of dimity at 45 cents a yard, \2\ yd. 
Cluny insertion at 25 cents a yard, findings, $2. If she 
charged $12 for making, how much did she gain on the 
material ? Make a bill for the same and receipt it. 

18. The materials for a dress cost a dressmaker $14.50. 
She sold them for 10 % more than cost and charged $ 15 for 
making. She paid her helper 20% of the amount received. 
What was the gain per cent ? 

19. If it takes 6^ yards of cloth 52 inches wide to make 
a dress, how many yards of cloth 22 inches wide will be 
needed to make the same dress ? 



210 VOCATIONAL MATHEMATICS FOR GIRLS 

20. A dressmaker agreed to make a dress for a customer for 
$25. She paid 2 assistants $1.25 a day each for 3^ days 
of work. The dress was returned for alterations, and the 
assistants were paid for one more day's work. How much did 
the dressmaker receive for her own work ? 

21. A dressmaker bought $1.50 worth of silk, receiving 
6 % discount for cash. She sold the silk for 40 % more than 
the original price. What was the gain per cent ? 

22. A dressmaker has an order for three summer dresses, 
for which 31J yd. of batiste are needed. She can buy three 
remnants of 10^ yd. each for 25 cents a yard, or she can buy a 
piece of 35 yd. for 25 cents a yard and receive 4 ^ discount 
for cash. Which is the better plan ? 

23. (a) How many inches in | yd. ? (b) How many inches 
in \ yd. ? (c) How many inches in | yd. ? (d) How many 
inches in | yd. ? (e) How many inches in | yd. ? (/) How 
many inches in ^ yd. ? (g) How many inches in ^ yd. ? 

24. Find the cost of each of the above lengths in lace at 
$ .12| a yard. 

25. Find the cost of 4^ yd. of lace at $1.95 per piece (ouq 
piece = 12 yd.). 

26. A dressmaker bought 2 pieces of white lining taffeta, 
one piece 42 yd. and another 48|^ yd., at $ .42^ a yard. What 
was the total cost ? 

27. A piece of crinoline containing 42^ yd. that cost $ 1.70 
a yard was made into dress models of 8^ yd. each. What 
was the cost of the crinoline in each model? 

28. What is the cost of a child's petticoat containing : 

2 J yd. longcloth at 15 cents a yard, 
1} yd. hamburg at 19 cents a yard, 
li yd. insertion at 15 cents a yard ? 



ARITHMETIC FOR DRESSMAKERS 211 

29. What is the cost of two petticoats requiring for one : 

2} yd. longcloth at 19 cents a yard, 
8 yd. hamburg at 25 cents a yard, 
2^ yd. insertion at 19 cents a yard ? 

30. What is the cost of a petticoat requiring : 

8 yd. longcloth at 12^ cents a yard, 
8J yd. hamburg at 17 cents a yard ? 

31. What is the total cost of the following ? 

Wedding gloves, J| 2.75. 

Slippers and stockings, $5.00. 

Six undervests, at 19 cents each. 

Six pairs of stockings, at 38} cents a pair. 

Two pairs of shoes, at $5.00 a pair. 

One pair of rubbers, 75 cents. 

One pair long silk gloves, $2.00. 

One pair of long lisle gloves, $ 1.00. 

Two pair^ of short silk gloves, $ 1.00. 

Veils and handkerchiefs, $5.00. 

Two hats, $ 10.00. 

Corsets, $3.00. 

Wedding veil of 3 yards of tulle, 2 yards wide, at 89 cents a yard. 

32. What is the cost of the following material for a top 
coat? 

Cotton corduroy, 32 inches wide : 4 J yards at 75 cents a yard. 
Lining, 36 inches wide : 4 J yards at $ 1.50 a yard. 
Buttons, sewing silk, pattern, 27 cents. 
Velvet for collar facing, J yard, at $1.50 a yard. 

33. What is the cost of the following dressmaking supplies ? 

} yard of China silk, 27 inches wide, at 49 cents a yard (for the lining). 

1} yard of mousseline de soie interlining 40 inches wide, at 80 cents 
a yard. 

I yard of all-over lace 86 inches wide, at $ 1.48 for front and lower 
back. 

i yard of organdie at $1.00, 32 or more inches wide, for collar and vest. 

Sewing silk, hooks and eyes, pattern, at 32 cents. 



212 VOCATIONAL MATHEMATICS FOR GIRLS 

34. What is the cost of the following ? 

Cotton gabardine, 36 inches wide : 5} yards at 39 cents a yard. 
Sewing cotton, braid, buttons, pattern, at 35 cents. 

35. Which of the following fabrics is the most economical 

to buy? 

Crepe meteor, 44" wide, at 3 3.26 a yard. 
Faille Fran9aise, 42" wide, at $3.00. 
Charmeuse, 40'' wide, at $2.25. 
Louisine, 38" wide, at $2.00. 
Armure, 20" wide, at $1.50. 
Satin duchesse, 21" wide, at $1.25. 

MILLINER7 PROBLEMS 

1. What would a hat cost with the following trimmings ? 

IJ yd. velvet, at $2.50 a yard. 

\ yd. satin for facing, at $ 1.98 a yard. 

2 feathers, at $ 5.50 each. 

Frame and work, at $ 2.50. 

Make out a bill. (See lesson on Invoice, Chapter XI, page 
243.) 

2. A leghorn hat cost $6.98. Four bunches of fadeless 
roses at $2.98, 2 bunches of foliage at $.98, and 1^ yd. of 
velvet ribbon at $ 1.49 were used for trimming. The milliner 
charged 76 cents for her work. How much did the hat cost ?• 

3. A milliner used the following trimmings on a child's 

bonnet: 

1 piece straw braid, at $1.49. 

2 yd. maline, at 25 cents a yard. 

4 bunches flowers, at 69 cents each. 
4 bunches foliage, at 49 cents each. 
Work, at $2.00. 

What was the total cost of the hat ? Make out a bill and 
receipt it. 



ARITHMETIC FOR MILLINERS 213 

4. An old lady's bonnet was trimmed with the following : 

3 yd. silk, at $ 1.50 a yard. 

1 piece of jet, $3.00. 

2 small aigrettes, at $ 1.50 each. 
Ties, 76 cents. 

Work, $1.60. 

How much did the finished bonnet cost ? 

5. What was the total cost of a hat with the following trim- 
mings? 

2 pieces straw braid, at $ 2.50 each. 

2 yd. velvet ribbon, at 98 cents a yard. 
5 flowers, at 59 cents. 

4 foliage, at 49 cents. 
Frame and work, at $ 2.60. 

6. A milliner charged $2.00 for renovating an old hat. 
She used 2 yd. satin at $ 1.60 a yard and charged $ 2.25 for 
an ornament. . How much did the hat cost ? 

7. The following trimmings were used on a child's hat : 

3 yd. velvet, at $ 1.60 a yard. 
8 yd. lace, at 15 cents a yard. 

2 bunches buds, at 49 cents a bunch. 
Work, $2.00. 

How much did the hat cost ? 

8. A milliner charged $ 6.00 for renovating three feathers, 
$2.60 for a fancy band, $4.75 for a hat, and 75 cents for 
work. How much did the customer pay for her hat ? 

9. A lady bought a hat with the following trimmings : 

2 yd. satin, at $ 1.76 a yard. 
2 bunches grapes, at $ 1.59 a bunch. 
2 J yd. ribbon, at 69 cents a yard. 
Work, 75 cents. 

How much did the hat cost ? 



214 VOCATIONAL MATHEMATICS FOR GIRLS 

10. What would a hat cost with the following trimmings ? 

2 pieces straw braid, at $ 1.98 each. 

3 yd. ribbon, at 89 cents a yard. 
Fancy feather, $6,98. 

Frame and work, $ 2.50. 

11. Estimate the cost of a hat using the following materials : 

2^ yd. plush, at $ 2.25 a yard. 
2 yd. ribbon, at 26 cents a yard, 
f yd. buckram, at 25 cents a yard. 
I yd. tarlatan, at 10 cents a yard. 
1 band fur, 75 cents. 
Foliage, 10 cents. 
Labor, $2.00. 

12. If the true bias from selvedge to selvedge is about ^ 
longer than the width of the goods, how many bias strips must 
be cut from velvet 18" wide in order to have a three-yard bias 
strip ? 

13. The edge of a hat measures 

46 inches in circumference; the 

velvet is 16 inches wide. How 

many bias strips of velvet would 

it take to fit the brim? 

Wire Hat Frame ^^ ^^^^ amount of velvet would 

be needed to cover brim if each strip cut measured f of a yard 

along the selvedge ? 

15. Give the number of 13^-in. strips that can be cut from 
3^ yards of material ; also the number of inches of waste. 

16. How many 22^in. scrips can be cut from 2^ yd. of 
material ? 

17. What length bias strip can be made from 1^ yd. of silk, 
each strip 1 yd. 10 in. long and 1^ in. wide? 

18. How many six-petal roses can be made from 1 ysird of 
velvet 18 inches wide, each petal cut 3 inches square ? 




ARITHMETIC FOR MILLINERS 215 

19. Estimate the total cost of roses, if velvet is $ 1.50 a 
yard, centers 18 cents a dozen, sprays 12 cents a dozen, stem- 
ming 6 cents a yard, using ^ of a yard for each flower. 

20. Find the cost of one flower; the cost of ^ of a dozen 
flowers, using the figures given above. 

21. What amount of velvet will be needed to fit a plain-top 
facing and crown of hat, width of brim 6 inches, diameter of 
headsize 7|- inches, diameter of crown 16^ inches, allowing 8^ 
inches on brim for turning over edges ? 

22. If the circumference of the brim measures 56 inches, 
what amount of silk will it take for a shirred facing made of 
silk 22 inohes wide, allowing twice around the hat for fullness, 
and also allowing 1 inch on depth of silk for casings ? 

23. At the wholesale rate of eight frames for one dollar, 
what is the cost of five dozen frames ? of twelve dozen ? 

24. A milliner had 2^ dozen buckram frames at $3.60 a 
dozen. She sold ^ of them at 75 cents each, but the others 
were not sold. Did she gain or lose and what per cent ? 

25. Flowers that were bought at $ 5.50 a dozen bunches 
were sold at 75 cents a bunch. What was the gain on 1^ 
dozen bunches ? 

26. A milliner bought ten rolls of ribbon, ten yards to the 
roll, for $ 8.50. Ten per cent of the ribbon was not salable. 
The remainder was sold at 19 cents a yard. How much was 
the gain ? what per cent ? 

27. A piece of velvet containing twelve yards was bought 
for $28.20 and sold for $2.75 per yard. How much was 
gained on the piece? 

28. A thirty-six yard piece of maline cost $ 7.02 and was 
sold at 29 cents a yard. One yard was lost in cutting. How 
much was gained on the piece ? 



216 VOCATIONAL MATHEMATICS FOR GIRLS 

29. Find cost of a velvet hat requiring 

IJ yd. of velvet, at $ 1.50 a yard. 
} yd. of fur band, at $4.00 a yard. 
1 feather ornament, at $3.00. 
Hat frame, 50 cents. 
Edge wire, 10 cents. 
Taffeta lining, 25 cents. 
Making, $ 2.50. 

30. A milliner charged $ 8.37 for a hat. She paid 37 cents 
for the frame, $ 2.80 for the trimming, and $ 1.60 for labor. 
What was the per cent profit ? 

31. A child's hat of organdie has two ruffles edged with 
Valenciennes lace. The lower ruffle is 3" wide ; the upper ruffle, 

2J". 2f yd. lace edging cost 12^ cents a yard, 
2 yd. of 3" ribbon cost 25 cents a yard, 1^ yd. 
of organdie cost 25 cents a yard, the hat frame 
cost 36 cents, and the lining cost 10 cents. 
Find the total cost. 

32. How much velvet at $2.00 a yard would you buy to 
put a snap binding on a hat that measures 43" around the 
edge ? Should the velvet be bias or straight ? 




CHAPTER X 

CLOTHING 

Since about one oighth of the income in the average working- 
man's family is spent for clothing, this is a very important 
subject. The housewife purchases the linen for the house and 
her own wearing apparel. It is not uncommon for her to have 
considerable to say about the clothing of the men, particularly 
about the underclothing. Therefore she should know some- 
thing about what constitutes a good piece of cloth, and be able 
to make an intelligent selection of the best and most economical 
fabric for a particular purpose. The cheapest is not always 
the best, although it is in some cases. 

All kinds of cloth are made by the interlacing (weaving) of 
the sets of thread (called yarn). The thread running length- 
wise is the strongest and is called the warp. The other thread 
is called thQ filling. Such fabrics as knitted materials and lace 
are made by the interlacing of a single thread. Threads 
(yarn) are made by lengthening and twisting (called spinning) 
short fibers. Since the fibers vary in such qualities as firmness, 
length, curl, and softness, the resulting cloth varies in the 
same way. This is the reason why we have high-grade, medium- 
grade, and low-grade fabrics. 

The principal fabrics are wool, silk, mohair, cotton, and flax 
(linen). 

The consumer is often tempted to buy the cheaper fabrics 
and wonders why there is such a difference in price. This 
difference is due in part to the cost of raw material and in part 
to the care in manufacturing. For example, raw silk costs 
from $1.35 to $5.00 a pound, according to the nature and 

217 



218 VOCATIONAL MATHEMATICS FOR GIRLS 

quality of the silk. The cost of preparing the raw silk aver- 
ages about 65 cents a pound, according to the nature of the 
twist, which is regulated by the kind of cloth into which it is 
to enter. The cost of dyeing varies from 55 cents to $ 1.50 a 
pound. Weavers are paid from 2 to 60 cents a yard for weav- 
ing, the price varying according to the desirability of the cloth. 
When we compare the relative values of similar goods 
produced by different manufacturers, there are a few general 
principles by which good construction can easily be determined. 
The density of a fabric is determined by the number of warp 
yarn and filling yarn to the inch. This is usually determined 
by means of a magnifying glass with a \" opening. To illus- 
trate : If there are 36 threads in the filling and 42 threads in 
the warp to \", what is the density of the cloth to the inch ? 

Solution. — 

36 X 4 = 144 threads in the filling. 

42 X 4 = 168 threads in the warp. 
EXAMPLES 

1. A 25-cent summer undervest (knitted fabric) will outwear 
two of the flimsy 15-cent variety in addition to retaining better 
shape. What is the gain, in wear, over the 15-cent variety ? 

2. A 50-cent undervest will outwear three of the 25-cent 
variety. What is gained by purchasing the 50-cent style ? 

3. A cotton dress for young girls, costing 75 cents ready 
made, will last one season. A similar dress of better material 
costs 94 cents, but will last two seasons. Why is the latter 
the better dress to buy ? What is gained ? 

4. A linen tablecloth (not full bleached) costing $1.04 a 
yard, will last twice as long as a bleached linen at % 1.25 a 
yard. Which is the better investment ? 

5. A sheer stocking at 50 cents will wear just half as long 
as a thicker stocking at 35 cents. What is gained in wear ? 
What kind of stockings should be selected for wear ? 



CLOTHING 219 



SHOES 



Our grandfathers and grandmothers wore handmade shoes, 
and wore them until they had passed their period of usef uhiess. 
At that time the consumption of leather did not equal its pro- 
duction. But, since the appearance of machine-made shoes, 
different styles are placed on the market at different seasons 
to correspond to the change in the style of clothing, and are 
often discarded before they are worn out. Thus far we have 
not been able to utilize cast-off leather as the shoddy mill uses 
cast-off wool and silk. The result is that the demand for 
leather is above the production ; therefore, as in the case of 
textiles, substitutes must be used. In shoe materials there is 
at present an astonishing diversity and variety of leather and 
its substitutes. Every known leather from kid to cowhide is 
used, and such textile fabrics as satins, velvets, and serges 
have rapidly grown in favor, especially in the making of 
women's and children's shoes. Of course, we must bear in 
mind that for wearing qualities there is nothing equal to 
leather. In buying a pair of shoes we should try to combine 
both wearing qualities and simple style as far as possible. 

EXAMPLE 

1. A pair of shoes at $ 1.75 was purchased for a boy. The 
shoes required 80 cents worth of mending in two months. If 
a $3.00 pair were purchased, they would last three times as 
long with 95 cents worth of mending. How much is gained 
by purchasing a $ 3.00 pair of shoes ? 

YARNS 

Worsted Tarns. — All kinds of yarns used in the manufacture 
of cloth are divided into sizes which are based on the relation 
between weight and length. To illustrate : Worsted yams are 
made from combed wools, and the size, technically called the 



220 VOCATIONAL MATHEMATICS FOR GIRLS 



counts, is Itased upon the number of lengths (called hanks') of 

d60 yards required to weigh one pound. 



ROVnjQ OB YABM SCALB8 

These gcalea will weigh one pound by tenths ot graios ot ooe Beyenty-thon- 

Bandch part of one ponnd aToirdapol8, rendering them well adapted for ubb 

in coDnectioD with yarn reels, for the onmberlng of yarn from the weight 

of hank, giving the weight in lentbe of grains to compare with tables. 

ThnB, il one hank weighs one pound, the yam will be number ona 

counts, while if 20 hanks are required for one pound, the yam is the 20's, 

etc. The greater the number of hanks necessary to weigh one pound, the 

higher the counts and the finer the yam. The hank, or 500 yards, is the 

unit of measuretnent for all worsted yams. 

Lenqth for Wobstbd Tabhs 



.0. 


k"l^. 


No. 


PK^'l^. 


No. 


PIB™. 


No. 


fti™. 


1 


660 


6 


2800 


B 


6040 


13 


7280 


2 


1120 


6 


3360 


10 


6600 


14 


7840 


3 


1680 


7 


3820 


11 


6100 


15 


8400 


4 


2240 


8 


4480 


12 


6720 


16 


8060 



Woolen Yams, — In worsted yarna the fibers lie parallel to 
ea«h other, while in woolen yams the fibers are entangled. 



CLOTHING 



221 



This difference is due entirely to the different methods used 
in working up the raw stock. 

In woolen yarna there is a great diversity of systems of grading, Taiy- 
ing according to the districts in which the grading is done. Among the 
many eysteniB are the Engiish sktin, which differs in various parts of Eng- 
land ; the Scotch sjiyn^le; the American rvii; the Philadelphia cut; EUid 
others. In these lessons the run system will be used unless otherwise 
stated. This Is the system used in New England. The run is based upon 
100 yards per ounce, or 1600 yards to the pound. Thus, if 100 yards of 
woolen yarn weigh one ounce, or if 1600 yards weigh one pound, it is 
technically termed a No. 1 run ; and if 1300 yards weigh one ounce, or 4800 
yards weigh one pound, the size will be No. 3 run. The finer the yam, 
or the greater the number of yards necessary 1« weigh one pound, the 
higher tbe run. 



Yarn Rbbi. 
Foi reeling and measuring lengths of cotton, woolen, and worsted yams. 

Lbnqth fob Woolbh Yabns (Run Ststbh) 



No. 


Yabi.« 


No. 


TlBIW 

PRH Ln. 


... 


Yard. 
rH Ld. 


No. 


.K. 


i 


200 


1 


1600 


2 


3200 


8 


4800 


i 


400 


H 


2000 


^ 


3«00 


31 


6200 


i 


800 


1* 


2400 


n 


4000 


H 


5600 


i 


1200 


n 


2800 


2J 


4400 







222 VOCATIONAL MATHEMATICS FOR GIRLS 

Raw Silk Tarns. — For raw silk yarns the table of weights 
is; 

16 drams = 1 ounce 
16 ounces = 1 pound 
266 drams = 1 pound 

The unit of measure for raw silk is 266,000 yards per pound. Thus, if 
1000 yards — one skein — of raw silk weigh one dram, or if 266,000 yards 
weigh one pound, it is known as 1-dram silk, and if 1000 yards weigh 
two drams, the yarn is called 2-dram silk ; hence the following table is 
made: 

1-dram silk = 1000 yards per dram, or 256,000 yards per lb. 
2-dram silk = 1000 yards per 2 drams, or 128,000 yards per lb. 
4-dram silk = 1000 yards per 4 drams, or 64,000 yards per lb. 



Dbahb riB 1000 Takds 


YABD8 PER Pound 


Yards per Ounce 


1 


266,000 


16,000 


U 


204,800 


12,800 


li 


? 


? 


^ 


146,286 


9143 


2 


128,000 


8000 


2J 


113,777 


7111 


2i 


102,400 


6400 


2J 


93,091 


6818 


3 


? 


? 


3J 


78,769 


4923 


3i 


73,143 


4671 



Linen Tarns. — The sizes of linen yarns are based on the lea 
or cuts per pound and the pounds per spindle. A cut is 300 
yards and a spindle 14,000 yards. A continuous thread of 
several cuts is a hank, as a 10-cut hank, which is 10 X 300 = 
3000 yards per hank. The number of cuts per pound, or the 
leas, is the number of the yarn, as 30's, indicating 30 x 300 = 
9000 yards per pound. Eight-pound yarn means that a spindle 
weighs 8 pounds or that the yarn is 6-lea (14,400 -r- 8) -f- 300 = 6. 



CLOTHING 223 

Cotton Tarns. — The sizes of cotton yarns are based upon the 
system of 840 yards to 1 hank. That is, 840 yards of cotton 
yarn weighing 1 pound is called No. 1 counts. 

Spun Silk. — Spun silk yams are graded on the same basis 
as that used for cotton (840 yards per pound), and the same 
rules and calculations that apply to cotton apply also to spun 
silk yams. 

Two or More Ply Yams. — Yams are frequently produced in 
two or more ply ; that is, two or more individual threads are 
twisted together, making a double twist yam. In this case 
the size is given as follows : 

2/30*8 means 2 threads of SO^s counts twisted together, and 8/30*s 
would mean 3 threads, each a 80's counts, twisted together. 

(The figure before the line denotes the number of threads twisted to- 
gether, and the figure following the line the size of each thread.) 

Thus when two threads are twisted together, the resultant 
yam is heavier, and a smaller number of yards are required to 
weigh one pound. 

For example : 30's 'worsted yarn equals 16,800 yd. per lb., but a two- 
ply thread of SO's, expressed 2/30' s, requires only 8400 yards to the pound, 
or is equal to a 15*s ; and a three-ply thread of 30*s would be equal to a 
lO's. 

When a yam is a two-ply, or more than a two-ply, and made 
up of several threads of equal counts, divide the number of the 
single yarn in the required counts by the number of the ply, 
and the result will be the equivalent in a single thread. 

To Find the Weight in Orains of a Given Number of Yards 
of Worsted Yarn of a Known Count 

Example. — Find the weight in grains of 125 yards of 20's 
worsted yams. 

No. I's worsted yam = 560 yards to a lb. 
No. 20'8 worsted yam = 11,200 yards to a lb. 
1 Jb. worsted yam = 7000 grains. 



224 VOCATIONAL MATHEMATICS FOR GIRLS 

125 



11,200 



If 11,200 yards of 20's worsted yarn weigh 7000 grains, then 

of 7000 = -i?5_ X 7000 = — = 78.126 grains. 
11,200 8 * 

Note. — Another method : Multiply the given number of yards by 

7000, and divide the result by the number of yards per pound of the 

given count. 

126 X 7000 = 876,000. 

1 pound 20's= 11,200. 

875,000 -f- 11,200 = 78.126 grains. Ans. 

To Find the Weight in Grains of a Given Number of Yards 
of Cotton Yarn of a Known Count 

Example. — Find the weight in grains of 80 yards of 20's 

cotton yarn. 

No. I's cotton = 840 yards to a lb. 

No. 20's cotton = 16,800 yards to a lb. 

1 lb. = 7000 grains. 

7000 
1 yd. 20's cotton = -^— — grains. 

16,800 

80 yd. 20's cotton = ^525. x 80 = 152 = 33.38 grains. Ans. 
^ 16,800 21 ^ 

It is customary to solve examples that occur in daily practice 

by rule. 

The rule for the preceding example is as follows : 
Multiply the given number of yards by 7000 and divide the 

result by the number of yards per pound of the given count. 

80 X 7000 = 560,000. 
560,000 -5- (20 X 840) = 33.33 grains. Aiis. 

Note. — 7000 is always a multiplier and 840 a divisor. 

To find the weight in ounces of a given number of yards of 
cotton yarn of a known count, multiply the given number of 
yards by 16, and divide the result by the yards per pound of 
the known count. 

To find the weight in pounds of a given number of yards 
of cotton yarn of a known count, divide the given number of 
yards by the yards per pound of the known count. 



CLOTHING 225 

To find the weight in ounces of a given number of yards of 
woolen yam (run system), divide the given number of yards 
by the number of runs, and multiply the quotient by 100. 

Note. — Calculations on the run basis are much simplified, owing to 
the fact that the standard number (1600) is exactly 100 times the number 
of ounces contained in 1 pound.- 

Example. — Find the weight in ounces of 6400 yards of 
5-run woolen yarn. 

6400-^ (6 X 100)= 12.8 oz. Ana, 

To find the weight in pounds of a given number of yards of 
woolen yam (run system) the above calculation may be used, 
and the result divided by 16 will give the weight in pounds. 

To find the weight in grains of a given number of yards of 
woolen yarn (run system), multiply the given number of yards 
by 7000 (the number of grains in > pound) and divide the 
result by the number of yards per pound in the given run, 
and the quotient will be the weight in grains. 

EXAMPLES 

1. How many ounces are tiiere (a) in 6324 grains? (6) in 
34^ pounds ? 

2. How many pounds are there in 9332 grains ? 

3. How many grains are there (a) in 168^ pounds ? (6) in 
2112 ounces ? 

4. Give the lengths per pound of the following worsted 
yarns : (a) 41's ; (6) 55's ; (c) 105's ; {d) 115's ; (e) 93's. 

5. Give the lengths per pound of the following woolen 
yarns (run system): (a) 9^'s ; (h) 6's; (c) 19's ; {d) 17's ; 
(e) H's. 

6. Give the lengths per pound of the following raw silk 
yams : (a) l^'s j (6) 3's ; (c) 3f 's ; (d) 20's ; (e) 28's. 

7. Give the lengths per ounce of the following raw silk 
yams : (a) 4|'s ; (6) 6i 's ; (c) 8's ; (d) 9's ; {e) 14's. 



226 VOCATIONAL MATHEMATICS FOR GIRLS 

a What are the lengths of linen yarns per pound : (a) 8's ; 
(6) 25's ; (c) 32's ; (d) 28's ; (e) 45'8 ? 

9. What are the lengths per pound of the following cotton 
yams : (a) lO's ; (b) 32's ; (c) 54's ; (d) 80's ; (e) 160's ? 

10. What are the lengths per pound of the following spun 
silk yarns : (a) 30's ; (b) 46's ; (c) 38's ; (d) 29's ; (e) 42's ? 

11. Make a table of lengths per ounce of spun silk yams 
from I's to 20's. 

12. Find the weight in grains of 144 inches of 2/20*3 worsted 
yam. 

13. Find the weight in grains of 25 yards of 3/30's worsted 
yarn. 

14. Find the weight in ounces of 24,000 yards of 2/40^8 
cotton yam. 

15. Find the weight m pounds of 2,840,000 yards of 2/60's 
cotton yam. 

16. Find the weight in ounces of 650 yards of l^run woolen 
yarn. 

17. Find the weight in grains of 80 yards of ^run woolen 
yam. . 

18. Find the weight in pounds of 64,000 yards of 5-run 
woolen yarn. 

Solve the following examples, first by analysis and then by 
rule; 

19. Find the weight in grains of 165 yards of 35's worsted. 

20. Find the weight in grains of 212 yards of 40's worsted. 

21. Find the weight in grains of 118 yards of 25's cotton. 

22. Find the weight in grains of 920 yards of 18's cotton. 

23. Find the weight in pounds of 616 yards of 16^'s woolen. 

24. Find the weight in grains of 318 yards of 184's cotton. 

25. Find the weight in grains of 25 yards of 30's linen. 



CLOTHING 227 

26. Find the weight in pounds of 601 yards of 60's spun 
silk. 

27. Find the weight in grains of 119 yards of 118's cotton. 

28. Find the weight in grains of 38 yards of 64's cotton. 

29. Find the weight in grains of 69 yards of 39's worsted. 

30. Find the weight in grains of 74 yards of 40's worsted. 

31. Find the weight in grains of 113 yards of 1^'s woolen. 

32. Find the weight in grains of 147 yards of If 's woolen. 

33. Find the weight in grains of 293 yards of 8's woolen. 

34. Find the weight in grains of 184 yards of 16J's worsted. 

35. Find th^ weight in grains of 91 yards of 44's worsted. 

36. Find the weight in grains of 194 yards of 68's cotton. 

37. Find the weight in pounds of 394 yards of 180's cotton. 

38. Find the weight in pounds of 612 yards of 60's cotton. 

39. Find the weight in grains of 118 yards of 44's linen. 

40. Find the weight in pounds of 315 yg^rds of 32's linen. 

41. Find the weight in grains of 84 yards of 25's worsted. 

42. Find the weight in grains of 112 yards of 20's woolen. 

43. Find the weight in grains of 197 yards of 16's woolen. 

44. Find the weight in grains of 183 yards of 18's cotton. 

45. Find the weight in grains of 134 yards of 28's worsted. 

46. Find the weight in grains of 225 yards of 34's linen. 

47. Find the weight in pounds of 369 yards of 16's spun silk. 

48. Find the weight in pounds of 484 yards of 18's spun silk. 

To Find the Size or the Counts of Cotton Tarn of Known 

Weight and Length 

Example. — Find the size or counts ot 84 yards of cotton 
yam weighing 40 grains. 



228 VOCATIONAL MATHEMATICS FOR GIRLS 

Since the counts are the number of hanks to the pound, 

7000 X 84 = 14,700 yd. in 1 lb. 
40 

14,700 -4- 840 = 17.6 counts. Ans. 

Rule. — Divide 840 by the given number of yards ; divide 
7000 by the quotient obtained ; then divide this result by the 
weight in grains of the given number of yards, and the 
quotient will be the counts. 

840 ^ 84 = 10. 
7000 -^ 10 = 700. 
700 -^ 40 = 17.5 counts. Ans. 

To Find the Run of a Woolen Thread of Known Length 

and Weight 

Example. — If 50 yards of woolen yarn weigh 77.77 grains, 

what is the run ? 

1600 -f- 60 = 32. 
7000 - 32 = 218.76. 
218.76 -^ 77.77 = 2.812-run yarn. Ans, 

Rule. — Divide 1600 (the number of yards per pound of 1- 
run woolen yarn) by the given number of yards ; then divide 
7000 (the grains per pound) by the quotient; divide this 
quotient by the given weight in grains and the result will be 
the run. 

To Find the Weight in Ounces for a Given Number of Yards of 

Worsted Yarn of a Known Count 

Example. — What is the weight in ounces of 12,650 yards of 
30's worsted yarn ? 

12,660 X 16 = 202,400. 
202,400 H- 16,800 = 12.047 oz. Ans, 

Rule. — Multiply the given number of yards by 16, and 
divide the result by the yards per pound of the given count, 
and the quotient will be the weight in ounces. 



CLOTHING 229 

To Find the Weight in Pounds for a Given Number of Yards 
of Worsted Yam of a Known Count 

Example. — Find the weight in pounds of 1,500,800 yards 
of 40's worsted yarn. 

1,600,800 -T- 22,400 = 67 lb. Ans, 

Rule. — Divide the given number of yards by the number 
of yards per pound of the known count, and the quotient will 
be the desired weight. 

EXAMPLES 

1. If 108 inches of cotton yam weigh 1.5 grains, find the 
counts. 

2. Find the size of a woolen thread 72 inches long which 
weighs 2.5 grains. 

3. Find the weight in ounces of 12,650 yards of 2/30's 
worsted yam. 

4. Find the weight in ounces of 12,650 yards of 40's worsted 
yam. 

5. Find the weight in pounds of 1,500,800 yards of 40's 
worsted yarn. 

6. Find the weight in pounds of 789,600 yards of 2/30's 
worsted yam. 

7. What is the weight in pounds of 851,200 yards of 3/60's 
worsted yarn ? 

8. If 33,600 yards of cotton yam weigh 5 pounds, find the 
counts of cotton. 

Buying Yarn, Cotton, Wool, and Rags 

Every fabric is made of yam of definite quality and quan- 
tity. Therefore, it is necessary for every mill man to buy 
yam or fiber of different kinds and grades. Many small mills 
buy cotton, wool, yarn, and rags from brokers who deal in 
these commodities. The prices rise and fall from day to day 



230 VOCATIONAL MATHEMATICS FOR GIRLS 

according to the law of demand and supply. Price lists 
giving the quotations are sent out weekly and sometimes 
daily by agents as the prices of materials rise or fall. The 
following are quotations of different grades of cotton, wool, 
and shoddy, quoted from a market list : 

QUANTITT PBIOS FEB Lb. 

8103 lb. white yam shoddy (best all wool) f 0.485 

8164 lb. white knit stock (best all wool) 366 

2896 lb. pure indigo blue 316 

1110 lb. fine dark merino wool shoddy 226 

410 lb. fine light merino woolen rags 115 

718 lb. cloakings (cotton warp) 02 

872 lb. wool bat rags 035 

96 lb. 2/20's worsted (Bradford) yam 725 

408 lb. 2/40's Australian yam 1.35 

598 lb. 1/50's delaine yam 1.20 

987 lb. 16-cut merino yarn (50 % wool and 50 % shoddy) . . .285 
697 lb. carpet yarn, 60 yd. double reel, wool filling 235 

Find the total cost of the above quantities and grades of 
textiles. 

EXAMPLES 

1. The weight of the fleece on the average sheep is 8 lb. 
Wyoming has at least 4,600,000 sheep ; what is the weight of 
wool raised in a year in this state ? 

2. A colored man picks 155 lb. of cotton a day ; how much 
cotton will he pick in a week (6 days) ? . 

3. The average yield is 558 lb. per acre ; how much cotton 
will be raised on a farm of 165 acres ? 

4. The standard size of a cotton bale in the United States 
is 54 X 27 X 27 inches ; what is the cubical contents of a bale ? 

5. In purchasing cotton an allowance of 4 % is made for 
tare. How much cotton would be paid for in 96 bales, 500 lb. 
to each bale ? 



CLOTHING 231 

6. Broadcloth was first woven in 1641. How many years 
has it been in use ? 

7. The length of "Upland" cotton varies from three- 
fourths to one and one-sixteenth inches. What is the differ- 
ence in length from smallest to largest ? 

a If a sample of 110 lb. of cotton entered a* mill and GS* lb. 
were made into fine yarn, what is the per cent of waste ? 

9. If a yard of buckram weighs 1.8 ounces, how many 
yards to the pound ? 

10. If a calico printing machine turns out 95 fifty-yard 
pieces a day, how many are printed per hour in a ten-hour day ? 

11. If a sample of linen weighing one pound and a half 
absorbs 12 % moisture, what is the weight after absorption ? 

12. A piece of silk weighing 3 lb. 4 oz. is " weighted " 175% ; 
what is the total weight ? 

13. If the textile industry in a certain year pays out 
$ 500,000,000 to 994,875 people, what is the wage per capita ? 

14. How much dyestuff, etc., will be required to dye 5 lb. of 
cotton by the following receipt ? 

6 ^ brown color, afterwards treated with 

1.6 ^ sulphate of copper, 
1,6^0 bichromate of potash, 
8 ^ acetic acid. 

15. How many square yards of cloth weighing 8 oz. per sq. 
yd. may be woven from 1050 lb. of yarn, the loss in waste be- 
ing 5 per cent ? 

16. A piece of union cloth has a warp of 12's cotton and is 
wefted with 30's linen yam, there being the same number of 
threads per inch in both warp and weft ; what percentage of 
cotton and what of linen is there in the cloth ? 

17. A sample of calico 3 in. by 4 in. weighs 30 grains. 
What is the weight in pounds of a 70-yard piece, 36 in. wide ? 



\ 



232 VOCATIONAL MATHEMATICS FOR GIRLS 

18. 4 yd. of a certain cloth contains 2 lb. of worsted at 67 
cents a pound and 1\ lb. of cotton at 18 cents a pound. Each 
is what per cent of the total cost of material ? 

19. A bale of worsted weighing 75 lb. loses 8 oz. in reeling 
off ; what is the per cent of loss ? 

20. If Ex. 19 worsted gains 0.45 lb. to the 75 lb. bale in dye- 
ing, what is the per cent of gain ? 

21. This 75 lb. cost $ 50.25 and it lost 4 oz. in the fulling 
mill, what was the value of the part lost ? 

22. The total loss is what per cent of the original weight ? 
What is its value at 67 cents a pound ? 



PARt IV — THE OFFICE AND THE STORE 

CHAPTER XI 
ARITHICETIC FOR OFFICE ASSISTANTS 

EvEBY office assistant should be quick at figures — that is, 
should be able to add, subtract, multiply, and divide accurately 
and quickly. In order to do this one should practice, addition, 
subtraction, multiplication, and division until all combinations 
are thoroughly mastered. 

An office assistant should make figures neatly so that there 
need be no hesitation or uncertainty in reading them. 

Rapid Calculations 

Add the following columns and check the results. Compare 
the time required for the different examples. 

1. 



27 


2. 37 


3. 471 


4. 668 


5. 1,039 


12 


20 


296 


284 


679 


8 


11 


194 


187 


381 


18 


20 


327 


341 


668 


12 


16 


287 


272 


669 


8 


12 


191 


184 


376 


8 


16 


237 

• 


193 


430 


8. 


9 


194 


166 


360 


7 


12 


169 


166 


336 


11 


16 


247 


232 


479 


12 


13 


194 


180 


374 


2 


3 


27 


26 


62 


12 


17 


263 


240 


493 


11 


14 


241 


212 


463 


12 


20 


366 


367 


722 


12 


14 


244 


222 


466 


8 


11 


93 


79 


172 


10 


16 


208 
233 


213 


421 



234 VOCATIONAL MATHEMATICS FOR GIRLS 



7 


7. 7 


8. 169 


9. 162 


10. 311 


2 


6 


60 


78 


138 


4 


7 


HI 


88 


199 


6 


10 


173 


121 


294 


4 


6 


112 


84 


196 


4 


4 


88 


76 


164 


4 


6 


104 


83 


187 


4 


6 


96 


104 


200 


4 


7 


120 


97 


217 


8 


9 


144 


123 


267 


4 


5 


60 


101 


161 


4 


5 


73 


92 


166 


8 


10 


186 


176 


362 


4 


4 


64 


76 


139 


4 


6 


114 


113 


227 


4 


4 


89 


88 


177 


6 


7 


91 


80 


171 


8 





204 


170 


374 


4 


13 


176 


166 


341 


4 


4 


73 


77 


160 


4 


7 


119 


127 


246 


4 


6 


84 


103 


187 


8 


11 


177 


166 


342 


6 


8 


166 


136 


292 


8 


4 


94 


61 


166 


12 


18 


310 


293 


603 


8 


12 


191 


189 


380 


8 


13 


268 


198 


466 


2 


2 


17 


17 


34 


4 


8 


122 


137 


269 


8 





193 


186 


378 




1 . 


4 


6 


10 




1 


9 


16 


24 




2 


16 


16 


32 




1 


11 


16 


26 




2 


34 


44 


78 




2 


27 


34 


61 




2 


26 


63 


79 




2 


36 


41 


76 




2 


17 


10 


27 




2 


38 


22 


60 



ARITHMETIC FOR OFFICE ASSISTANTS 235 



11. $162.24 


12. $37,000.00 


13. $31.26 


14. $8,627.08 


15. $630.33 


266.46 


300,000.00 


73.70 


2,907.31 


408.32 


277.66 


410,000.00 


2.00 


3,262.68 


399.99 


12,171.44 


82,000.00 


4 26 


8,096.90 


28.00 


17.72 




.89 


9,369.21 


644.15 


6.00 


51,000.00 


31.16 


2,177.30 


18,000.00 


83.16 


40,000.00 


3.20 


8,386.50 


32.86 


23.66 




16.75 


7,229.20 


164.66 


3.18 


34,500.00 


4.61 


8,462.38 




82.35 






3,066.34 


1,768.13 


617.60 


17,000.00 


2,666.76 


6,236.32 


25.00 


1128.13 






6,147.42 


639.24 


36.00 


16,600.00 


3.20 


4,443.88 




2.60 




30.00 


3,386.72 


79.90 


4.00 


6,600.00 




3,927.78 


1,143.00 


289.22 


1,000.00 


29.12 


4,797.46 




266.60 






2,612.00 


727.00 


17.82 


70,500.00 


1.00 


2,476.31 


141.33 


199.87 




33.27 


3,706.00 




2314.76 


10,000.00 


19.09 


6,417.42 


3,091.72 


2.40 


12,500.00 


720.00 


1,574.60 


1,049.96 


9.26 


1,500.00 


28.80 


3,121.97 


166.64 


66.80 


300.00 


96.00 


120.00 




494.03 




3.41 


26,146.93 


1,483.84 


18.00 


800.00 


6.00 


51.397.19 


657.62 


1.66 


50.00 


7.37 


99.56 


1,416.68 


3.16 


100.00 


3.60 


3,606.93 


135.50 


2.65 


200.00 




22,830.14 


208.33 


4,010.92 


250.00 


9.08 


85,706.13 


42.84 


126.46 


300.00 




36,361.19 


362.26 


2.26 




4.60 


39,056.23 


234.47 


162.70 


2,000.00 




30,000.00 


31.60 


10.26 




36.84 


179,346.77 


49.76 


3.62 


1,000.00 




3,375.31 


160.22 


4.00 




2.00 


12,638.86 


2.64 


111.10 


1,200.00 


3.50 


30,992.76 


2.40 


324.83 




11.06 


179,346.77 


22.60 


302.10 


114,360.00 


.74 


3,376.31 


8.92 


346.04 


40,000.00 


7.26 


12,638.86 


176.91 


301.10 


120,000.00 


6.00 


30,992.76 


11.30 


1.20 


9,476.00 


3.00 


16,503.48 


17.00 



236 VOCATIONAL MATHEMATICS FOR GIRLS 



16. $437.58 


17. $81.33 


18. $144.40 


19. $61.45 


2.75 


31.66 


16.00 


14.50 


1.40 


9.91 


1,124.04 


L80 


70.06 


20.00 


110.69 


2.00 


3.54 


23.25 


44.83 


24.17 


396.89 


129.99 


318.40 


272.90 


33.00 


9.01 


22.35 


5.13 


18.24 


208.01 


757.00 


482.09 


6.75 


160.98 


674.37 


.50 


68.70 




14.60 


220.50 


1.53 


10.60 


27.30 


36.60 


9.20 




280.00 


6.50 


.90 


3.60 


83.78 


.32 


98.95 


2.60 


36.90 


216.60 


117.13 


31.00 


246.00 


40.00 


192.71 


91.87 


481.30 


542.25 


58.43 


18.97 




67.96 


2.11 


26.49 


59.35 


53.07 


2.92 




3.76 


2.54 


43.34 


8.14 


1,863.74 


36.08 


5.80 




165.70 


21.25 


108.81 


22.38 


1,076.82 




1.75 


6.47 


8,699.46 


449.85 


10.10 


132.28 


4,437.97 




3.25 


4.00 


391.00 


394.48 


881.69 


3.00 


72.00 




82.80 


24.00 


35.00 


85.12 


.75 


10.00 


310.49 


47.90 


3.00 


10.40 


1,078.50 


31.68 


26.50 




.85 


49.50 


19.04 


37.70 


77.91 


39.76 


2.24 




64.43 


17.21 


19.50 


2.20 


168.26 




2,676.35 




186.99 


1.50 


25.25 


2.40 




6.00 


.70 




53.49 


8.62 


36.53 


2.50. 


7.50 


3.85 


3.60 


1.70 


5.05 


23.65 


3.00 


2.00 


7.60 


259.00 


168.66 


.70 


2.00 


701.47 


67.60 


92.00 


11^ 


3,148.00 



ARITHMETIC FOR OFFICE ASSISTANTS 237 

Horizontal Addition 

Reports, invoices, sales sheets, etc., are often written in such 
a way as to make it necessary to add figures horizontally. In 
adding figures horizontally, it is customary to add from left to 
right and check the answer by adding from right to left. 

EXAMPLES 

Add the following horizontally : 

1. 38 + 76 + 49 = 

2. 11 + 43 + 29 = • 

3. 27 + 57 + 15 = 

4. 34 + 16 + 23 = 

5. 47 + 89 + 37 = 

6. 53 + 74 + 42 = 

7. 94 + 17 + 67 = 
a 79 + 37 + 69 = 
9. 83 + 49 + 74 = 

10*. 19 + 38 + 49 = 

. Add the following and check by adding the horizontal and 
vertical totals : 

11. 36 + 74 + 19 + 47 = 

29 + 63 + 49 + 36 = 

+ + + = 

12. 74 + 34 + 87 + 27 = 

37 + 19 + 73 + 34 = 

+ + + = 

13. 178+ 74 + 109+ 83 = 

39 + 111 + 381 + 127 = 
+ + + = 

14. 217 + 589 + 784 = 

309 + 611 + 983 = 

+ + = 



238 VOCATIONAL MATHEMATICS FOR GIRLS 



15. ^ 1118 + 3719 + 8910 

3001 + 5316 + 6715 

+ + 



Add the following and check by adding horizontal and verti- 
cal totals. Compare the time required for the different examples. 



16. 



17. 



18. 



$702,000 $14,040 


$370,000 


$6,475.00 


$1,072,000 


$20,516.00 


626,000 


10,600 


20,000 


350.00 


666,000 


11,300.00 


1,267,500 


25,360 


447,260 


7,826.88 


1,724,750 


33,401.88 


333,000 


6,660 


340,000 


5,960.00 


833,000 


16,022.60 


380,000 


7,600 


351,000 


6,142.50 


790,000 


16,070.00 


1,077,000 


21,640 


60,000 


875.00 


1,127,000 


22,415.00 


702,000 


14,040 


370,000 


6,475.00 


1,072,000 


20,516.00 


625,000 


10,600 


20,000 


350.00 


665,000 


11,300.00 


1,264,600 


25,290 


447,260 


7,826.87 


1,721,760 


33,341.87 


333,000 


6,660 


200,000 


3,600.00 


693,009 


13,672.60 


356,000 


7,100 


348,000 


6,090.00 


768,000 


14,427.60 


1,072,000 


21,440 


50,000 


876.00 


1,122,000 


22,315.00 


318,143 


28,760 


9.04 


491.86 


189.64 


77,751,393 


295,187 


18,363 


6.22 


498.23 


188.74 


78,426,000 


300,789 


23,398 


7.96 


479.80 


187.88 


76,180,746 


279,736 


22,290 


7.97 


611.43 


187.24 


79,864,039 


302,737 


28,699 


9.48 


523.56 


187.80 


82,001,180 


302,338 


22,149 


7.33 


678.00 


188.83 


91,025,879 


341,086 


27,766 


8.14 


664.30 


192.87 


89,161,101 


336,776 


24,080 


7.17 


534.23 


192.13 


85,603,137 


311,730 


20,366 


6.63 


521.79 


192.17 


83,627,195 


336,360 


21,299 


6.36 


524.17 


192.76 


84,266,576 


281,481 


18,032 


6.41 


600.09 


194.89 


81,283,747 


306,370 


20,866 


6.83 


496.12 


196.06 


81,122,670 


380,782,161 


461,880,223 620,781,017 889,692,401 1,743,186,792 


452,491,808 


480,722,907 637. 


,837,674 481,628,491 1,962,580,780 


71,709,667 


28,842,684 17, 


066,567 91,836,090 


209,444,988 


1,686 




600 


317 


1,907 


1,102 


283,448,988 


282,640,795 326,283,015 291,835,161 1,184,157,949 


6,264 




5,879 


6,066 


6,061 


6,068 


97,333,163 


169,239,428 194,548,002 97,867,260 


668,977,843 



ARITHMETIC FOR OFFICE ASSISTANTS 239 

19. 3,200,000 17,000,000 28,000,000 7,000,000 66,700,000 
27,200,000 26,000,000 31,400,000 23,000,000 106,600,000 

6,100,000 6,100,000 

860,000 66,100,000 64,200,000 12,300,000 142,460,000 

3,600,000 12,000,000 16,600,000 

626,000 6,200,000 2,900,000 8,726,000 

1,416,363 7,263,712 2,000,000 11,866,463 22,646,628 

666,907 642,639 443,392 416,631 1,967,369 

3,600,000 11,200,000 13,200,000 7,400,000 36,300,000 

12,600,000 2,600,000 3,600,000 2,600,000 21,100,000 

20. 29,000,000 22,600,000 14,200,000 16,600,000 82,300,000 
13,600,000 10,200,000 9,600,000 8,600,000 41,900,000 

327,998 330,916 608,266 368,262 1,626,441 

1,122,906 1,222,262 1,296,344 1,317,004 4,968,616 

2,400,000 1,100,000 1,660,000 1,800,000 6,960,000 

1,600,000 860,000 900,000 900,000 4,160,000 

260,000 305,000 360,000 300,000 1,206,000 

Add the following decimals and cheek the answer : 

21. 21.61 36.21 36.17 20.32 28.30 
18.91 12.42 5.96 20.96 14.66 

15.86 6.00 3.17 19.07 11.02 

22. 44.33 73.16 71.69 14.36 8.16 
43.20 47.14 126.04 85.05 70.42 
93.35 80.13 31.15 62.51 49.17 
49.17 . 29.37 47.26 31.10 206.38 
37.69 47.26 36.59 60.47 73.26 

23. On the following page is an itemized list of invest- 
ments. 

What is the total amount of investments ? 
What is the average rate of interest ? 

Review Interest, page 60. 



240 VOCATIONAL MATHEMATICS FOR GIRLS 

List of Investments Held by the Sinking Punds of Fall Biver^ Mass. 

January 1, 1913 



Name 


Rate 


Maturity 


Amount 


City of Boston Bonds 


H 


July 1, 


1939 


$16,000 


City of Cambridge Bonds 


H 


Nov. 1, 


1941 


26,000 


City of Chicago Bonds 


4 


Jan. 1, 


1921 


27,600 


City of Chicago Bonds 


4 


Jan. 1, 


1922 


100,000 


City of Los Angeles Bonds 


4J 


June 1, 


1930 


60,000 


City of So. Norwalk Bonds 


4 


July 1, 


1930 


23,000 


City of So. Norwalk Bonds 


4 


Sept. 1, 


1930 


22,000 


City of Taunton Bonds 


4 


June 1, 


1919 


39,000 


Town of Revere Note 


4.36 disc. 


Aug. 13, 


1913 


10,000 


Boston & Albany R. R. Bonds 


4 


May 1, 


1933 


67,000 


Boston & Albany R. R. Bonds 


4 


May 1, 


1934 


67,000 


Boston Elevated R. R. Bonds 


4 


May 1, 


1936 


50,000 


Boston Elevated R. R. Bonds 


4i 


Oct. 1, 


1937 


68,000 


Boston Elevated R. R. Bonds 


4i 


Nov. 1, 


1941 


60,000 


Boston & Lowell R. R. Bonds 


4 


April 1, 


1932 


16,000 


Boston & Maine R. R. Bonds 


4i 


Jan. 1, 


1944 


160,000 


Boston & Maine R. R. Bonds 


4 


June 10, 


1913 


20,000 


C. B. & Q. R. R. Bonds (111. Div.) 


4 


July 1, 


1949 


60,000 


C. B. & Q. R. R. Bonds (111. Div.) 


H 


July 1, 


1949 


65,000 


Chi. & N. W. R. R. Bonds 


7 


Feb. 1, 


1915 


92,000 


Chi. & St. P., M. & 0.. R. R. Bonds 


6 


June 1, 


1930 


20,000 


Cleveland & Pittsburg R. R. Bonds 


4i 


Jan. 1, 


1942 


36,000 


Cleveland & Pittsburg R. R. Bonds 


^ 


Oct. 1, 


1942 


10,000 


Fitchburg R. R. Bonds 


H 


Oct. 1, 


1920 


60,000 


Fitchburg R. R. Bonds 


3i 


Oct. 1, 


1921 


20,000 


Fitchburg R. R. Bonds 


4i 


May 1, 


1928 


60,000 


Fre. Elk. & Mo. Val. R. R. Bonds 


6 


Oct. 1, 


1933 


85,000 


Great Northern R. R. Bonds 


^ 


July 1, 


1961 


. 25,000 


Housatonic R. R. Bonds 


5 


Nov. 1, 


1937 


46,000 


Louis. & Nash. R. R. Bonds 










(N. 0. & M.) 


6 


Jan. 1, 


1930 


20,000 


Louis. & Nash. R. R. Bonds 










(St. L. Div.) 


6 


March 1, 


1921 


6,000 


Louis. & Nai^h. R. R. Bonds 










(N. & M.) 


H 


Sept. 1, 


1945 


10,000 


Louis. & Nai^h. R. R. Bonds 


5 


Nov. 1, 


1931 


36,000 


Mich. Cent. R. R. Bonds 


6 


March 1, 


1931 


37,000 


Mich. Cent. R.R. Bonds 










(Kal. & S. H.) 


2 


Nov. 1, 


1939 


60,000 



ARITHMETIC FOR OFFICE ASSISTANTS 



241 



24. What is total amount of the following water bonds ? 
What is the average rate of interest ? 

Water Bonds of Fall Biver, Mass. 



Datk 01 


I* Ibbub 


Rate 


TSBM 


Maturity 


Amount 


June 1. 


,1893 


^L 


30 years 


June 1, 


, 1923 


$76,000 


May 1 


, 1894 




30 years 


May 1, 


1924 


26,000 


Nov. 1 


, 1894 




29 years 


Nov. 1, 


1923 


25,000 


Nov. 1, 


, 1894 




30 years 


Nov. 1, 


, 1924 


26,000 


May 1, 


1896 




30 years 


May 1. 


, 1926 


25,000 


June 1 


, 1895 




30 years 


June 1, 


, 1925 


50,000 


Nov. 1, 


, 1896 




30 years 


Nov. 1 


, 1925 


25,000 


May 1 


,1896 




30 years 


May 1, 


, 1926 


26,000 


Nov. 1, 


, 1896 




30 years 


Nov. 1, 


, 1926 


26,000 


April 1, 


, 1897 




30 years 


April 1 


, 1927 


26,000 


Nov. 1 


, 1897 




30 years 


Nov. 1, 


1927 


26,000 


April 1. 


,1898 




30 years 


April 1. 


, 1928 


26,000 


Nov. 1, 


,1898 




30 years 


Nov. 1, 


, 1828 


26,000 


May 1, 


, 1899 




30 years 


May 1, 


, 1929 


60,000 


Aug. 1, 


, 1899 




30 years 


Aug. 1 


, 1929 


160,000 


Nov. 1. 


, 1899 


H 


80 years 


Nov. 1, 


, 1929 


176,000 


Feb. 1, 


, 1900 


H 


30 years 


Feb. 1. 


, 1930 


100,000 


May 1, 


, 1900 


H 


30 years 


May 1, 


, 1930 


20,000 


April 1, 


1901 


H 


30 years 


April 1. 


,1931 


20,000 


April 1, 


1902 


H 


30 years 


April 1. 


, 1932 


20,000 


April 1, 


, 1902 


H 


30 years 


April 1, 


1932 


60,000 


Dec. 1. 


, 1902 


H 


30 years 


Dec. 1, 


, 1932 


50,000 


April 1, 


, 1903 


H 


30 years 


April 1 


,1933 


20,000 


Feb. 1 


,1904 


3i 


30 years 


Feb. 1. 


,1934 


176,000 


May 2 


, 1904 


4 


30 years 


May 2, 


1934 


20,000 



1 

SUBTRACTION 








Drill Exercise 








1. 33 2, 35 3. 37 4. 38 5. 36 


6. 32 


7. 


26 


7 9 8 9 7 


4 




9 


8. 42 9. 49 10. 46 U. 43 


12. 


41 




17 18 19 16 




15 





242 VOCATIONAL MATHEMATICS FOR GIRLS 

13. 45 14. 44 15. 364 16. 468 17. 566 

17 17 126 329 328 

18. 661 19. 363 20. 465 21. 362 

324 127 228 129 

22. 865,900 23. 891,000 24. 200,000 25. 30,071 

697,148 597,119 121,314 28,002 

26. 581,300 27. 481,111 28. 681,900 29. 868,434 

391,111 310,010 537,349 399,638 

iS _^_^,^_^_^^^_^^^ V.^__^-^_H^_^i^H ^_M^.^_^^_^^^^^^^ 

30. 753,829 31. 394,287 32. 567,397 33. 487,196 

537,297 277,469 297,719 311,076 

34. 291,903 35. $835.00 36. $1100.44 37. $2881.44 

187,147 119.00 835.11 1901.33 

38. $3884.59 39. $4110.59 40. $2883.40 41. $3717.17 

1500.45 1744.43 1918.17 1999.18 

42. $1911.84 43. $2837.73 44. $5887.93 

1294.95 1949.94 4999.99 



MULTIPLICATION 

Drill Exercise 
By inspection, multiply the following numbers : 

1. 1600x900. 11. 80x11. 

2. 800 X 740. 12. 79 x 11. 

3. 360 X 400. 13. 187 x 11. 

4. 590x800. 14. 2100x11. 

5. 1700x1100. 15. 2855x11. 

6. 1900x700. 16. 84x25. 

7. 788,000x600. 17. 116x50. 

8. 49,009 X 400. 18. 288 x 25. 

9. 318,000x4000. 19. 198x25. 
10. 988,000 X 50,000. 20. 3884 x 25. 
Keview rules on multiplication, pages 8-9. 



ARITHMETIC FOR OFFICE ASSISTANTS 243 

BILLS (Invoices) 

When a merchant sells goods (called merchandise), he sends 
a bill (called an invoice) to the customer unless payment is 
made at the time of the sale. This invoice contains an itemized 
list of the merchandise sold and also the following : 

The place and date of the sale. 

The terms of the sale (usually in small type) — cash or a 
number of days' credit. Sometimes a small discount is given 
if the bill is paid within a definite period. 

The quantity, name, and price of each item is placed on the 
same line. The entire amount of each item, called the exten- 
sion, is placed in a column at the right of the item. 

Discounts are deducted from the bill, if promised. 

Extra charges, such as cartage or freight, are added after 
taking off the discount. 

Make all Checks payable to We handle only highest grades 

Union Coal Company of Anthracite and Bitu- 

of Boston minous Coals 

UNION COAL COMPANY 

40 Center Street 

BRANCH EXCHANGE TELEPHONE 
CONNECTING ALL WHARVES AND OFFICES 

SOLD TO L. T. Jones, 

5 Whitney St. , 

Mattapan, Mass. 





BOSTOW, 


Sept. 3 


, 1914. 


6000 lb. 


Stove Coal 


7.00 


$21.00 


4000 " 


Nut 


7.25 


14.50 



35.50 



REC'D PAYMENT 

SEPT. 28, 1914 
UNION COAL CO. 



244 VOCATIONAL MATHEMATICS FOR GIRIJS 

When the amount of the bill or invoice is paid, the invoice 
is marked. 

Received payment^ 
Name of firm. 

Per name of authorized person. 

This is called receipting a bill. 

Ledger 

Whenever an invoice is sent to a customer, a record of the 
transaction is made in a book called a ledger. The pages of 
this book are divided into two parts by means of red or double 
lines. The left side is called the debit and the right side the 
credit side. At the top of each ledger page the name of a 
person or firm that purchases merchandise is recorded. The 
record on this page is called the account of the person or firm. 
When the person or firm purchases merchandise, it is recorded 
on the debit side. When merchandise or cash is received, it is 
recorded on the credit side. The date, the amount, and the 
word Mdse. or cash is usually written. 

We debit an account when it receives value, and credit an 
account when it delivers value. 



E. D. REDINGTON 



1917 










1 1917 










Jan, 2 


Cash 


109 


1000 




I Jail, 1 


Ac&t to Perkins 


114 


810 


5S 




Note, 60 ds. 


114 


1500 




2 


Mdse. 


100 


3057 


50 


9 


Pagers Order 


115 


575 




10 


(i 


100 


575 




25 


Cash 


109 


500 




22 


Order to Jenness 


115 


375 




27 


Mdse. 


93 


157 


50 




688.05 




1*818 


08 


31 


Browne's Ace, 


115 


397 

U130 


53 

03 













Specimen Lbdobb Page 



ARITHMETIC FOR OFFICE ASSISTANTS 245 

A summary of the debits and credits of an account is called 
a statement. The difference between the debits and credits 
represents the standing of the account. If the debits are 
greater than the credits, the customer named on the account 
owes the merchant. If the credits are greater than the debits, 
then the merchant owes the customer. 



EXAMPLES 



Balance the following accounts : 



BLANEY, BROWN & CO. 



1917 



Jan. 14 



28 



Cons't #1 
** Co.il 









1917 


177 


669 


98 


Jan. 6 


179 


386 


25 


30 


179 


1200 


75 





Mdse, 

D/t. favor Button 



171 
180 



1303 
900 



75 



LUDWIG & LONG 



1917 












1917 










Jan. 6 


ConsU #2 




177 


1939 


50 


Jan. 6 


Cash 


172 


1000 




20 


** #^ 


St7.60 


177 


1327 


50 


15 
28 


n 


172 
172 


939 
1000 


50 



CHARLES N. BUTTON 



1917 








Jan. 7 


Mdse. 


168 


651 


12 


Cash 


173 


1000 


20 


<< 


173 


2000 


29 


ShipH Co. #1 


179 


795 


30 


D/t. on Blaneyt B. 


180 


900 





1 1917 


88 


\jan. 9 




1 ^^ 


37 









Ship't Co. §2 
ConsH §2 t08.Bi 



177 
176 



856 
4699 



67 
09 



246 VOCATIONAL MATHEMATICS FOR GIRLS 



D. K. REED & SON 



1917 










1917 










Jan, 8 


ComH #J 


177 


625 


42 


Jan, 8 


Note at 60 ds. 


180 


625 


42 


17 


Mdse, 


170 


202 


50 


17 


Cash 


172 


202 


60 


26 


Cons't SI 
" Co. #i 


177 
179 


243 
206 


75 













PROFIT AND LOSS 

(Review Percentage on pages 60-66) 

A merchant must sell merchandise at a higher price than he 
paid for it in order to have sufficient funds at the end of the 
transaction to pay for clerk hire, rent, etc. Any amount above 
the purchasing price and its attendant expenses is called 
profit; any amount below purchasing price is called loss, 

A merchant must be careful in figuring his profit. He 
must have a set of books so arranged as to show what caused 
either an increase or reduction in the profits. 

There are certain special terms used in considering profit 
and loss. The first cost of goods is called the net or prime 
cost. After the goods have been received and unpacked, and 
the freight, cartage, storage, commission, etc. paid, the cost 
has been increased to what is called gross or full cost. The 
total amount received from the sale of goods is called gross 
selling price. The sum of expenses connected with the sale of 
goods subtracted from the gross selling price is called the net 
selling price. A merchant gains or loses according as the net 
selling price is above or below the gross cost. 

There are two methods of computing gain or loss, each 
based on the rules of percentage. In the first method, the 
gross cost is the base, the per cent of gain or loss the rate, the 
gain or loss the percentage. The second method considers 
the selling price the base and will be explained in detail later. 



ARITHMETIC FOR OFFICE ASSISTANTS 



247 



EXAMPLES 

1. Make extensions after deducting discounts and give total : 

CndH not allowed on goods returned wUbout our permission 

PETTINGELL-ANDREWS COMPANY 

ELECTRICAL MERCHANDISE 

General Offices and Warerooms 
166 to 160 PEARL STREET and 401 to 611 ATLANTIO AVBNUB 

Terms : 30 Days Net 
NEW YORK, Nov 17 1911 

SOLD TO City of Lowell School Dept, Lowell, Mass. 
SHIPPED TO Same Lowell Industrial School, Lowell, Mass. 

SHIPPED BY B &. L 11/14/11 * OUR REG. NO. 3786 

ORDER REC'D 11/13/11 REELS COILS BUNDLES CASES BBLS. 



&-D 


^7 


: ' 










3 "S 


II 


Order No. 78158 Reg. No. 


52108 


PRICE 






CO 


O'in 












1 


1 


#4Comealong#ll293 


Ea 


4 00 
15% 


■ 




1 


1 


#14492 16" Extension Bit 


Ea 


2 00 
50% 






36 


36 


2 oz cans Nokorode Soldering Paste 


Doz 


2 00 
50% 






15 


15 


#8020 Cutouts 


Ea 


36 
40% 






2 


2 


#322 H & H Snap Sws 


Ea 


76 
30% 






125 


125 


#9395 Pore Sockets 


Ea 


30 
45% 






125 


125 


# 1999 Fuseless Rosettes 


Ea 


08 
45% 






100 


100 


C Ball Adjusters for Lp Cord 


M 


7 00 


, 




50 


50 


J" Skt Bushings 


C 


50 






200 


200 


Pr #43031 Std#328#l Single Wire Cleats M Pr 


26 68 














40% 






200 


200 


Pr #43033 Single Wire Cleats 


MPr 


40 00 
40% 






2 


2 


Lb White Exemplar Tape 


Lb 


45 







248 VOCATIONAL MATHEMATICS FOR GIRLS 
2. Make extensions on the following items and give total : 

Gooda are Charged for the Convenience of Cuatomeri and Accounta are Rendered Monthly 

R A. Mc"Whirr Co. 

DEPARTMENT STORE 



FALL RIVER, MASS. 



A. A. MILLS. Pret't&Treas. 
J. H. MAHONEY, Supt. 
R. S. THOMPSON, Sec'y. 



Purchases for 




Fall River 


Technical High School 


September, 1913 


City 


No. Ordei 


r Number 719 

• 


Datb 


Ahticlbs 


Amounts 


Daily Total 


Credits 


Sept 4 


2 Doz C Hangers 
2 " Skirt " 


90 
45 








5 


120 Long Cloth 
34S Cambric 


15 
5J 








6 


522 B Cambric 
100 B Nainsook 
24 Doz Kerr L Twist 
8 Doz Tape Measures 
84 •• W Thread 
1 10/12 Doz Tape 


18 

16 

120 

25 

51 

25 








9 


1 Gro Tambo Cotton 
i Doz Bone Stillettos 
J '• Steel 
40 Paper Needles 
20 " " 


520 
46 
46 
3} 
3} 










2 Doz M Plyers 


600 




• 






2 Boxes Edge Wire 


125 










12 '* Even Tie Wire 


180 










24 " Brace 


225 










2 •• Lace 


160 










2 Pk Ribbon 


125 










2 Roils Buckram 


90 










48 Yd Cape Net 


15 








13 


100 Crinoline 
125 


5 
5 









ARITHMETIC FOR OFFICE ASSISTANTS 



249 



3. Make extensions on the following items and give total ; 

Goods are Charged for the Convenience of Customera and Accounts are Rendered Monthly 

R. A. Mc Whirr Co. 

DEPARTMENT STORE 

FALiLi RIVER, MASS. 

A. A. MILLS, PretH & Treat. 
J. H. MAHONEY, Vice-Pre»'t. 
R. S. THOMPSON, Sec'y. 



Purchases for 

September, 1913 



Fall River Public Buildings 
City 



No. 


For Technical H 


igh School 






Date 


Articlxs 


Amounts 


Daily Total 


Cbbdits 


Sept 4 


1 Dinner Set 1700 
100 Knives 9 
100 Forks 9 
100 D Spoons 10 
100 Tea Spoons 09 

1 Doz Glasses 90 
8i Doz Tumblers 45 
8i " Bowls 96 
54 Crash \\\ 
7J " 11} 
50 •• 3i 
} Doz Napkins 270 
J " " 415 

2 Table Cloths 360 








12 


120 Crash II } 








15 


2 Stock Pots 325 
1 Lemon Squeezer 14 
1 Doz Teaspoons 500 
1 Butter Spreader 75 
} Doz Forks 625 









250 VOCATIONAL MATHEMATICS FOR GIRLS 

Example. — A real estate dealer buys a house for $4990 
and sells it to gain $ 50. What is the per cent of gain over 
cost ? 

Solution. ^ x 100 = — = lAs%. Arts. 

4990 499 ^'^ '^ 

Drill Exercisb 



Find per cent of gain or loss : 



Cost Oain Cost LoM 

1. $1660 $175 6. $6110 $112 

2. $1845 $135 7. $5880 $ 65 

3. $1997.75 $412.50 8. $3181.10 $108.75 

4. $2222.50 $319.75 9. $7181.49 $213.60 

5. $3880.11 $610.03 10. $3333.19 $ 28.90 

EXAMPLES 

1. A dealer buys wheat at 91 cents a bushel and sells to 
gain 26 cents. What is the per cent of gain? 

2. A farmer sold a bushel of potatoes for 86 cents, and gained 
20 cents over the cost. What was the per cent of gain ? 

3. Real estate was sold for $ 19,880 at a profit of $ 3650. 
What was the per cent of gain ? 

4. A provision dealer buys smoked hams at 19 cents a pound 
and sells them at 31 cents a pound. What is the per cent of 
gain? 

5. A grocer buys eggs at 28 cents a dozen and sells them 
at 35 cents a dozen. What is the per cent gain ? 

6. A dealer buys sewing machines at $22 each and sells 
them at $ 40. What is the per cent gain ? 

7. A dealer buys an automobile for $ 972 and sells it for 
$ 1472 and pays $ 73.50 freight. What is the per cent gain ? 



ARITHMETIC FOR OFFICE ASSISTANTS 251 

Drill Exercise 
Find the per cent gain or loss on both cost and selling price : 

Cost Selling Price Cottt Selling Price 

1. $1200 $1500 6. $2475 $2360 

2. $1670 $1975 7. $1650 $1490 

3. $2325 $2980 8. $4111.50 $2880.80 

4. $4250.50 $5875.75 9. $4335.50 $4660.60 

5. $3888.80 $4371.71 10. $2880.17 $2551.60 

REVIEW EXAMPLES 

1. A dealer buys 46 gross of spools of. cotton at $11.12. 
He sells them at 5 cents each. What is his profit ? What is 
the per cent of gain on cost ? on selling price ? 

2. Hardware supplies were bought at $ 119.75 and sold for 
$ 208.16. What is the per cent of gain on cost and on selling 
price ? 

3. A grocer pays $ 840 f .o.b. Detroit for an automobile 
truck. The freight costs him $ 61.75. What is the total cost 
of automobile truck ? What per cent of the total cost is 
freight ? 

4. A dry goods firm buys 900 yards of calico at 5 cents a 
yard, and sells it at 9 cents. What is the profit ? What per 
cent of cost and selling price ? 

5. A grocer buys a can (8J qt.) of milk for 55 cents and sells 
it for 9 cents a quart. What is the per cent of gain ? 

EXAMPLES 

1. A dealer sold a piano at a profit of $ 115, thereby gaining 
18 % on cost. What was the selling price ? 

Solution. — If $ 115 = 18 % of cost, which is 100 %, 

J % = j^5 = 6.3889 

100% =.$638.89 cost 
Addin g 115.00 profit 

$753.89 selling price. 



252 VOCATIONAL MATHEMATICS FOR GIRLS 

2. A dealer sold furniture at a profit of $ 98. What was 
the cost of the furniture, if he sold to gain 35 % ? 

3. A coal dealer buys coal at the wharf and sells it to gain $ 2 
per ton. What is the cost per ton if he gains 31 % ? 

4. A shoe jobber buys a lot of shoes for $ 1265 and sells to 
gain 26 %. What is the selling price ? 

5. An electrician buys a motor for $ 48 and sells it to gain 
18 %. What is the selling price ? 

6. A pair of shoes was sold to gain 26 %, giving the shoe 
dealer a profit of 97 cents. What was the cost price ? What 
was the selling price ? 

FORMULAS 

Gain or loss = Cost x rate of gain or loss 

Gain or loss 



C08t = 



Rate of gain or rate of loss 
Selling Price = Cost (100 % + rate of gain) or (100 % - rate of loss) 
Cost ^ Selling Price Selling Price 

"" 100% + rate of gain ^' 100 9{> - rate of loss 

Drill Exercise 
Find the selling price in each of the following problems : 



Sold to Lose 


Cost 


Sold to Gain 


Cost 


1. i&i% 


$96 


6. 37% 


$250 


2. 20% 


$115 


7. 33%^ 


$644.50 


3. 30% 


$48 


8. 41% 


$ 841.75 


4. 19% 


$ 112.50 


9. 29% 


$ 108.19 


5. 20^% 


$ 187.75 


10. 22^% 


$ 237.75 



COMPUTING PROFIT AND LOSS 

Second Method, — Many merchants find that it is better busi- 
ness practice to figure per cost profit on the selling price rather 
than on the cost price. Many failures in business can be 



ARITHMETIC FOR OFFICE ASSISTANTS 253 

traced to the practice of basing profits on cost. We must bear 
in mind that no comparison can be made between per cents of 
profit or cost until they have been reduced to terms of the 
same unit value or to per cents of the same base. 

To illustrate: It costs $100 to manufacture a certain article. The 
expenses of selling are 22%. For what must it sell to make a net 
profit of 10%? Most students would calculate $132, taking the first 
cost as the basis of estimating cost of sales and net profit. The average 
business man would say that the expenses of selling and cost should be 
quoted on the basis of the selling price. 

Solution. — Expenses of selling = 22 % 

Profit = 10 % 

32 % on selling price. 

. •. Cost on $ 100 = 68 % selling price. 
100 % = $ 147 selling price. 

Example 1. — An article costs $ 5 and sells for $ 6. What 
is the percentage of profit? .dns, 16 J %. 

Process. — Six dollars minus $6 leaves $1, the profit. One dollar 
divided by $6, decimally, gives the correct answer, 16J%. 

Example 2: — An article costs $ 3.75. What must it sell 
for to show a profit of 25 % ? Ans, $ 5. 

Process. — Deduct 25 from 100. This will give you a remainder of 
76, the percentage of the cost. If $3.76 is 75%, 1% would be $3.75 
divided by 76 or 6 cents, and 100 % would be $ 5. Now, if you marked 
your goods, as too many do, by adding 26 % to the cost, you would ob- 
tain a selling price of about $ 4.69, or 31 cents less than by the former 
method. 

EXAMPLES 

1. What is the percentage of profit, if an article costs $ 8.50 
and sells for $ 10 ? 

2. What is the percentage of profit on an automobile that 
cost $ 810 and sold for $ 1215 ? 

3. An article costs $ 840. What must I sell it for to gain 
30%? 



254 VOCATIONAL MATHEMATICS FOR GIRLS 

4. A case of shoes is bought for $ 30. For what must I sell 
them to gain 26 % ? 

Table for Finding the Selling Price of any Article 



COBT 


Net Per Cent Profit Desired 


TO PO 






Business 


















^^ - - 1 - t 


















1 
84 


88 


3 

82 


4 
81 


6 

80 


6 

79 


7 
78 


8 

77 


9 

76 


10 

76 


11 

74 


IS 

78 


18 

72 


14 

71 


16 

70 


SO 

66 


S6 

60 


80 

66 


88 

60 


40 

46 


60 


15% 


35 


16% 


88 


82 


81 


80 


79 


78 


77 


76 


76 


74 


78 


72 


71 


70 


69 


64 


69 


54 


49 


44 


84 


1T% 


82 


81 


80 


79 


78 


77 


76 


76 


74 


78 


72 


71 


70 


69 


68 


68 


68 


68 


48 


48 


88 


18% 

19% 
20% 

21% 


81 


80 


79 


78 


77 


76 


76 


74 


78 


72 


71 


70 


69 


68 


67 


62 


67 


52 


47 


42 


82 


80 


79 


78 


77 


76 


76 


74 


78 


72 


71 


70 


69 


68 


67 


66 


61 


66 


51 


46 


41 


81 


79 


78 


77 


76 


76 


74 


78 


72 


71 


70 


69 


68 


67 


66 


66 


60 


56 


50 


45 


40 


80 


78 


77 


76 


75 


74 


73 


72 


71 


70 


69 


68 


67 


66 


66 


64 


69 


54 


49 


44 


89 


29 


22% 
28% 


77 


76 


75 


74 


78 


72 


71 


70 


69 


68 


67 


66 


66 


64 


68 


68 


58 


48 


48 


88 


28 


76 


75 


74 


78 


72 


71 


70 


69 


68 


67 


66 


66 


64 


63 


62 


67 


62 


47 


42 


87 


27 


24% 


75 


74 


78 


72 


71 


70 


69 


68 


67 


66 


66 


64 


68 


62 


61 


66 


51 


46 


41 


86 


26 


26% 


74 


78 


72 


71 


70 


t9 


68 


67 


66 


66 


64 


68 


62 


61 


60 


66 


50 


45 


40 


36 


25 



The percentage of cost of doing business and the profit are 
figured on the selling price. 



Rule 

Divide the cost (invoice price with freight added) by the 
figure in the column of " net rate per cent profit desired " on 
the line with per cent it cost you to do business. 

Example. — If a wagon cost $ 60.00 

Freight 1.20 

$ 61.20 

You desire to make a net profit of 6 per cent 

It costs you to do business 19 per cent 

Take the figure in column 5 on line 19, which is 76. 

76|$61.2000 |$80.52, the selling price. 
608 
400 
880 
200 
162 



ARITHMETIC FOR OFFICE ASSISTANTS 255 

Solve the following examples by table : 

1. I bought a wagon for $84.00 f.o.b. New York City. 
Freight cost $ 1.05. I desire to sell to gain 8 %. If the cost 
to do business is 18 %, what should be the selling price? 

2. I buy goods at $97 and desire a net profit of 7%. It 
costs 16 % to do business. What should be my selling price ? 

3. Hardware supplies are purchased for $489.75. If it 
costs 23 % to do the business, and I desire to make a net profit 
of 11 %, for what must I sell the goods ? 

EXAMPLES 

1. I bought 15 cuts of cloth containing 40^ yd. each, at 
7 cents a yd., and sold it for 9 cents a yd. What was the 
gain? 

2. A furniture dealer sold a table for $ 14.50, a couch for 
$ 45.80, a desk for $ 11.75, and some chairs for $ 27.30. Find 
the amount of his sales. 

3. Goods were sold for $367.75 at a loss of $125. Find 
the cost of the goods. 

4. Goods costing $145.25 were sold at a profit of $ 28.50. 
For how much were they sold ? 

5. A woman bought 4^ yards of silk at $ 1.80 per yard, and 
gave in payment a $ 10 bill. What change did she receive.? 

6. I bought 25 yards of carpet at $2.75 per yard, and 6 
chairs at $ 4.50 each, and gave in payment a $ 100 bill. 
What change should I receive ? 

TIME SHEETS AND PAY ROLLS 

Office assistants must tabulate the time of the different em- 
ployees and compute the individual amount due each week. 
In addition, they must know the number of coins and bills of 
different denominations required so as to be able to place the 
exact amount in each envelope. This may be done by making 
out the following j)ay roll form. 



256 VOCATIONAL MATHEMATICS FOR GIRLS 



FoBM Used to Determine the Number of Different Denominations 



Noi Persons 


Amt. Rec'd 


$10 
2 

2 


$5 

3 
2 
9 


$2 

2 
6 

/6 


$1 

2 

2 


50 j^ 

2 
3 

5 


25^ 
3 

7 


10^' 

3 
8 
2 

/3 


5^ 

2 
2 


\f 


2 


/d.60 




8 


^.86 




f 


7.^8 


/2 


2 


^./8 


6 








Total Number Coins 




/8 



Time Card 



Week Ending. 

No. 

NAME 



.191-- 





MORNING 


AFTERNOON 


LOST OR 
OVERTIME 


^ 


Toe 

Wed 

Tim 

FrI 

tet 

Sun 


U 


OCT 


II 


OUT 


n 


OIT 


? 



Tot»l Time Hr$. 

Rate 

Total Wage* for Week $ 



Form Used to Send to the Bank 
FOR THE Monet for Pat Koll 



MEMORANDUM OF 

CASH FOR PAY ROLL 



WANTED BY 



J9— 



Twenties 

Tens 

Fives 

Twos 

Ones 

Halves 

Quarters 

Dimes . 

Nickels 

Pennies 



Total 



ARITHMETIC FOR OFFICE ASSISTANTS 



257 



TABLE OF WAGES 1 

To find the amount due at any rate from 30 cents to. 56 
cents per hour, look at the column containing the number of 
hours and the amoimt will be shown. Time and a half is 
counted for overtime on regular working days, and double 
time for Sundays and holidays. 





* • 








• 
















1 


P4 

a 


s 


II 
a 

S 

s 


m 


S 


1 






g 


s 


1 


1 


S 


• 




§ 


i 


1 


• 

n 


s 


s 


s 


n 


M 


M 


« 


o 


Q 


(4 


M 


^ 


Q 


$0 45 


& 


o 


» 


%••• 


$0 80 


$0 15 


$0 22^ 


$0 80 


$0 82^ 


$0 16i 


$0 24| 


$0 32) 


$0 22) 


$0 88f 


$0 46 


1... 


80 


80 


46 


60 


82^ 


82^ 


48| 


66 


46 


45 


67i 


90 


2... 


30 


60 


90 


1 20 


82^ 


66 


97^ 


1 80 


46 


90 


1 85 


1 80 


Oi • • 


80 


90 


185 


1 80 


82^ 


97^ 


1 46i 


1 96 


45 


135 


2 02) 


2 70 


4... 


80 


1 20 


180 


240 


82^ 


1 80 


1 95 


2 60 


45 


1 80 


2 70 


360 


6... 


80 


1 60 


2 25 


8 00 


82^ 


1 62i 


248| 


8 25 


45 


225 


8 87i 


460 


o< • • 


80 


1 80 


2 70 


8 60 


82J 


196 


2 92^ 


3 90 


45 


2 70 


405 


5 40 


7... 


80 


2 10 


8 15 


4 20 


82i 


2 27i 


8 41i 


466 


45 


8 15 


4 72) 


6 80 


vl • • • 


80 


2 40 


8 eo 


4 80 


32^ 


2 60 


3 90 


620 


45 


3 60 


540 


7 20 


9... 


80 


2 70 


405 


640 


32i 


2 92i 


4 88| 


586 


45 


405 


6 07) 


8 10 


10... 


80 


8 06 


460 


6 00 


82i 


8 25 


4 87i 


660 


45 


450 


6 75 


9 00 


%••• 


$0 47i 


$0 28| 


$0 86| 


$0 47i 


10 60 


$0 25 


$0 87i 


$0 50 


$0 65 


$0 271 


$0 41J 


$0 56 


1... 


47i 


47i 


7U 


96 


60 


60 


76 


1 00 


65 


66 


82) 


110 


2... 


47i 


95 


1 42| 


1 90 


60 


1 00 


1 50 


2 00 


55 


1 10 


1 65 


2 20 


o* • • 


4H 


1 42| 


2 1df 


285 


60 


1 60 


225 


8 00 


56 


1 65 


2 47i 


8 80 


4... 


47i 


1 90 


2 86 


8 80 


50 


2 00 


8 00 


4 00 


. 55 


2 20 


8 80 


440 


o< .* 


47i 


2 87i 


8 56i 


4 76 


50 


2 60 


8 75 


6 00 


55 


2 75 


4 12) 


560 


o« . * 


47i 


2 85 


4 27i 


5 70 


60 


8 00 


450 


6 00 


65 


8 80 


4 96 


6 60 


7... 


47i 


8 82i 


4 98| 


665 


60 


8 50 


525 


7 00 


55 


3 86 


6 77) 


7 70 


o* • • 


47i 


880 


6 70 


7 60 


50 


4 00 


6 00 


8 00 


55 


440 


6 60 


880 


9... 


47i 


4 27i 


6 411 


8 65 


60 


450 


6 75 


9 00 


55 


4 96 


7 42) 


9 90 


10... 


47i 


4 76 


7 12J 


9 50 


50 


500 


7 60 


10 00 


56 


560 


825 


11 00 



EXAMPLES 

1. Find the amount due a carpenter who has worked 8 
hours regular time and 2 hours overtime at 55 cents per hour. 

^ Similar tables may be constracted for other rates. 



258 VOCATIONAL MATHEMATICS FOR GIRLS 



2. A plasterer worked on Sunday from 8 to 11 o'clock. If 
his regular wages are 45 cents per hour, how much will he 
receive ? 

3. A machinist's regular wage is 55 cents an hour. How 
much money is due him for working July 4th from 8-12 a.m. 
and 1^.30 p.m. ? 

4. A plumber works six days in the week; every morning 
from 7.30 to 12 m. ; three afternoons from 1 to 4.30 p.m. ; two 
afternoons from 1 to 5.30 ; and one from 1 until 6 p.m. What 
will he receive for his week's wages at 50 cents per hour? 

Wages op Employees 

Superintendent $1,200.00 per annum 

Matron 700.00 per annum 

Nurses, 2 at 45.00 per month 

Nurses, 1 at 40.00 per month 

Nurses, 3 at 35.00 per month 

Attendant 6.00 per week 

Cook 12.00 per week 

Assistant cook 1.00 per day 

Kitchen maid 6.00 per week 

Ward maids, 4 at 6.00 per week 

Waitresses, 2 at 6.00 per week 

Laundress 8.00 per week 

Washwomen, 2 at 6.00 per week 

Janitors, 1 day and 1 night 16.00 per week 

Barber . . . • 6.00 per week 

5. Find the total of coins and bills of all different denomi- 
nations necessary to make up the weekly pay roll (52 weeks 
= a year) of the above. Assume full time for a week. Make 
out the currency memorandum for baiik. 

6. Find the total of coins and bills of the different denomi- 
nations necessary to make up the following pay roll ; 

47^ hours, at 30 cents. 
48 hours, at 45 cents. 
48 hours, at 47 J cents. 
46 hours, at 32^ cents. 



ARITHMETIC FOR OFFICE ASSISTANTS 



259 



7. Make a pay roll memorandum for the following pay 
roll: 

48at42i, 39 at 45, 46iat48i. 

TEMPORARY LOANS 

The following is a statement of the temporary loans of a 
New England city negotiated during the year, — amount, time, 
rates. 



Datr 


Amount of 

Loan 


TiMB 


Rate of 
Intbbbst 


Amount of 


JL^J^ A JM 




— ^» 


Intbbbst 






Months 


Imys 






Feb. 28 


350,000 




243 


2.76 




Feb. 28 


26,000 




243 


2.76 




Feb. 28 


26,000 




243 


2.76 




June 6 


100,000 


6 




3.26 




June 19 


26,000 




126 


3.52 




June 19 


26,000 




126 


3.52 




June 19 


25,000 




126 


3.62 




June 19 


26,000 




126 


3.62 




July 3 


25,000 




124 


3.66 




July 3 


26,000 




124 


3.55 




July 8 


26,000 




124 


3.56 




July 3 


26,000 




124 


3.66 




July 3 


26,000 




124 


3.55 




July 3 


25,000 




124 


3.65 




Aug. 14 


26,000 


2 




4. 




Aug. 20 


26,000 




80 


4.07 




Aug. 20 


26,000 




80 


4.07 




Aug. 20 


25,000 




80 


4.07 




Aug. 20 


26,000 




80 


4.07 




Sept. 4 


25,000 




40 


4. 




Sept. 4 


25,000 




40 


4. 




Sept. 4 


16,000 




40 


4. 





Write in a column after each loan, as suggested above, the 
amount of interest on each loan for the time and at the rate. 



CHAPTER XII 
ARITHMETIC FOR SALESGIRLS AND CASHIERS 

• 

The majority of employees in a department store are sales- 
girls. It may be well to describe briefly the method of 
operation of such a store and to indicate what part a salesgirl 
has in it. 

A department store is a combination of a number of distinct 
stores or departments under one roof and general manage- 
ment. It is organized in this way for the purpose of economy. 
Each department is conducted as a separate store, and is 
in charge of a buyer, who both buys and plans the sales 
for his department. His department is charged for rent, 
according to its location, and must also pay for overhead 
charges. 

The buyer in charge of each department has under him 
salesgirls or saleswomen, who sell the goods. Each salesgirl 
has a book containing sales slips in duplicate and a card to 
show the amount of sales. 

The sales slip shows the name and address of the purchaser 
if the merchandise is to be sent to the customer's home. In 
the case of a charge accoimt a special form of sales slip is 
used. The name and quality of the article purchased are 
written in large space and the amoimt extended to th^ right. 
The amount of money received from the purchaser is placed 
at the top of the sales slip. 

A carbon copy of each sales slip is made. The carbon copy 

is given to the customer and the original is sent with the money 

to the cashier. It is then used to tabulate data in regard to 

sales, etc. 

260 



ARITHMETIC FOR SALESGIRLS AND CASHIERS 261 



8606 ^^^^^*' ^^^'^ ^^-- 

Name 

Address — , 



80LD 
BY... 



Pur. by 



Ha- 



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oo'S 



lis- 



D 

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AMT 
REC'D. 



Am't Rec'd Sold by Am't of Sile 



8606 




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J. n. BmBRSOBi CO. 

8606 ^^^^^*' ^^^-^ ^^-- 



Name- 
Addrei 

80LI 
BY.. 








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3 P AMT 
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Oustamerit loiU please report any failure 
to deliver bill vdth goods 



Tkis Slip miut go in CDRtAiner'i Ptreel. ViolfttioB 
of tiis Knle is cane for Initaiit DlimiiMl 



1 



Department. 



SaIjESMAN- 











Date 








Cash Sales 


Charge Sales 




Cash Sales 


Charge Sales 


1 












Forward 






2 










10 










3 










11 










4 










12 










5 










13 










6 










14 










7 










15 










8 










16 




• 






9 










17 











262 VOCATIONAL MATHEMATICS FOR GIRLS 

Salesgirls should be able to do a great many calculations at 

sight. This ability comes only through practice. 

EXAMPLES 

Find the amount of the following : 

1. 10 yd. percale at 12^ cents. 

2. 12 yd. voile at 16 1 cents. 

3. 27 yd. silesia at 33^ cents. 

4. 60 yd. serge at $ 1.50. 

5. 28 yd. mohair at $ 1.25. 

6. 48 yd. organdie at 37^ cents. 

7. 91|^ yd. gingham at 10 cents. 
a 112 yd. calico at 4^ cents. 

9. 36 yd. galatea at 16 cents. 

10. 11 yd. lawn at 19 cents. 

11. 64 yd. dotted muslin at 62^ cents. 

12. 24 yd. gabardine at $ 1.75. 

13. 18 yd. poplin at 29 cents. 

14. 16 yd. hamburg at 15 cents. 

15. 12 yd. lace at 87^ cents. 

16. 19 yd. val lace at 9 cents. 

17. 26 yd. braid at 26 cents. 

18. 48 dz. hooks and eyes at 12 centSo 

19. 19 yd. cambric at 15 cents. 

20. 18 pc. binding at 16 cents. 

21. 6 yd. canvas at 24 cents. 

22. 56 yd. linen at 62^ cents. 

23. 18 yd. albatross at $ 1.60. 

24. 22 yd. silk at $ 2.25. 



ARITHMETIC FOR SALESGIRLS AND CASHIERS 263 

PROBLEMS 

1. I bought cotton cloth valued at $ 6.25, silk at $ 13.75, 
handkerchiefs for $ 2.50, and hose for $ 2.75. What was the 
whole cost ? 

' • • 

2. Ruth saved $ 15.20 one month, $ 20.75 a second month, 
and the third month $4.05 more than the first and second 
months together. How much did she* save in the three 
months ? 

3. Goods were sold for $ 367.75, at a loss of $ 125. Find 
the cost of the stock. 

4. Goods costing $ 145.25 were sold at a profit of $ 28.50. 
For how much were they sold ? 

' 5. A butcher sold 8f pounds of meat to one customer, 
9^ pounds to a second, to the third as much as the first plus 
1^1^ pounds, to a fourth as much as to the second. How many- 
pounds did he sell ? 

6. Edith paid $ 42.75 for a dress, one-half as much for a 
cloak, and $ 7.25 for a hat. How much did she pay for all ? 

7. A merchant sold four pieces of cloth; the first piece 
contained 24 yards, the second 32 yards, the third 16 yards, 
and the fourth five-eighths as many yards as the sum of the 
other three. How many yards were* sold? 

8. From a piece of cloth containing 65f yards, there were 
sold 23;J^ yards. How many yards remained ? 

9. A merchant sold goods for $ 528.40 and gained $ 29.50. 
Find the cost. 

10. From 11 yards of cloth, 3f were cut, for a coat, and 
6^ yards for a suit. How many yards remained ? 

11. I bought 15 cuts of cloth containing 40^ yards each at 
7 cents a yard and sold it for 9 cents a yard. What was the 
gain? 



264 VOCATIONAL MATHEMATICS FOR GIRLS 

12. What is the cost of 13| yards of silk at $ 3.76 per yard ? 

13. What is the cost of 16^ yards of broadcloth at $ 2.25 
per yard ? 

14. What is the cost of 3 pieces of cloth containing 12f , 
14 J, and 15^ yards at 12^ cents per yard ? 

15. What will 6| yards of velvet cost at $ 2.75 per yard ? 

16. What is the cost of three-fourths of a yard of crgpe de 
chine at $ 1.75 per yard ? 

17. A saleslady is paid $1.00 per day for services and a 
bonus of 2 % on all sales over $ 50 per week. If the sales 
amount to $ 175 per week, what will be her salary ? 

18. At $ 1.33^ a yard, how much will 15 yards of lace cost ? 

19. At $ 1.16| a yard, how much will 9 yards of silk cost ? 

20. At $ 1.12^ per yard, how much will 6 yards of velvet 
cost ? 

21. At 33^ cents each, find the cost of 101 handkerchiefs. 

22. A salesgirl sold 14|^ yards of gingham at 25 cents, 9 
yards of cotton at 12^ cents, 10^ yards of Madras at 35 cents. 
Amount received, $ 10. How much change will be given to the 
customer ? 

23. Sold 6^ yards of cheviot at $ 1.10, 5f yards of silk at 
$ 1.25, 9^ yards of velveteen at 98 cents. Amount received, 
$ 25.00. How much change will be given to the customer ? 

24. Sold 11^ yards of Persian lawn at $ 1.95, 6f yards of 
dimity at 25 cents, 12|^ yards of linen suiting at 75 cents. 
Amount received, $ 40. How much change will be given to 
the customer ? 

25. Sold 9^ yards of Persian lawn at $ 1.37^, 5\ yards of 
cheviot at $ 1.25, 15 yards of cotton at 12|^ cents. Amount 
received, $30. How much change will be given to the cus- 
tomer ? 



ARITHMETIC FOR SALESGIRLS AND CASHIERS 265 

26. Sold 7 yards of muslin at 25 cents, 12^ yards of lining 
at 11 cents, 6f yards of lawn at $ 1.50, 7 yards of suiting at 
75 cents. Amount received, $ 20. How imucli change will be 
given to the customer ? 

27. Sold 16 yards of velvet at $ 2.25, 14^ yards of suiting 
at 48 cents, 23 yards of cotton at 15 cents, 6f yards of dimity 
at 24 cents, 7^ yards of ribbon at 25 cents. Amount received, 
$ 50. How much change will be given to the customer ? 

2a At 12^ cents a yard, what will 8f yards of ribbon cost ? 

29. At $ 2.50 a yard, what will 2.8 yards of velvet cost ? 

30. If it takes 5^ yards of cloth for a coat, 3J yards for a 
jacket, and ^ a yard for a vest, how many yards will it take 
for all ? 

31. I gave $ 16.50 for 33 yards of cloth. How much did 
one yard cost ? 

32. Mary went shopping. She had a $ 20 bill. She bought 
a dress for $ 9.50, a pair of gloves for $ .75, a fan for $ .87, 
two handkerchiefs for $ .37 each, and a hat for $ 4.50. How 
much money had she left ? 

33. Emma's dress cost $ 11.25, and Mary's cost | as much. 
How much did Mary's cost? How much did both cost ? 

34. What is the cost of 16f yards of silk at $ 2.75 a yard ? 

35. What is the cost of 14^ yards of cambric at 42 cents a 
yard ? 

36. If 5| yards of calico cost 33 cents, how much must be 
paid for 14| yards ? 

37. One yard of sheeting cost 22| cents. How many yards 
can be bought for $ 15.15 ? 

38. From a piece of calico containing 33|^ yards there have 
been sold at different times llf , 7f , and 1^ yards. How many 
yards remain ? 



266 VOCATIONAL MATHEMATICS FOR GIRLS 

39. I bought 16 J yards of cloth for $ 3J per yard, and sold 
it for $ 4^ per yard. What was the gain ? 

40. A merchant has three pieces of cloth containing, respec- 
tively, 28|, 35^, and 41 1 yards. After selling several yards 
from each piece, he finds that he Has left in the three pieces 
67 yards. How many yards has he sold ? 

* 

ARITHMETIC FOR CASHIER 

How to Make Change. — Every efficient cashier or saleslady 
makes change by adding to the amount of the sale or purchase 
enough change to make the sum equal to amount presented. 
The change should be returned in the largest denominations 
possible. 

To illustrate : A young lady buys dry goods to the amount 
of $1.52. She gives the saleslady a $5 bill. What change 
should she receive ? 



iy will say: $1.52, $1.65, $1.66, $1.75, $2.00, $4.00, 
«6.00. That is, $1.62 + $.0.3 = $1.55; $1.65 -h $.10 = $ 1.65 ; $1.66 
^5; $1.76 + $.26 = $2.00; $2.00 + $2.00 = $4.00 ; $4.00 



The saleslady 
» 5.00. That is, ^ i.oz -\- ^ .u.> = ^ i.oo ; ^ i.oo + 
+ $.10 = $1.75; $1.76 + $.26 = $2.00; $2.00 + 
+ $1.00 = $5.00. 

EXAMPLES 

1. What change should be given for a dollar bill, if the 
following purchases were made ? 

a. $.87 c. $.43 e. $.20 

6. $.39 d. $.51 /. $.23 

2. What change should be given for a two-dollar bill, if the 
following purchases were made ? 



a. $1.19 


d. $1.57 


g* $ .63 


5. $.89 


e. $1.42 


h, $ .78 


c. $1.73 


/. $1.12 


i, $.27 



ARITHMETIC FOR SALESGIRLS AND CASHIERS 267 

3. What change should be given for a five-dollar bill, if the 
following pui'chases were made ? 

a. $3.87 d. $2.81 g. $1.93 

b. $2.53 e. $3.74 h, $.17 

c. $4.19 /. $4.29 I $.47 

4. What change should be given for a ten-dollar bill,, if the 
following purchases were made ? 

a. $8.66 d. $6.23 g. $3.16 

b. $9.31 e. $5.29 h. $2.29 

c. $ 7.42 /. $ 4.18 i. $ 1.74 

5. What change should be given for a twenty-dollar bill, if 
the following purchases were made ? 

a. $18.46 c. $17.09 e. $8.01 

b. $19.23 d $12.03 /. $6.27 



CHAPTER XIII 

CIVIL SERVICE 

Almost every government position open to women has to be 
obtained through an examination. In most cases Arithmetic 
is one of the subjects tested. It is wise to know not only the 
subject, but also the standards of marking, and for this reason 
some general rules on this subject follow. 

Marking Arithmetic — Civil Service Papers 

1. On questions of addition, where sums are added across and the 
totals added, for each error deduct 16} ^o, 

2. For each error in questions containing simple multiplication or 
division, as a single process, deduct 50 9^ ; as a double process, deduct 

3. In questions involving fractions and problems other than simple 
computation, mark as follows : 

(a) Wrong process leading to incorrect result, credit 0. 
(6) For inconvenient or complex statement, process, or method, giving 
right result, deduct from 6 to 26 9^?. 

(c) If the answer is correct but no work is shown, credit 0. 

(d) If the answer is correct and the process is clearly indicated, but 
not written in full, deduct 26 ^o, 

(e) If no attempt is made to answer, credit 0. 

(/) If the operation is incomplete, credit in proportion to the work 
done. 

(g) For the omission of the dollar sign (|) in final result or answer, 
deduct 6. 

(h) In long division examples, to be solved by decimals, if the answer 
is given as a mixed number, deduct 26. 

4. For questions on bookkeeping and accounts, mark as follows : 

(a) For omission of total heading, deduct 25 ; for partial omission, a 
commensurate deduction. 

(b) For every misplacement of credits or debits, deduct 25. 

268 



CIVIL SERVICE 269 

(c) For every omission of date or item, deduct 10. 

(d) For omissions or misplacement of balance, deduct 26. 

NoTB. — Hard and fast rales are not always applicable because the impor- 
tance of certain mistakes differs with the type of example. Before, a set of 
examples is marked, the deductions to be made for various sorts of errors 
are decided upon by the examiners. In general, examples in arithmetic for 
high-grade positions are marked on practically the same basis as clerical 
arithmetic. Arithmetic in lower-grade examinations, such as police and fire 
service and the like, is marked about 60% easier than clerical. 

CIVIL SERVICE EXAMPLES 

(Give the work in full in each example.) 

1. Multiply 83,849,619 by 11,079. 

2. Subtract 16,389,110 from 48,901,001. 

3. Divide 18,617.03 by .717. 

4. At $0.37 per dozen, how many dozen eggs can be 
bought for $ 33.67 ? 

5. What would 372 pounds of com meal cost if 4 lb. cost 
12 cents ? 

6. If a man bought 394 cows for $ 23,640 and sold 210 
for $ 14,700, what was the profit on each cow ? 

7. What is the net amount of a bill for $ 93.70, subject to 
a discount of 37 J % ? 

8. How many pints in a measure containing 14,784 cubic 
inches ? 

9. What number exceeds the sum of its fourth, fifth, and 
sixth by 23 ? 

10. If a man's yearly income is $ 1600, and he spends $ 25 
a week, how much can he save in a year ? 

11. What will 16 J pounds of butter cost at 34 cents a pound ? 

12. How many hogs can be bought for $ 1340 if each hog 
averages 160 pounds and costs 9 cents a pound ? 

13. How many tons of coal can be bought for $446.25, if 
each ton costs $ 8.76 ? 



270 VOCATIONAL MATHEMATICS FOR GIRLS 

14. A young lady can separate 38 letters per minute. If a 
letter averages 6^ ounces, how many pounds of mail does she 
handle in an hour ? 

15. Multiply 53| by 9f and divide the product by 2^. 
(Solve decimally.) ' 

16. Roll matting costs 73 J cents per sq. yd. What will be 
the cost of 47 rolls, each roll 60 yd. long and 36 in. wide ? 

17. A man paid $ 5123.25 for 27 mules and sold them for 
$ 6500. How much did he gain by the transaction ? 

18. A wheel measures 3' 7" in diameter. What is the dis- 
tance around the tire ? 

19. A bricklayer earns 70 cents an hour. If he works 129 
days, 8 hours a day, and spends $ 50 a month, how much does 
he save a year ? 

20. A rectangular courtyard is 48' 5" long and 23' 7" wide. 
How many square yards is it in area ? 

21. How many days will it take a ship to cross the Atlantic 
Ocean, 2970 miles, if the vessel sails at the rate of 21 miles an 
hour? 

22. Eleven men bought 7 tracts of land with 22 acres in 
each tract. How many acres will each man have ? 

23. A. merchant sends his agent $10,228 to buy goods. 
What is the value of the goods, after paying $ 28 for freight 
and giving the agent 2 ^o for liis commission ? 

24. If milk costs 6 cents a quart, and you sold it for 9 cents 
a quart, and your profit for the milk was $48, how many 
quarts of milk did you sell? 

25. A traveler travels llf miles a day for 8 days. How 
many more miles has he yet to travel if the journey is 134 
miles ? 

26. What is the net amount of a bill for $ 29.85, subject to 
a discount of 16| % ? 



CIVIL SERVICE 271 

27. Add across, placing the totals in the spaces indicated ; 
then add the totals and check : 

Totals 



8,431 


• 17,694 


18,630 


91 


707 


5,912 


305 


3,777 


871 


8,901 


6,801 


29,006 


5,891 


30 


16,717 


5,008 


10,008 


7,771 


144 


9,001 


13,709 


10,999 


39 


1,113 


3,444 



28. Divide 37,818.009 by .0391. 

29. A pile of wood is 136 ft. long, 8 ft. wide, and 6 ft. high, 
and is sold for $ 4.85 per cord, which is 20 % more than the 
cost. What is the cost of the pile ? 

30. Add the following column and from the sum subtract 
81,376,019 : 

80,614,304 
68,815,519 
32,910,833 
54,489,605 
96,315,809 
75,029,034 
21,201,511 

31. A man bought 128 gal. cider at 23 cents a gallon ; he 
sold it for 28 cents a gallon. How much did he make ? 

32. A laborer has $48 in the bank. He is taken sick and 
his expenses are $ 7.75 a day. How many days will his fund 
last? 

33. In paving a street If mi. long and 54 ft. wide, how 
many bricks 9 in. long and 4 in. wide will be required ? 

34. Find the simple interest on $ 841.37 for 2 yr. 3 mo. 17 da. 
at 5%. 

35. Find the simple interest on $ 367.49 for 1 yr. 7 mo. 19 da. 
at 4 %. 



272 VOCATIONAL MATHEMATICS FOR GIRLS 

SPECDfEN ARITHMETIC PAPERS 

Clerks, Messengers, etc. 

Rapid Computation 

1. Add these across, placing the totals in the spaces in- 
dicated ; then add the totals : 



16,863 


3,176 


368 


61,461 


36,196 


Totals 
27,368 


7,242 


82,463 


24,176 


62,837 


3,724 


61,493 


68,317 


68,417 


41,682 


4,738 


16,837 


6,281 


62,683 


26,364 


73,642 


26,164 


42,626 


70,463 


1,476 


18,672 


7,368 


16,726 


71,394 


62,968 



2. Multiply 82,473,659 by 9874. Give the work in full. 
3. From 68,515,100 subtract 24,884,574. Give the work in 
full. 4. Divide 29,379.7 by .47. Give the work in full. 

5. What is the net amount of a bill for $19.20, subject to a 
discount of 16| % ? Give the work in full. 

Arithmetic 

1. How many times must 720 be added to 522 to make 
987,642 ? Give the work in full. 2. If the shadow of an up- 
right pole 9 ft. high is 8^ ft. long, what is the height of a church 
spire which casts a shadow 221 ft. long ? Give the work in full. 
3. How many sods, each 8 in. square, will be required to sod a 
yard 24 feet long and 10 feet 8 inches wide ? Give the work 
in full. 4. A retired merchant has an income of $ 25 a day, 
his property being invested at 6 %. What is he worth ? Give 
the work in full. 5. Find the principal that will yield $ 38.40 
in 1 yr. 6 mo. at 4 % simple interest. Give the work in full. 

6. If the time past noon increased by 90 minutes equals ^ 
of the time from noon to midnight, what time is it ? Give the 
work in full. 7. A merchant deducts 20 % from the marked 
price of his goods and still makes a profit of 16 % . At what 



CIVIL SERVICE 273 

advance on the cost are the goods marked? Give the work 
in full. 8. If a grocer sells a tub of butter at 22 cents a pound, 
he will gain 168 cents, but if he sells it at 17 cents a pound, he 
will lose 112 cents. Find (a) the weight of the butter and (6) 
the cost per pound. Give the work in full. 9. The product of 
four factors is 432. Two of the factors are 3 and 4. The other 
two factors are equal. What are the equal factors ? Give the 
work in full. 

Stenographer-Typewriter 

1. From what number can 857 be subtracted 307 times and 
leave a remainder of 49 ? Give the work in full. 

2. What number exceeds the sum of its fourth, fifth, sixth, 
and seventh parts by 101 ? Give the work in full. 

3. A sells to B at 10'% profit; B sells to C at 5 % profit; 
if C paid $ 5336.10, what did the goods cost A ? Give the 
work in full. 

4. Find the simple interest of $ 297.60 for 3 yr. 1 mo. 15 da. 
at 6 %. Give the work in full. 

5. A man sold \ of his farm to B, ^ of the remainder to C, 
and the remaining 60 acres to D. How many acres were in 
the farm at first ? Give the work in full. 

« 

Sealers op Weights and Measures 
(Keview Weights and Measures, pages 43, 276) 

1. A measure under test is found to have a capacity of 
332.0625 cu. in. What is its capacity in gallons, quarts, etc. ? 
Give the work in full. 

2. How many quarts, dry measure, would the above meas- 
ure hold ? Give the work in full, carrying the answer to four 
decimal places, 

3. What is the equivalent of 175 lb. troy in pounds avoir- 
dupois ? Give the work in full. 1 av. lb. = 7000 grains.* 



274 VOCATIONAL MATHEMATICS FOR GIRLS 

4. How many grains in 12 lb. 15 oz. avoirdupois ? Give 
the work in full. 

5. Reduce 15 lb. 10 oz. 20 grains avoirdupois to grains 
troy weight. Give the work in full. 

6. What part of a bushel is 2 pecks and 3 pints ? Give 
the work in full and' the answer both as a decimal and as a 
common fraction. 

7. What will 10 bushels 3 pecks and 4 quarts of seed cost 
at $ 2.10 per bushel ? Give the work in full. 

8. What part of a troy pound is 50 grains, expressed both 
decimally and in the form of a common fraction ? 

9. A strawberry basket was found to be 65.2 cubic inches 
in capacity, (a) How many cubic inches short was it? 
(b) What percentage of a fidl quart did it contain ? Give the 
work in full. 

10. In testing a spring scale it was found that in weighing 
22 lb. of correct test weights on same, the scale indicated 
22 lb. 10^ oz. What was the percentage of error in this scale 
at this weight ? Give the work in full. 

Visitor 

1. A certain "home" had at the beginning of the year 
$ 693.07, and received during the year donations amoimting 
to $ 1322.48. The expenses for the year were : salaries, 
$387.25 ; printing, etc., $175 ; supplies, $651.15 ; rent, $104.25 
heat, etc., $ 75 ; interest, $ 100 ; miscellaneous, $ 72.83. Find 
the cash on hand at the end of the year. Give the work in 
fulL 

- 2. Of the 72,700 persons relieved in a certain state at public 
expense in the year ending March 31, 1912, 76 % were aided 
locally, and the remainder by the state. Find the number 
relieved by the state. Give the work in full. 



CIVIL SERVICE 275 

3. There was spent in state, city, and town public poor relief 
in Massachusetts in one year the sum of $3,539,036. The 
number of beneficiaries was 72,700. What was the average 
sum spent per person ? Give the work in full. 

4. Of the 72,900 persons aided by public charity in this 
state in a certain year -j^ were classed as sane. Of the re- 
mainder, ^ were classed as insane, J as idiotic, and the rest as 
epileptic. How many epileptics received public aid?. Give, 
the work in full. 



PART V — ARITHMETIC FOR JfURSES 

CHAPTER XIV 

A NURSE should be familiar with the weights and measures 
used in dispensing medicines. There are two systems used — 
the English, based on the grain, and the Metric system, based 
on the meter. 

Apothecaries^ Weight 
(Troy Weight) 

20 grains (gr.)= 1 scruple (3) 

8 3 =ldram (3)=60gr. 

8 3 =1 ounce ( 3 ) = 24 3 = 480 gr. 

12 3 =1 pound (»))= 96 3 = 288 3 = 5760 gr. 

The number of units is often expressed by Roman numerals 
written after the symbols. (See Roman Numerals, p. 2.) 

EXAMPLES 

1. How many grains in iv scruples ? 

2. How many grains in iii drams ? 

3. How many grains in iv ounces ? 

4. How many scruples in lb i ? 

5. How many grains in lb iii ? 

6. How many drams in lb iv ? 

7. How many grains in 3 ii ? 

8. How many scruples in 5 v ? 

9. How many drams in 5 vii ? 

10. How many ounces in lb viii ? 

276 



ARITHMETIC FOR NURSES 277 

U. Salt S i will make how many quarts of saline solution, 
gr. xc to qt. 1 ? 

12. How many drams of sodium carbonate in 10 powders of 
Seidlitz Powder ? Each powder contains gr. xl. 

Apothecaries^ Fluid Measure 

60 minims (m) = 1 fluid dram = (f 3 ). 

8f 3 =1 fluid ounce (f 3). 

16 f 3 =1 pint (O) = 128 f 3 = 7680 m. 

8 =1 gaUbn (C) = 128 f 3 =1024 f 3 . 

EXAMPLES 

1. How many minims in f 3 iv ? 

2. How many minims in f 5 iii ? 

3. How many fluid drams in 1 ? 

4. How many minims in 5 pints ? 

5. How many pints in 8 gallons ? 

6. How many fluid drams in ii ? 

7. How many minims in f 5 viii ? 

8. How many fluid drams in C vii ? 

9. How many pints in C v ? 

10. How many minims in f 5 ix ? 

11. If the dose of a solution is m xxx and each dose contains 
^^ gr. strychnine, how much of the drug is contained in f 5 i 
of the solution ? 

12. 3 ii of a solution contains gr. i of cocaine. How much 
cocaine is given when a doctor orders m x of the solution ? 

Approximate Measures of Fluids 

(With Household Measures) 

* 

An ordinary teaspoonful is supposed to hold 60 minims of 
pure water and is approximately equal to a fluid dram. A 



278 VOCATIONAL MATHEMATICS FOB GIRI^ 

drop is ordinarily considered equiTalent 
to a minim, but this is only approxi- 
mately true in the case of water. The 
specific gravity, shape, and surface ftom 
which the drop is poured influence the 
size. In preparing medicines to be 
taken internally, minima should never 
be measured out as drops. There are 
minim droppers and measures for this 
purpose. 

A level teaspoonful of either a fluid 

or solid preparation is equal to a dram. 

Level spoonfuls are always considered 

A Qkaddatb. 



1 teaspoonful = 1 fluid dram. 

1 dessertspoonful = 2 fluid drHjns. 

I tablespoonful = 4 fluid drams or } fluid ouDce. 

1 wineglassful = 2 fluid ounces. 

1 teacupful — fluid ounces. 

1 tumblerful = 8 fluid ounces. 

EXAMPLES 

1. How many dessertspoonfuls in 8 fluid ounces? 

2. How many wineglassfuls in 2 tumblerfuls ? 

3. How many tablespoonfuls in 3 fluid drams ? 

4. How many teaspoonfuls in 6 fluid ounces ? 

5. How many teacupfuls in 4 fluid drams ? 

6. How many dessertspoonfuls in 6 fluid drams ? 

7. How many teaspoonfuls in 1 gallon ? 

8. How many drops of water in 1 quart ? 

9. How many teaspoonfuls in 3 ounces ? 
10. How many minims in 3 pints ? 



ARITHMETIC FOR NURSES 279 

U. What household measure would you use to make a solu- 
tion, 3 i to a pint ? 

12. Read the following apothecaries' measurements and give 
their equivalents : 

a, 3 iv. /. 3 ss.^ 

6. gr. V. g. iv. 

c. ii. h, 3 ii. 

d. 5 ii« *• 5 iv. 

e. 5 ij. j. 5 ss. 

Metric System of Weights and Measures 

(Review Metric System in Appendix.) 

The metric system of weights and measures is used to a 
great extent in medicine. The advantage of this system over 
the English is that, in preparing solutions, it is easy to change 
weights to volumes and volumes to weights without the use of 
common fractions. 

In medicine the gramme (so written in prescriptions to 
avoid confusion with the dram) and the milligramme are the 
chief weights used. 

1 gramme = wt. of 1 cubic centimeter (cc. ) of water at 4° c. 

1000 grammes = 1 kilogram or ** kilo.** 

1 kilogram of water = 1000 cc. = 1 liter. 

Conversion Factobs 

1 gramme = 16.4 or approx. 16 grains. 

1 grain = 0.064 gramme. 

1 cubic centimeter = 16 minims. 

1 minim = 0.06 cc. 

1 liter = 1 quart (approx.). 

The liter and cubic centimeter are the principal units of 
volume used in medicine. 

^ ss means one-half. 



280 VOCATIONAL MATHEMATICS FOR GIRLS 

A micro-millimeter is used in measuring microscopical dis- 
tances. It is j^ mm. and is indicated by the Greek letter /lu 

To convert cc. into minims multiply by 15. 
To convert grammes into drams divide by 4. 
To convert cc. into ounces divide by 30. 
To convert minims into cc^ divide by 16. 
To convert grains into grammes divide by 15. 
To convert fluid drams into cc. multiply by 4. 
To conveH drams into grammes multiply by 4. 

1 grain = 0.064 gramme. 

2 grains = 0.1 gramme. 
5 grains = 0.3 gramme. 
8 grains =0.5 gramme. 

10 grains = 0.6 gramme. 

15 grains = 1 gramme. 

1 milligramme = 0.01^ grain. 

Review Troy (apothecary) and avoirdupois weights, pages 
43 and 276. 

EXAMPLES 

1. A red corpuscle is 8 ft in diameter. Give the diameter in 
a fraction of an inch. 

2. A microbe is ^5^00 ^^^^ ^ diameter. What part of a 
millimeter is it ? 

3. Another form of microbe is ^^^^^ of an inch in diameter. 
What part of a millimeter is it ? 

4. A bottle holds 48 cc. What is the weight of water in the 
bottle when it is filled ? 

5. How many liters of water in a vessel containing 4831 
grams of water ? 

6. Give the approximate equivalent in English of the 
following : 

a. 48 grammes d, 8 kilos 

6. 3.6 kilograms e. 3:9 grammes 

c. 3.5 liters /. 53 milligrammes 



ARITHMETIC FOR NURSES 281 

7. Give the approximate equivalents in the metric system 
of the following : 

tt. 39 grains ^ e. 13 quarts 

b. 4 drams /. 2 gallons 

c. 7 fluid drams g, 39 minims 

d. 47 lb h, 8321 grains 

Approximate Equivalents between Metric and Household 

Measures 

• 

1 teaspoonful = 4 cc. or 4 grams of water. 
1 dessertspoonful = 8 cc. or 8 grams of water. 
1 tablespoonful = 16+ cc. or 15+ grams of water. 
1 wineglassful = 60 cc. or 60 grams of water. 
1 teacupful = 180 cc. or 180 grams of water. 

1 glassful = 240 cc. or 240 grams of water. 

EXAMPLES 
(Give approximate answers.) 

1. What is the weight of two glassfuls of water in the 
metric system ? 

2. What is the weight of a gallon of water in the metric 
system ? 

3. What is the weight of three liters of water in the 
English system ? 

4. What is the volume of four ounces of water in the 
metric system ? 

5. What is the volume of twelve cubic centimeters of water 
in the English system ? 

6. What is the volume of f 3 iii in the metric system ? 

7. What is the volume of eighty grammes of water ? 
• 8. What is the weight of 360.1 cc. of water ? 

9. What is the volume of 4 kilos of water ? 

10. What is the weight of 6.1 liters of water ? 

11. With ordinary household measures how would you 
obtain the following : 5 gm., m xv, 1.5 L., 25 cc, S ii, f 5 ss ? 



282 VOCATIONAL MATHEMATICS FOR GIRLS 

METRIC SYSTEM 

EXAMPLES 

1. Change the following to milligrammes : 
8 gm., 17 dg., 13 gm. 

2. Change the following to grammes : 
13 mg., 29 dg., 7 dg., 21 mg. 

3. Add the following : 

11 mg., 18 dg., 21 gm., 4.2 gm. 

Express answer in grammes. 

4. Add the following : 

25 mg., 1.7 gm., 9.8 dg., 21 mg. 

Express answer in milligrammes. 

5. The dose of atropine is 0.4 mg. What fraction of a 
gramme is necessary to make 25 cc. of a solution in which 1 cc. 
contains the dose ? 

6. Give the equivalent in the metric system of the following 
doses : 

a. Extract of gentian, gr. ^. 

6. Tincture of quassia, 3 i. 

c. Tincture of capsicum, m iii. 

d. Spirits of peppermint, 3 L 

e. Cinnamon spirit, m x. 
/. Oil of cajuput, m xv. 

g. Extract of cascara sagrada, gr. v. 
h. Eluid extract of senna, 3 ii. 
i. Agar agar, 5 ss. 

7. Give the equivalent in the English system of the follow- 
ing doses : 

a. Ether, 1 cc. 

b. Syrup of ipecac, 4 cc. 

c. Compound syrup of hypophosphites, 4 cc. 



ARITHMETIC FOR NURSES 283 

d, Pancreatin, 0.3 gm. 

e. Zinc sulphate, 2 gm. 

/. Copper sulphate, 0.2 gm. 

gr. Castor oil, 30 ee. 

h. Extract of rhubarb, 0.6 gm. 

i. Purified aloes, 0.5 gm. 

DOSES 

Since all drugs are harmful or poisonous in sufficiently large 
quantities, it is necessary to know the least amount needed to 
produce the desired change in the body — the minimum dose. 
This has been ascertained by careful and prolonged experiments. 
Similar experiments have told us the largest amount of drug 
that one can take without producing dangerous effect — the 
maximum dose. 

On the average, children under 12 years of age require smaller 
doses than adults. To determine the fraction of an adult dose 
of a drug to give to a child, let the child's age be the numer- 
ator, and the sum of the child's age plus twelve be the denomina- 
tor of the fraction. For infants under one year, multiply the 

adult dose by the fraction ^ge in months , 
•^ 150 

To illustrate: How much of a dose should be given to a 

child of four ? 

Age of child = 4. 

Age of child + 12 = 16. 

Fraction of dose ^ = J. Ans. J of a dose. 

EXAMPLES 

1. What is the fraction of a dose to give to a child of 8 ? 

2. What is the fraction of a dose to give to a child of 6 ? 

3. What is the fraction of a dose to give to a child of 3 ? 

4. What is the fraction of a dose to give to a child of 10 ? 



284 VOCATIONAL MATHEMATICS FOR GIRLS 

5. If the normal adult dose of aromatic spirits of ammonia 
is 1 dram, what is the dose for a child of 7 ? 

6. If the normal adult dose of castor oil is one-half ounce, 
what is the dose for a child of 6 ? 

7. If the normal adult dose of epsom salts is 4 drams, 
what is the dose for a child of 4 ? 

8. If the normal adult dose of strychnine sulphate is ^^^ gr., 
what is the dose for a child of 8 ? 

9. If the normal adult dose of ipecac is 15 grains, what is 
the dose for a child of 11 ? 

10. If the normal adult dose of aromatic spirits of ammonia 
is 4 grammes, what is the dose for a child of 5 m'onths ? 

U. If the normal adult dose of ipecac is 1 gramme, what is 
the dose for a child 10 months old ? 

12, The normal adult dose of strychnine sulphate is 3.2 mg. 
How much should be given to a child 2 years old ? 

STRENGTH OF SOLUTIONS 

A nurse should know about the strength of substances used 
in treating the sick. Most of these substances are drugs which 
are prepared according to formulas given in a book called a 
Pharmacopoeia, Preparations made according to this standard 
are called official preparations, and often have the letters 
U. S. P. written after them to distinguish them from patented 
preparations prepared from unknown formulas. 

Drugs are applied in the following forms : solutions, lini- 
ments, oleates, cerates, powders, lozenges, plasters, ointments, 
etc. 

An infusion is a liquid preparation of the drug made by 
extracting the drug with boiling water. The strength of an 
infusion is 5% of the drug, unless otherwise ordered by the 
physician. 



ARITHMETIC FOR NURSES . 285 

The strength of a solution may be written as per cent or in 
the form of a ratio. A 10% solution means that in every 
100 parts by weight of water or the solvent there are 10 parts 
by weight of the substance. This may be written in form 
of a fraction — ^^^ or ^. In other words, for every ten parts 
of solvent there is one part of substance. Since a fraction may 
be written as a ratio, it may be called a solution of one to ten, 
written thus, 1 : 10. 

EXAMPLES 

1. Express the following per cents as ratios i 5%, 20%, 
2%, 0.1%, 0.01%. 

Since per cent represents so many parts per hundred, a 
ratio may be changed to per cent by putting it in the form 
of a fraction and multiplying by 100. The quotient is the per 
cent. 

2. Express the following in per cents : 1 : 4, 1 ; 3, 1 ; 6, 
1 : 15, 1 : 25, 1 : 40. 

3. Arrange the following solutions in the order of their 
strength : 3 %, 8 %, 24 %, 6 %, 1 : 10, 1 ; 14, 1 : 50, 40 %, 1 : 45, 
50%. 

4. Express the strength of the following solutions as per 
cents, and in ratios. 

a. 80 ounces of dilute alcohol contains 40 ounces of absolute 
alcohol. 

6. 6 pints of dilute alcohol contains two pints of absolute 
alcohol. 

5. Change the following ratios into per cents : 1 : 18, 1 : 20, 
1:5, 1 : 35, 1 : 100. Arrange in order, beginning with the 
highest. 

6. Change the following per cents to ratios: 33%, 12%, 
15%, .5%, 1%. 

7. Is it possible to make an 8 % solution from 4 % ? Ex- 
plain. 



286 VOCATIONAL MATHEMATICS FOR GIRLS 

8. Express the following strengths in terms of ratio : 

a. 25 CO. of alcohol in 100 cc. solution. 

b. 5 pints of alcohol in 3 qts. 

c. f S i contains f 3 iii. 

9. Express the following strengths in terms of per cent : 

a. 50 cc. of , solution containing 5 cc. of peroxide of hydrogen. 
6. f S iii of dilute alcohol containing ^ ii of pure alcohol. 

How to Make Solutions of Different Strengths from Crude 
Drugs or Tablets of Known Strengths 

Exact Method 

Illustrative Example. — How much water will be neces- 
sary to dissolve 5 gr. of powdered bichloride of mercury to 
make a solution of 1 part to 2000 ? 

Since the whole powder ia dissolved, 

1 part is 5 gr. 
2000 parts = 10,000 grains. 
480 gr. = 1 oz. 
82 oz. = 1 qt. 

^m^ = 20{. Approz. 21 oz. or 1^ pints of water should be used to 
dissolve it. 

The above example may be solved by proportion, when x = no. oz. of 
water necessary to dissolve powder ; then wt. of powder : drug ::x: water. 

,f ^ : 1 : : ac : 2000. 

^ ^ 5j<J000 ^ 125 ^ 20| oz. Approx. 21 oz. 
480 6 ' 

EXAMPLES 

Solve the following examples by analysis and proportion : 

1. How much water will be required to dissolve 5 gr. of 
powdered corrosive sublimate to make a solution of 1 part to 
1000? 



ARITHMETIC FOR NURSES 287 

2. How much water will be required to dissolve a TJ-grain 
tablet of corrosive sublimate to make a solution 1 part to 2000 ? 

Illustrative Example. — How much of a 40 % solution 
of formaldehyde should be used to make a pint of 1 : 500 
solution ? 

480 minims = 1 oz. 
7680 minims = 1 pint. 

^^ = I62V iiiinims = amt. of pure formaldehyde necessary to make a 
pint of 1 : 600. 

Since the strength of the solution is 40 9^, 15/^ minims represents but 
^ or f of the actual amount necessary. Therefore, the full amount of 
40 % solution is obtained by dividing by |. 

192 

^ X 2 = 1??= 38| minims to apmt. 

6 

To Determine the Amount of Orvde Drug tfecessary to Make a 
Certain Quantity of a Solution of a Given Strength 

To illustrate : To make a gallon of 1 : 20 carbolic acid solu- 
tion, how much crude carbolic acid is necessary ? 

1 : 20 : : X : 1 gal. 
1 : 20 : : 05 : 8 pints or 128 ounces. 
20 X = 128 ounces. 

a; = 6| ounces crude carbolic acid. 

EXAMPLES 

1. How much crude boric acid is necessary to make 6 pints 
of 5 % boric acid ? 

5 : 100 : : a : 6 pts. 
5 : 100 ::x: 576 drams. 
100 x = 2880. 

X = 28.8 drams. 

2. How much crude boric acid is necessary to make 2 quarts 
of 1 : 18 boric acid ? 



288 VOCATIONAL MATHEMATICS FOR GIRLS 

3. How much crude drug is necessary to make f S iii of 2 % 
cocaine? 

4. How many T^grain tablets are necessary to make 2 gal- 
lons of 1 : 1000 bichloride of mercury ? ^ 

5. How much crude drug is necessary to make O vi of 1 : 20 
phenol solution ? 

6. How much crude drug is necessary to make vii of 1 : 500 
bichloride of mercury ? 

7. How much crude drug is necessary to make iii of 1 : 10 
chlorinated lime ? 

Hypodermic Doses 

Standard strong solutions and pills are kept on hand in a 
hospital and from these weaker solutions are made as required 
by the nurse for hypodermic use. This is done by finding out 
what part the required dose is of the tablet or sol.ution on 
hand. The hypodermic dose is not administered in more than 
25 or less than 10 minims. The standard pill or solution is 
dissolved or diluted in about 20 minims and the fractional 
part, corresponding to the dose, is used for injection. 

To illustrate : A nurse is asked to give a patient ^kif S^^ 
strychnine. She finds that the only tablet on hand is -^ gr. 
How will she give the required dose ? 

TOTT "^ TIT == ^iir X 30 = T^. 

The required dose is ^^ of the stock pill. Therefore she dissolves the 
pill in 80 minims of water and administers 12 minims. The reason for 
dissolving in 80 rather than in 20 minims is to have the hypodermic 
dose not less than 10 minims. 

EXAMPLES 

1. Express the dose, in the illustrative example, in the 
metric system. 

^ Hospitals usually use 1 tablet for a pint of water to make 1 : 1000 solation. 



ARITHMETIC FOR NURSES 289 

2. How would you give a dose -^ gr. strychnine sulphate 
from stock tablet -^ gr,? 

3. How would you give gr. ^^y if only ^ grain were on 
hand? 

4. How would you give gr. ^, if only ^grain tablets were 
on hand? 

5. How would you give gr. ^, if only ^grain tablets were 
on hand? 

6. How would you give gr. -^^^ if only y^grain tablets were 
on hand ? 

7. How would you give gr. y^ ^^ atropine sulphate, if only 
y^grain tablets were on hand ? 

a How would you give gr. -^ of apomorphine hydrochloride 
if only iVgrain tablets were on hand ? 

To Estimate a Dose of a Different Fractional Part of a Grain 

from the Prepared Solution 

Nurses are often required to give a dose of medicine of a 
different fractional part of a grain from the drug they have. 

To illustrate : Give a dose of -^ gr. of strychnine when the 
only solution on hand is one containing -^ gr. in every 10 
minims. 

Since ^ grain is contained in 10 minims, 
1 grain or 30 x ^ grain is contained in 300 minims. 
Then, ^ of a grain is^of300 = |/5x300 = 12m. 

EXAMPLES 

1. What dose of a solution of 60 minims containing -^ gr. 
will be given to get y^ gr. ? 

2. Reckon quickly and accurately how much of a tablet 
gr. ^ should be given to have the patient obtain a dose gr. ^. 



290 VOCATIONAL MATHEMATICS FOR GIRLS 

3. What dose of a solution of m x containing gr. ^ morphine 
sulphate will be given to give gr. ^ ? 

4. What dose of a solution of m xx containing gr. -^ strych- 
nine sulphate will be given to give gr. ^ ? 

5. What dose of a solution of 1 cc. containing 0.1 cc. of the 
fluid extract of nux vomica will be given to give 0.06 cc. ? 

To Obtain a Definite Dose from a Stock Solution 

of Definite Strength 

To illustrate: To give a patient a ^grain dose when the 
stock solution has a strength of 1%. 

1 ^0 solution means that each drop of the solution contains j^ part or 

—^ of strychnine. 
100 

^ gr. is contained in as many drops as y^ is contained in it. 

A-T*7r=J^xlOO = 4. 
Therefore 4 drops of the 1 % solution contains '^ gr. 

EXAMPLES 

1. To give ^ gr. strychnine from 2 % solution. 

2. To give ^j gr. strychnine from solution containing in 
ten minims t^^ gr. 

3. To give 3 gr. of caffeinic sodium benzoate from a 25 % 
solution. 

4. To give Y^ir S^* ^^ atropine from 1 % solution. 

5. To give j^ gr. of strychnine from ^ % solution. 

6. To give -^jf gr. atropine from solution containing in ten 
minims -^ gr. 



ARITHMETIC FOR NURSES 



291 



n 



Temperature 

The temperature of the body is due to the combined activity 
of all its various systems but is regulated chiefly by the skin and 
circulatory system. It remains very nearly constant in the nor- 
mal person, in spite of the variations of the outdoor temperature. 
A variation of more than one degree from the normal tempera- 
ture, that is, above 99^° F. or below 97^® F., may be regarded as 
a sign of a disease. The temperature is obtained 
by means of a small thermometer — called a clinical 
thermometer. See Appendix, page 337, for descrip- 
tion of the different thermometers. 

Temperature readings are usually expressed in 
the Fahrenheit scale, but scientific data gathered 
in laboratories are expressed according to the Centi- 
grade scale. Therefore, we should be able to change 
readings from one scale to another. 

Fahrenheit readings may be obtained by adding 
32® to f of the Centigrade reading. This rule may 
be abbreviated into a formula as follows ; 

i^=|C+32°, 

where F = Fahrenheit reading, 
C = Centigrade reading. 

• Centigrade readings may be obtained by sub 
tracting 32° from the Fahrenheit and taking ^ of 
the remainder. This may be abbreviated into a 
formula as follows : 



HTr 



0=1(2^-32°). 



Clinical 
Thbbmom- 

BTEB 



EXAMPLES 



1. Albumin is coagulated by heat at 165** F. What is the 
degree Centigrade ? 



292 VOCATIONAL MATHEMATICS FOR GIRLS 

2. When milk is heated above 170® F., the albumin coagulates 
and forms a scum on the milk. To what degree on Centigrade 
scale does this correspond ? 

3. Egg albumin (white of egg) coagulates at 138** F. At 
what degree on the Centigrade scale ? 

4. Milk is pasteurized by bringing milk in the bottle to a 
temperature of 165® F. To what degree on the Centigrade 
scale? 

5. " Gentle heat " is a term used to denote the temperature 
between 32® to 38° C. What are the corresponding degrees on 
the Fahrenheit scale ? 

Baths 

(Change the following temperatures to Centigrade scale.) 

A bath with a temperature between 33® and 65® F. is known 
as a cold bath. 
A bath with a temperature between 65® and 75® F. is known 

as a cool bath. 

A bath with a temperature between 75® and 85® F. is known 
as a temperate bath. 

A bath with a temperature between 85^ and 92® F. is known 
as a t^id bath. 

A bath with a temperature between 92® and 98® F. is known 
as a warm bath. 

A bath with a temperature between 98® and 112® F. is known 
as a hot bath. 

Medical Chart (Graph) 

(See Graphs in the Appendix.) 

In order to follow the condition of a patient from day to 
day, the temperature, the pulse beats, and respirations are 
recorded morning and night on a special ruled chart. The 
name of the patient is placed on each chart. 



ARITHMETIC FOR NURSES 



293 



NAMtf.. 



WARD.. 



OATS.. 



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40* 

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lor 








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TOP 






































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180 
140 
ISO 

110 
110 
MA 












































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4... 


































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WW 

to 
































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TO 

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294 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Chart the following case of pneumonia : 





Morning 


Evening 


2 day 


102° 


104° 


3 day 


102.6° 


106° 


4 day 


102.4° 


104.2° 


5 day 


102.4° 


103.6° 


6 day 


102.4° 


104° 


7 day 


102.4° 


104.4° 


8 day 


101.8° 


103° 


9 day 


102.9° 


104° 


10 day 


102° 


102.8° 


11 day 


98.4° 


98.5° 


12 day 


97.4° 


98.2° 


13 day 


97.4° 


98.2° 


14 day 


98.2° 


98.4° 



PROBLEM^ IN HOUSEHOLD CHEMISTRY 

Bacteria are low forms of vegetable and animal life, and some 
are capable of producing disease. 

Chemicals that are employed to destroy bacteria are known 
as germicides. Those which limit the growth or destructive 
power of bacteria are called antiseptics. Deodorants remove or 
neutralize unpleasant odors. 

1. Bacteria multiply in all temperatures between 2® and 
70° C. What are the temperatures in the Fahrenheit scale 
within which bacteria will grow ? 

2. Creolin is used as a germicide and deodorant for offen- 
sive wounds in solutions of from 2 to 5 %. The creolin must 
never be added to water over 98° C, as its strength is impaired. 
What is the corresponding temperature on the Fahrenheit 
scale ? 

3. The most important medium or preparation for growing 
bacteria is nutrient bouillon. It is made of the following : 



ARITHMETIC FOR NURSES 295 



Meat extract 


5 grams 


Peptone 


10 grams 


Salt 


6 grams 


Water 


inter 



Wliat per cent of each ? 

4. A sugar bouillon culture is used for artificially cultivat- 
ing bacteria. It is made by adding 1 % of glucose to nutrient 
bouillon. How many grams of glucose to a liter of solution ? 

5. Carbolic acid is bought by hospitals in a 95 ^J solution 
and diluted as required. A solution of carbolic acid 1 : 20 is 
used to destroy germs. How much 95 ^o solution will be 
required to make 5 gallons 1 : 20 ? 

6. 1 : 1000 solution means how many grams to the gallon ? 

7. A normal salt solution is made by dissolving 9 grams 
of salt to the quart. How many teaspoonfuls to the quart ? 
How many grains to the quart ? 

8. What is the ratio of a pure drug ? What is the per- 
centage of purity of a pure drug ? 

9. If I desire to make a lotion of 1 : 1000 corrosive subli- 
mate, how much of the substance would be added and how 
much water used ? 

10. How much water and corrosive sublimate are required 
for a gallon of the following strengths? 

a. 1:2000. d 1:20,000. 

6. 1:4000. e. 1:100,000. 

c. 1:10,000. /. 1:150,000. 

11. A saturated solution of boric acid may be* made by dis- 
solving 3 V to pint (0 i) of water. What is the per cent of the 
saturated solution ? 

12. A saturated solution of KMn04 may be made by dis- 
solving I i to i ? What is the per cent ? 

13. How much of the saturated solution should be added to 
water i to make 1 % solution ? 



296 VOCATIONAL MATHEMATICS FOR GIRLS 

Water Analysis 

Every nurse should be able to interpret a biological and 
chemical analysis of water. 

Terms used in Chemical and Bacteriological Reports 

The following brief explanation of the terms used in chemi- 
cal and bacteriological examinations of water is given in order 
that the reports of analyses of samples may be clearly imder- 
stood. As the quantities to be obtained by analyses are usu- 
ally very small, they are ordinarily expressed in parts per 
million (p. p. m.), and always by weight. 

Turbidity of water is caused by fine particles such as clay, 
silt, and microscopic organisms. 

Sediment is self-explanatory. The amount and nature of 
the sediment are usually noted. 

Color is measured by comparing the sample with artificial 
standards made by dissolving certain salts in distilled water, 
or sometimes with colored gla^s disks. The color of large 
lakes is usually below 0.10. 

Odor, This requires no explanation. 

Residue on Evaporation^ or Total Solids, indicates the total 
solid matter, both organic and inorganic, in 1,000,000 parts 
of water. The determination is made by placing about 100 
grams of water in a platinum dish and weighing the whole 
accurately. The water is then evaporated to dryness by mod- 
erate heat and the dish again weighed ; the difference between 
this and the weight of the empty dish gives the total solids in 
the water. The dish is then heated red hot, to bum out the 
organic matter, when the weight of the remaining ash gives 
the inorganic or fixed solids. The loss on ignition, sometimes 
reported, is a measure of the organic solids. 

Ammonia. Ammonia in water indicates the presence of 
organic matter in an advanced stage of decay, and although 



ARITHMETIC FOR NURSES 297 

the amount is small, it affords a valuable indication of what 
is going on in the water. It is determined in two forms, 
called "free" and "albuminoid." 

Free Ammonia is that which has actually been set free in 
the water in the process of decay of organic matter, while 
Albuminoid Ammonia is that which has not yet been set free, 
but which is liable to be freed under the action of the oxygen 
in the water. The sum of the two gives an indication of the 
total amount of organic matter in the water. 

Water which has 0.05 p. p. m. of free ammonia is probably 
pure, while if it has more than 0.1 p. p. m., it is perhaps dan- 
gerous. A low figure for albuminoid ammonia is 0.06 p. p. m., 
and a high one is 0.60. 

Chlorine in water usually represents sodium chloride, or 
common salt. It may be due to sewage pollution or to near- 
ness to the ocean. It is always found in natural waters, the 
normal amount decreasing from the seacoast inland. If the 
amount exceeds 20 p. p. m., it may cause corrosion in boilers 
and plumbing fixtures. Properly interpreted, the chlorine 
content is one of the most useful indexes of the extent of 
sewage pollution. 

Nitrogen is usually determined in the form of nitrates and 
nitrites, the former being the final result of decomposition, 
while the latter is the incomplete result of the same action. 
If an analysis shows the ammonia to be low and the nitrates 
high, it indicates that the water has become completely puri- 
fied, while the reverse indicates that the decaying process 
is going on and the water is dangerous. In good drinking 
water the nitrates may be as high as 1 or 2 p. p. m., while 
the nitrites, if present, are practically always a sign of pol- 
lution. 

Oxygen Consumed. This is the amount of oxygen absorbed 
by the water from potassium permanganate. As the oxygen 
is absorbed by the organic matter present in the water, the 
amount consumed gives a measure of the amount of impurities 



298 VOCATIONAL MATHEMATICS FOR GIRLS 

contained in it. Less than 1 p. p. m. indicates probable pur- 
ity, while as high as 4 or 5 p. p. m. indicates danger in drink- 
ing water. 

Hardness, A water is said to be " hard " when it contains 
in solution the carbonates and sulphates of calcium or mag- 
nesium. When a hard water is used for washing, these salts 
have to be decomposed by soap before a lather can be formed. 
In boilers, a hard water forms scale. Hardness is expressed 
by the number of parts of calcium carbonate in 1,000,000 
parts of water. Rain water has a hardness of about 5, and 
river waters of from 50 to 100. 

Iron may be troublesome in a water used for domestic pur- 
poses if it is present in quantities greater than 0.3 to 0.5 
p. p. m. 

Alkalinity or Temporary Hardness is that part of the total 
hardness which is due to carbonates removable by boiling, thus 
causing the formation of scale. For purposes of softening 
water for boiler use, it is necessary to know both the total 
hardness and the alkalinity. 

Bacteria, While it is obvious that the quality of a water of 
turbid appearance and unpleasant odor is suspicious, it does 
not follow that it is dangerous, nor is a water which is entirely 
free from color and odor necessarily a safe drinking water, for 
epidemics of typhoid have been caused by such. The bacteri- 
ological examination of water, by which the number of bacteria 
present in one cubic centimeter (1 cc.) is determined, is there- 
fore an important part of an analysis. 

As a general statement, it may be said that fresh water con- 
taining less than 100 bacteria per cc. is pure, that water contain- 
ing 500 bacteria per cc. should be viewed with suspicion, and 
that water containing 1000 bacteria per cc. is undoubtedly con- 
taminated. In considering these figures with relation to a 
water supply, it must be remembered that all natural surface 
waters contain some bacteria and that, except where there 
is pollution, the greater part of them are absolutely harmless. 



ARITHMETIC FOR NURSES 299 

The bacteria are so small that they may be seen only with 
the aid of a high-powered microscope. In order to count them 
a culture jelly of gelatine, albumin, and extract of beef is 
prepared and 1 cc. of the water is thoroughly mixed with 
10 cc. of the culture jelly, a small measured portion of this 
mixture then being poured in a thin layer on a sterilized plate 
to harden. Each bacterium eats and multiplies to such an 
extent that in about forty-eight hours a visible colony is 
produced. From a count of these colonies within a measured 
area of the plate the number of bacteria in the original 1 cc. 
of water is determined. 

Different species of bacteria may be detected by the use of 
different media for development, or they may be found by 
further examination with the microscope. The well-known 
colon bacillus (B. coli)y which, although harmless itself, is an 
indication of sewage pollution, is detected by the gas which it 
produces in a closed tube. As B. coli are found in practically 
all warm-blooded animals and sometimes in fish and elsewhere, 
the finding of a few in large samples of water, or their occa- 
sional discovery in small samples, is of no special significance ; 
but if they are found in a larger proportion in small samples 
and in considerable numbers in larger ones, sewage pollution is 
indicated. 

EXAMPLES 

1. If a bacterium multiplies tenfold every half hour in a 
person's mouth, how many will be produced in twenty-four 
hours ? 

2. A sample of water contains 0.24 parts per million of free 
ammonia. How many parts per 100,000 ? 

3. A sample of water contains 1.1 parts per million of iron. 
How many parts per 100,000 ? 

4. A sample of water contains 10 parts per million of lime. 
How many parts per 10,000 ? 



300 VOCATIONAL MATHEMATICS FOR GIRLS 



EXAMPLES ON ANALYSES OP WATER 

(Parts in 100,000) 





Bbsidub on 
Evaporation 


Ammonia 


H 

1 

n 
o 

.72 


NiTBOGEN 

AS 


• OXYGBN 

•-* Consumed 


< 

n 

1.3 






Total 


Loss 
on 

Igni- 
tion 


Fixed 


Free 


Albuminoid 


CO 

1 


00 

1 






Total 


In 
Solu- 
tion 


In 

Sus- 
pen- 
sion 


1 


a. 


4.00 


1.65 


2.35 


.0026 


.0190 


.0156 


.0034 


.0030 


.0001 


.0160 


h. 


4.65 


2.00 


2.65 


.0028 


.0172 


.0148 


.0024 


.68 


.0030 


.0000 


.28 


1.3 


.0080 


c. 


3.85 


1.15 


2.70 


.0014 


.0148 


.0130 


.0018 


.68 


.0000 


.0000 


.31 


1.1 


.0080 


d. 


4.20 


1.50 


2.70 


.0062 


.0140 


.0128 


.0012 


.71 


.0000 


.0000 


.32 


1.1 


.0050 


e. 


4.15 


1.35 


2.80 


.0018 


.0170 


.0152 


.0018 


.71 


.0000 


.0000 


.26 


1.0 


.0080 


/. 


5.00 


1.75 


3.25 


.0014 


.0162 


.0142 


.0020 


.73 


.0000 


.0000 


.36 


1.0 


.0120 


ff- 


4.36 


1.60 


2.75 


.0020 


.0178 


.0160 


.0028 


.70 


.0010 


.0001 


.24 


1.3 


.0080 


h. 


4.10 


1.15 


2.95 


.0018 


.0162 


.0136 


.0026 


.71 


.0010 


.0001 


.24 


1.3 


.0100 



1. Give the number of parts of free ammonia in 10,000 in a. 

2. Give the number of parts of nitrates in 10,000 in b, 

3. Give the number of parts of nitrites in 10,000 in d. 

REVIEW EXAMPLES 

1. Give the number of cubic centimeters of water you 
would measure out to get the following : 

a. 70 gm. b, 11 kg. c. 0.4 gm. d. 61 mg. 

2. How much would the following amounts of water weigh ? 
a. 9 1. b, 4.7 cc. c. ^ 1. d. 48 cc. 

3. If the dose of aromatic spirits of ammonia is 30 minims, 
what is the dose for a child 6 years old ? 

4. Give the approximate equivalents in household measures 
of the following : 

a. 7 drams c. 4 ounces e, 12 fluid ounces 

6. 36 grams d, 90 minims /. 3 fluid drams 



ARITHMETIC FOR NURSES 301 

5. Give the approximate equivalents in household measures 
of the following : 

a. 1500 cc. c. 3 liters e. 1 gramme 

b, 11 CO. d, 0.003 grain /. 0.008 gramme 

6. How many grammes in 3 ounces of 1 % solution ? 

7. How many drams in 1 gallon of 1 ; 50 solution ? 

8. How many grammes in a liter of 10 % solution ? 

9. How many grammes in 5 liters of 1 : 25 solution ? 

10. How many teaspoonf uls of pure carbolic acid in a gallon 
of 1 % solution ? 

11. How many drops (minims) of carbolic acid in a quart 
of 1 : 1000 solution ? 

12. A basin of rain water has a temperature of 94® F. Give 
the equivalent on the Centigrade scale. 

13. A cool bath registers a temperature of 26® C. Give the 
equivalent on the Fahrenheit scale. 

14. A dose of ipecac is 20 to 30 grammes. What is the dose 
for a child of seven years ? 

15. A dose of 1 : 500 solution means how many grammes to 
a quart ? 

16. Given a 5 % solution of- silver nitrate, how would you 
make a gallon of 1 : 5000 solution ? 

17. How would you make a gallon of 3 ^J? solution of acetic 
acid from the pure acid ? 

18. How would you make two quarts of 5 % solution of car- 
bolic acid from pure acid ? (Consider pure acid 95 % .) 

19. A 1 : 50 solution is used for disinfecting wounds. How 
would you make a gallon of this fluid from standard solution ? 
(Consider standard strength about 40 %.) 



302 VOCATIONAL MATHEMATICS FOR GIRLS 

20. A 2^0 solution of boric acid is used for eye and ear 
irrigations. How much boric acid will be necessary to make a 
quart of the solution ? 

21. Give the approximate equivalents of metric and 
apothecaries' measures of the following : 

a. 31 cc. d. 50 minims 

b. y^^ gram e, 5 pints 

c. 1.6 gram /. 101 cc. 

22. If the pharmacy nurse buys 3 oz. of trional, how many 
powders of 10 grains each can she make ? 

23. The dose of the tincture of opium is 0.5 cc. ; 10 cc. of 
the tincture contains 1 gm. of opium ; 12 % of opium is 
morphine. How many milligrams of morphine in one dose of 
the tincture ? 

24. a. Convert the following to milligrams : 5 dg. and 0.27 gm. 
h. Convert the following to grams : 483 dg. and 7 mg. 

25. How much alcohol (15 % strength) will be necessary to 
make a quart of alcohol containing 80 % volume of absolute 
alcohol? 66%? 37%? 75%? 

26. If lactic acid is composed of 75 % of absolute acid, how 
much absolute acid in a pound of the official preparation ? 

27. Diluted alcohol contains 41.5 % absolute alcohol. How 
much absolute alcohol in a gallon of dilute alcohol ? 

28. The dose of morphine sulphate is 0.008 gm. What is the 
dose for a baby 7 months old ? 

29. The dose of camphorated tincture of opium (paregoric) 
is f 3 i. What is the dose for a baby 6 months old ? 

30. Hands and arms are often disinfected by washing in a 
solution of permanganate of potash (two ounces to four quarts 
of water) followed by immersion in a solution of oxalic acid 
(eight ounces to four quarts of water). What is the percentage 
of each ? 



ARITHMETIC FOR NURSES 303 

31. Adhesive iodoform gauze is made by saturating sterilized 
gauze in the following solution : 

Iodoform 22 grams 
Resin 10 grams 
Glycerine 6 cc. 
Alcohol 26 cc. 

(Consider specific gravity of alcohol and glycerine as 1.) 
What per cent of each ? Give quantity in English system. 

32. How much of each ingredient should be used in prepar- 
ing a pound of the following mass ? 

Zinc oxide 6 parts 

Gelatine 5 parts 

Glycerine 12 parts 

Water 10 parts 

33. What per cent of the following solution is atropine 

sulphate? 

Atropine sulphate 1^ gr. 

Water J fluid ounce 

34. What amount of carbolic acid crystals is used to make 
4 oz. of 3 % carbolized petrolatum ? 

35. What per cent of the following solution is boric acid ? 

Boric acid 18 gr. 
Water 1 oz. 

36. How much bichloride of mercury is required to make 
1 qt. of a 1 : 25,000 solution ? 

37. How much potassium permanganate will be necessary 
to make a pint of a 1 : 1000 solution ? 



PART VI — PROBLEMS ON THE FARM 



CHAPTER XV 

Every young person who lives on the farm has more or less 
to do with the bookkeeping and the arithmetic connected with 
the selling of the eggs, milk, and other products. Very few 
of the men on the farm have the time or the inclination to do 
this work, and it is usually performed by the wife or daughter. 

EXAMPLES 

1. I sold 16 dozen eggs at 30 cents a dozen and took my 
pay in butter at 40 cents a pound. How many pounds did I 
receive ? 

2. A dealer bought 16 cords of wood at $ 4 a cord and sold 
it for $ 96. Find the gain. 

3. Three men bought a farm. Henry paid $ 1135.75, 
Philip $2400.25, and Carl as much as Henry and Philip. 
Find the value of the farm. 

4. A farmer divided his farm as follows : to his elder son 
he gave 257f acres, to his younger son 200^^ acres, and to his 
wife as many acres as to his two sons. How many acres in 
the farm ? 

5. One farm contains 287f acres and another 244J acres. 
Find the difference between them. 

6. One bin contains 165^ bushels of grain and the other 
bin 184y^Tj^ bushels. How many bushels more does the larger 
bin contain than the smaller ? 

304 



PROBLEMS ON THE FARM 305 

7. From a farm of 375^ acres, 84^^ acres were sold. How 
many acres remained ? 

8. A farmer owning 67f acres of land sold 28^ acres and 
afterwards bought 14J acres. How many acres did he then 
own? 

9. A farm contained 132 acres, one-eighth of which is 
woodland, one-sixth is pasture, and the remainder is culti- 
vated. What part of the farm is cultivated? How many 
acres are cultivated ? 

10. From four trees, 14| barrels of apples were gathered. 
One man bought 5^ bbl., another S\ bbl. How many barrels 
remained ? 

11. I owned two-fifths of a farm and sold three-fourths of 
my share for $ 1360. Find value of the whole farm. 

12. I bought 5 loads of potatoes containing 33^ bushels, 
27f bushels, 40^ bushels, 35^ bushels, and 29J bushels. I 
sold 12f bushels to each of three men, and 25^ bushels to each 
of four men. How many bushels were left ? 

13. If two-thirds of a farm costs $2480, what is the cost 
of the farm ? 

14. Mr. Thomas bought 168 sheep at $5.50 a head. He 
sold three-sevenths of them at $ 6 a head, and the remainder 
at $ 7 a head. Find the gain. 

15. A farm is divided into four lots. The first contains 
30^ acres, the second 42|^ acres, the third 35^ acres, the 
fourth 28f acres. How many acres in the farm ? 

16. A farmer sold sheep for $ 62.50, cattle for $ 102.60, a 
horse for $ 125.75, and a plow for $ 18.25. How much did he 
receive ? 

17. Farmer Blake raised 114 bushels of apples and 73f 
bushels of pears. How many more bushels of apples than 
pears did he raise ? 



306 VOCATIONAL MATHEMATICS FOR GIRLS 

18. A farmer paid $ 78 for a cow, $ 165 for a horse. How 
much more did the horse cost than the cow? 

19. Mr. Borden has 450^2^ acres of woodland and sells 304f 
acres. How much has he left ? 

20. Mr. Sherman bought ten acres of land at $ 65 an acre 
and sold it for $ 24.60 an acre. How much did he lose ? 

21. A's farm contains 265f acres, B's 43^ acres. What is 
the difference in the size of their farms ? 

22. Mr. Grover had 110 acres of land, and sold 7^ acres. 
How many acres had he left ? 

23. Mr. Dean sold one-third of his farm to one man, one- 
fourth to another, and one-eighth to another. What part had 
he left ? 

24. I paid $ 365.75 for a horse, and sold him for four-fifths 
of what he cost. What was the loss ? 

25. How many bushels of grain can be put into 16 bags, if 
they hold 2| bushels each ? 

26. A farmer carries 35 bushels of apples to market. What 
is half this load worth at 75 cents a bushel ? 

27. I paid $76.50 for 18 sheep. What was the average 
price ? 

28. Mr. Piatt gave 435 acres of land to his sons, giving each 
72^ acres. How many sons had he ? 

29. If 4^ bushels of potatoes were bought for $ 3.60, how 
many bushels can be bought for $ 10.80 at the same price per 
bushel ? 

30. Mr. White paid $ 16.25 for 2^ cords of wood. How 
many cords could he buy for $ 74.75 at the same price per 
cord? 

31. A father divided 183 acres of land equally among his 
sons, giving to each 45f acres. How many sons had he ? 



PROBLEMS ON THE FARM 307 

FARM MEASURES 

(Review Mensuration and Table of Measures.) 

1. If a bushel of shelled corn contains IJ cubic feet, how 
many bushels in a bin 8' x 4' x 2' 6" ? 

2. A bushel of ear corn contains 2^ cubic feet. How many 
bushels in a crib 10' x 4' 3" x 2' 4" ? 

3. A ton of tame hay contains 512 cubic feet. How many 
tons in a space 14' x 12' x 13' ? 

4. A ton of wild hay contains 343 cubic feet. How many 
tons in a space 28' 6" x 18' 9" x 13' 5" ? 

5. A bushel of potatoes contains 1^ cubic feet. How 
many bushels in a bin 8' 6" x V 5" x 9' 3" filled with 
potatoes ? 

6. How many bushels of com on the ear in a pointed heap 
12' X 8' and 6' high ? 

7. How many bushels of com in a circular crib with a 
diameter 12' 6" and a height 8' ? 

8. How many gallons of water in a rectangular trough 
6' 3" X 2' 6" X 3' 4" ? (Consider a gallon | cubic foot.) 

9. How many acres in 694 sq. rods ? 

10. A 60-acre piece of land, half a mile across, is 6' 8" 
higher on one side than the other. How much of a fall (grade) 
to the rod ? 

11. How many bushels of corn in a rectangular crib with 
sloping sides 16' long, 7' high and 4' 6" wide at the bottom and 
6' 8" wide at the top ? 

ENSILAC^E PROBLEMS 

1. A farmer with the purpose of filling his silo with com 
began the preparation of one acre of land for planting : 8 loads 
of stable fertilizer were used in dressing the land. What is 
the average number of square rods a load will fertilize ? 



308 VOCATIONAL MATHEMATICS FOR GIRLS 

2. The field was plowed in a day. Mr. A receives, when 
working for others, 20 cents per hour for his horses and 15 
cents per hour for his own work. How much is his time 
worth for the day of 10 hours ? 

3. Mr. A paid $ 12 for his plow and two extra points. The 
regular price without extras was $ 10.50. Mr. A broke a plow 
point on a rock. How much was the loss ? 

4. It took three-fifths as long to harrow the field (see ex- 
ample 2) as to plow it. If the work was begun at 7 o'clock in 
the morning, at what time would the com piece be harrowed ? 
(Noon hour from 12 m. to 1 p.m.) • 

5. Mr. A bought seed corn at $1.25 per bushel. What 
did the seed cost, 12 quarts being the amount used ? 

6. He bought 4 one-hundred-pound bags of fertilizer at 
$ 1.40 per hundred. How much did the fertilizer cost ? 

7. Mr. A is agent for Bradley fertilizers and receives a 
commission of 10 % on what he sells for the company. How- 
much must he sell to receive a commission equal to the cost of 
fertilizer used on his own corn piece, and also the expense of 
hauling from the railroad station, which amounted to $ 2.50 ? 

8. Mr. A hires a man to plant his corn with a horse planter. 
He pays $ 2 for the planting, which is at the rate of 30 ^ per 
hour. How long did it take ? 

9. Mr. A cultivated his com three times, each time requir- 
ing about 8 hours. Besides this he and his hired man spent 3 
days hoeing the com once. Which was more expensive, the 
hoeing or the cultivating ? How much ? 

10. The corn was planted June 1st. It was ready for cut- 
ting September 1st. Some of the stalks had grown to a height 
of 6 ft. What was the average weekly growth ? 

11. Mr. A's silo is rectangular, 10 ft. long, 10 ft. wide, and 
20 ft. deep. The floor is cemented. How many sq. yd. of 
cement in the floor ? 



PROBLEMS ON THE FARM 309 

12. If the lumber is 1 inch thick, how many board feet in 
one thickness of the walls ? 

13. How many cubic feet of ensilage will the silo hold? 
How many cubic feet below the level of the barn floor, which 
is 5 ft. higher than the cemented floor of the silo ? 

14. How many bushels of the cut and compressed corn 
stalks must hare been produced on the acre of land to fill the 
space ? 

15. On September 1st a gang of men helped Mr. A fill the 
silo. Two men worked in the field cutting down the stalks at 
$ 1.50 per day each. Two men hauled to the barn with teams at 
$ 3 per day each. Two men, a cutting machine, and horses for 
power cost $ 7. One man leveled corn in the silo at $ 1.50 
per day. What did Mr. A pay these men for the work of the 
day ? The next day the men with the cutting machine, one 
man with a team, and the man for the silo worked two hours 
to finish the work. Add this expense to that of the previous 
day. 

16. A week later the ensilage had settled 8 feet and Mr. A 
filled the space with surplus corn. He and a helper hoisted it 
with a pulley in a two-bushel basket. How many times must 
he fill the basket ? 

17. The mass was left to the fermenting process for two 
months. When Mr. A opens the silo, he begins feeding regu- 
larly to his 10 cows, giving each one-half bushel twice a day. 
At this rate when will the silo be emptied ? When should 
the ensilage be even with the barn floor ? 

18. It is estimated that 1 ton of ensilage is equal in value 
to one-third of a ton of hay. If ensilage weighs 50 pounds 
per bushel, how many pounds of hay equal a feed of ensilage ? 

19. How many tons of hay is the ensilage worth ? What 
is the value at $ 15 per ton ? 



310 VOCATIONAL MATHEMATICS FOR GIRLS 

20. Does it pay the farmer to raise ensilage ? 

Note. — Ensilage could not be used as a substitute for hay, but is ex- 
cellent as a milk producer when fed in moderate quantities. Cows like 
it better than hay. 

DAIRY PRODUCE 

Milk is graded according to the amount of cream (fat) in it. 
In addition to cream, it contains casein (cheese), milk sugar, 
and -about 84 % water. Milk is usually sold by the farmer by 
weight and the per cent cream. 

To illustrate : A sample of milk from a large can weighing 
50 lb. contains 4 % cream. The large can contains 2 lb. of 
butter fat. 

EXAMPLES 

1. A sample of milk from a cooler containing 48^ lb. tested 
3f % butter fat. How much butter fat in the cooler ? 

2. A cow gives 3J gallons of milk per day. If a gallon 
weighs 8f lb., what is the weight of milk per day ? per week ? 
per month ? 

3. If the milk in example 2 contains 4.7 per cent of cream, 
how much butter fat does it yield per week ? per month ? 

4. If butter fat is worth 26 cents a pound, how much is ob- 
tained per week from the butter fat in example 3 ? How much 
per month ? 

5. Another cow gives 3^ gallons of milk a day that tests 
4.6 % butter fat. Is it more profitable to keep this cow or the 
one in examples 2 and 3, and by how much ? 

6. Skim milk from the butter fat is usually sold to feed the 
pigs at 5\ cents a gallon. Is it cheaper to sell milk at 5^ cents 
a quart or to make butter and sell it at 26 cents a pound and 
give the skim milk to the pigs ? 



PROBLEMS ON THE FARM 311 

PROBLEMS ON EQUIPPING A COOPERATIVE CHEESE FACTORY 

Seventy-three farmers came together, and after the election 
of officers it was decided that a stock company of seventy-three 
shares should be formed, and each member bought a share at 
the rate of $ 75. Part of the money was used to erect a cheese 
factory, and the rest was deposited in a bank and drawn out 
as it was needed to run the business until the sale of the 
products should be sufficient to supply money for carrying on 
the business and paying a small per cent on the money invested 
by each man. The following are the items of expense : 

Half acre of land at $0.03 a square foot. 

The building cost $ 2000 for material and work. 

Three large vats, $ 60 each ; 4 % discount. 

A Babcock tester $30 ; 2| </o discount. 

A small engine, belts, etc., $63.86. 

Whey trough and leads, $ 64 ; 4 9^ discount. 

Cheese press, $ 28 ; S^o discount. 

Rennet, salt, coloring, wood, cheesecloth, boiler, and piping, $15. 

Boxes, acid for test, etc., $67 ; S^o commission. 

Scales, weights, and weighing can, $27.86. 

A year's salary to the cheese maker, $620. 

The money left after these expenses was put at 3 9^ interest. 

PROBLEMS 

1. How much money was put into the business ? 

2. How much did the cheese maker average a week ? 

3. What was the cost of the land ? 

4. The man who sold the boiler and piping and also the 
engine and belt to the company received 6 % commission. 
What did he receive for his sales ? 

5. The man who bought the whey trough, the leads, and 
the large vats received the discount as his commission. How 
much did he receive ? 

- 6. How much did the company that sold the whey trough, 
leads, and vats receive ? 



312 VOCATIONAL MATHEMATICS FOR GIRLS 

7. How much did the buying company pay out for the whey 
trough, leads, and vats ? 

a An agent sold the tester ; his commission was 6 %. How 
much did he receive ? 

9. How much did the tester cost the company ? 

10. The man who bought the press and material received 
3 % commission. How much did the press and materials cost 
the company ? 

11. How much did it cost to buy the land, build the fac- 
tory, and equip the plant ? 

12. How much was left at interest ? 

13. How much would the interest be for 3 years 6 months 
and 16 days ? 

14. What is the interest for one year ? 

15. What per cent of the whole investment is this interest ? 

16. What per cent of the whole was left at interest ? 

PROBLEMS ON POULTRY 

One hen has to have five square feet of room in the house. 

It costs about ten cents a month to feed one hen. 

One dozen eggs sell on the average for 30 cents. 

One hen lays about 100 eggs per year. 

Broilers are sold at 25 cents a pound. 

Hens are sold for 15 cents a pound. 

An incubator costing $ 20 holds 150 eggs. 

Setting eggs cost $ 1.00 a dozen. 

Brooders cost $7.50. 

A small chicken coop costs $ 8.00. 

One hen costs 60 cents. 

Little chickens 1 week old cost 10 cents. 

Chicken wire, 6 ft. wide, costs 4^ cents per foot. 



PROBLEMS ON THE FARM 313 

PROBLEMS 

1. How large would the floor of my poultry house have to 
be for 30 chickens ? for 50 ? 80 ? 200 ? 

2. If I have a poultry house the floor of which is 30 ft. by 
50 ft., how many chickens can I put in it? 

3. How much will it cost to keep the chickens one month ? 
one year ? 

4. If I have one hen, how much does it cost me to feed her 
one year ? Suppose she lays 90 eggs, how much will I receive 
for them ? Does it pay me to keep the hen ? 

5. Suppose I sold 25 broilers, 12 weighing 3 lb., 5 weigh- 
ing 5 lb., and the rest an average of 4 lb. How much would I 
receive for them ? If I had kept them 14 weeks, how much 
would they have cost me ? Would I gain or lose in keeping 
them ? How much ? 

6. If I bought an incubator for $ 20, a brooder for $ 7.50, 
a chicken coop for $ 8, and 150 eggs to put into the incubator, 
how much did I pay in all ? 

7. If from the 150 eggs only 139 were hatched and lived, 
how much would I receive for the little chickens when I sold 
them? 

8. Suppose I had a chicken yard 100 by 250 ft. How many 
feet of wire would I need to fence it in ? How much would 
it cost me to put wire around it ? 

9. How many eggs would I receive from 60 hens in one 
year ? If I sold all from 40 hens, how much would I receive 
for them ? 

10. If I bought 50 little chickens, kept them 16 weeks, and 
then sold them, each weighing on the average 3 lb., how much 
profit did I make on them ? 



314 VOCATIONAL MATHEMATICS FOR GIRLS 

POULTRY RAISING 

1. A man wishes to build and stock a henhouse for $ 125. 
If he has $ 75, how much will he have to borrow ? How much 
interest will he have to pay for 1 year at 5 % ? 

2. If he pays $ 20 for labor, three times as much for mate- 
rial, one-fourth as much for . apparatus as for material, how 
much will he have left ? How many hens could he buy with 
the remainder if each hen cost 50 cents ? 

3. If it cost $ 1 per year to keep one hen, how much would 
it cost to keep all of his hens for 1 year ? for 5 years ? 

4. If each hen lays 100 eggs a year, how many eggs would 
they yield in one year ? how many dozen ? 

5. If he sold 400 dozen at 25 cents per dozen, how much 
would he receive for them ? 

6. If he sold the remaining dozen " for setting " at 50 cents 
a dozen, how much would he receive for these ? How much 
did he receive for all his eggs ? 

7. If it cost him the above amount to keep the hens for a 
year, how much did he gain from selling his eggs ? 

8. If, from 100 dozen eggs sold for " setting," 9 chickens 
were hatched from each dozen, how many chickens were 
hatched in all ? 

9. If it cost him 27 cents to raise oiie broiler,' how much 
would it cost to raise all the chickens for broilers ? 

10. If for each pair of broilers he received $ 1.50, how 
much would his entire stock net him ? 

11. After considering the cost of raising the broilers and 
the price received for them, what was his profit ? 

12. After he had paid his interest, what was his net 
profit ? 



PROBLEMS ON THE FARM 315 

REVIEW EXAMPLES 

1. A crib of com is 12' wide, 34' long, and has an average 
depth of 11' of corn in it. How many bushels ? 

2. How many bushels of oats in a bin 12' wide, 12' long, 
18' deep ? 

3. A freight car is 8' x 32' x 11'. If it is filled 3|' deep 
with apples for the cider mill, how many bushels in the car ? 

4. At 26 cents a barrel, what is the car of apples worth ? 
{21 bu. = 1 bbl.) 

5. A field of hay is 88 rods long and 64 rods wide. How 
much is it worth at $ 98 an acre ? 

6. A cow gives 3f gallons of milk a day. The milk tests 
4.2 % butter fat. At 27 cents a pound for butter, and 5 cents 
a quart for skim milk, how much is obtained a week from this 
cow ? 

7. A flock of 200 hens averaged 135 eggs a year, and at 
the end of four years were sold for 10^ cents a pound, the 
average weight being 6^ lb. If the cost of feed for a year is 
$ 27.05 for the whole flock, what is the average gain per hen ? 

8. A man receives S 35 a month. How much per hour, if 
the month contains 26 working days of 10 hours a day ? 

9. What is the cost of 963^ bushels of oats at 47 cents per 
bushel ? 

10. If I buy 125 bushels of com at 41| cents per bushel 
and sell it at 62^ cents a bushel, how much do I gain ? 



APPENDIX 

METRIC SYSTEM 

The metric system is used in nearly all the countries of 
Continental Europe and among scientific men as the standard 
system of weights and measures. It is based on the meter as 
the unit of length. The meter is supposed to be one ten- 
millionth part of the length of the meridian passing from the 
equator to the poles. It is equal to about 39.37 inches. The 
unit of weight is the gram^ which is equal to about one 
thirtieth of an ounce. The unit of volume is the liter, which 
is a little larger than a quart. 

Measures of Length 

10 millimeters (mm.) . . . . =1 centimeter cm. 

10 centimeters =1 decimeter dm; 

10 decimeters =1 meter m. 

10 meters =1 dekameter Dm. 

10 dek3,meters =1 hektometer Hm. 

10 hektometers =1 kilometer Em. 

Measures of Surface {not Land) 

100 square millimeters (mm.) . . = 1 square centimeter . . sq. cm. 
100 square centimeters . . . . = 1 square decimeter . . sq. dm. 
100 square decimeters . . . . = 1 square meter sq. m. 

. Measures of Volume 

1000 cubic millimeters (mm.) . . = 1 cu. centimeter . . . cu. cm. 
1000 cubic centimeters . . . . = 1 cubic decimeter . . . cu. dm. 
1000 cubic decimeters . . . . = 1 cubic meter cu. m. 

I The gram is the weight of one cubic centimeter of pure distilled water at 
a temperature of 39.2^ F. ; the kilogram is the weight of 1 liter of water ; the 
metric ton is the weight of 1 cubic meter of water. 

817 



318 VOCATIONAL MATHEMATICS FOR GIRLS 



Measures of Capacity 

10 miliaiters (ml.) =1 centiliter 

10 centiliters =1 deciliter 

10 deciliters =1 liter i . 

10 liters =1 dekaliter 

10 dekaliters =1 hektoliter 

10 hektoliters . . . . ,» . . =1 kiloliter 



el. 

dl. 

L 

Dl. 

HI. 

Kl. 



Measures of Weight 



10 milligrams (mg.) 

10 centigrams . . 

10 decigrams . . 

10 grams . . . 

10 dekagrams . . 

10 hektograms . . 
1000 kilograms 



= 1 centigram eg. 

= 1 decigram dg. 

= 1 gram g. 

= 1 dekagram ...... Dg. 

= 1 hektogram Hg. 

= 1 kilogram Kg. 

= 1 ton T. 



1 meter 
1 centimeter 
1 millimeter 
1 kilometer 
Ifoot 
1 inch 



Metric Equivalent Measures 
Measures of Length 

- 39.87 in. = 3.28083 ft.= 1.0936 yd. 

= .8937 inch 

= .03937 inch, or ^ inch nearly 

= .62137 mile 

= .3048 meter 

= 2.64 centimeters = 26.4 millimeters 



1 square meter 
1 square centimeter 
1 square millimeter 
1 square yard 
1 square foot 
1 square inch 



Measures of Surface 

10.764 sq. ft. = 1.196 sq. yd. 
.166 sq. in. 
.00165 sq. in. 
.836 square meter 
.0929 square meter 
6.462 square centimeters =646. 2 square millimeters 



Measures of Volume and Capacity 

1 cubic meter = 36.314 cu. ft. = 1.308 cu. yd. = 264.2 gal. 

1 cubic decimeter = 61.023 cu. in. = .0363 cu. ft. 
1 cubic centimeter = .061 cu. in. 

1 The liter is equal to the volume occupied by 1 cubic decimeter. 



METRIC SYSTEM 319 

1 liter = 1 cubic decimeter = 61.023 cu. in. = .0353 cu. ft. = 

1.0667 quarts (U. S.)=.2642 gallon (U. S.) = 
2.202 lb. of water at 62° F. 

1 cubic yard = .7645 cubic meter 

1 cubic foot = .02832 cubic meter = 28.317 cubic decimeters = 

28.317 Uters 
1 cubic inch = 16.387 cubic centimeters 

1 gallon (British) = 4.543 liters 
1 gallon (U. S.) = 3.785 liters 

Measures of Weight 

1 gram = 15.432 grains 

1 kilogram = 2.2045 pounds 

1 metric ton = .9842 ton of 2240 lb. = 19.68 c\\i;. = 2204.6 lb. 

1 grain = .0648 gram 

1 ounce avoirdupois = 28.35 grams 

1 pound = .4536 kilogram 

1 ton of 2240 lb. = 1.016 metric tons = 1016 kilograms 

Miscellaneous 

1 kilogram per meter = .6720 pound per foot 

1 gram per square millimeter = 1.422 pounds per square inch 

1 kilogram per square meter = .2084 pound per square foot 

1 kilogram per cubic meter = .0624 pound per cubic foot 

1 degree centigrade = 1.8 degrees Fahrenheit 

1 pound per foot = 1.488 kilograms per meter 

1 pound per square foot = 4.882 kilograms per square meter 

1 pound per cubic foot = 16.02 kilograms per cubic meter 

1 degree Fahrenheit = .5556 degree centigrade 

1 Calorie (French Thermal Unit) = 3.968 B. T. U. (British Thermal Unit) 

1 horse power = 33,000 foot pounds per minute = 746 watts 

1 watt (Unit of Electrical Power) = .00134 horse power = 44.24 foot 

pounds per minute 
1 kilowatt = 1000 watts = 1.34 horse power =44,240 foot pounds per minute 

Table of Metric Conversion 

To change meters to feet multiply by 3.28083 

feet to meters multiply by .3048 

square feet to square metera . . . multiply by .0929 

square meters to square feet . . . multiply by 10.764 



320 VOCATIONAL MATHEMATICS FOR GIRLS 

To change square centimeters to square inches . multiply by .156 

square inches to square centimeters . multiply by 6.452 

inches to centimeters multiply by 2.54 

centimeters to inches multiply by .8937 

grams to grains multiply by 15.43 

grains to grams multiply by .0648 

grams to ounces multiply by .0853 

ounces to grams multiply by 28.35 

pounds to kilograms multiply by .4536 

kilograms to pounds multiply by 2.2045 

liters to quarts multiply by 1.0567 

liters to gallons multiply by .2642 

gallons to liters multiply by 8.78543 

liters to cubic inches multiply by 61.023 

cubic inches to cubic centimeters . . multiply by 16.387 

cubic centimeters to cubic inches . . multiply by .061 

cubic feet to cubic decimeters or liters multiply by 28.317 

kilowatts to horse power multiply by 1.34 

calories to British Thermal Units . . multiply by 3.068 



EXAMPLES 

1. Change 8 m. to centimeters ; to kilometers. 

2. Reduce 4 Km., 6 m., and 2 m. to centimeters. 

3. How many square meters of carpet will cover a floor 
which is 25.5 feet long and 24 feet wide ? 

4. (a) Change 6.5 centimeters into inches. 

(b) Change 48.3 square centimeters into square inches. 

5. A cellar 18 m. x 37 m. x 2 m. is to be excavated ; what 
will it cost at 13 cents per cubic meter to do the work ? 

6. How many liters of capacity has a tank containing 
5.2 cu. m.? 

7. What is the weight in grams of 31 cc. of water ? 

8. Give the approximate value of 36 millimeters in inches. 

9. Change 84.9 square meters into square feet. 
10. Change 23.6 liters to cubic inches. 



METRIC SYSTEM 321 

11. Change 7.3 m. to millimeters; to centimeters; to 
kilometers. 

12. Reduce 9.8 m. to kilometers ; to centimeters ; to milli- 
meters. 

13. What is the difference in millimeters between 2.7 m. 
and 48.1 mm. ? 

14. What part of a kilometer is 1.8 mm. ? 

15. What part of a meter is 1.3 cm. ? 

16. How many square centimeters are there in 26 square 
kilometers ? 

17. How many square meters in 4 rectangular gardens, 
3.4 Dm. long and 85.7 dm. wide ? 

la How many cubic meters in a wall 43 m. long, 8.4 dm. 
high, and 69 cm. wide ? 

19. Reduce 869.7 eg. to milligrams ; to kilograms ; to grams. 

20. What is the weight in grams of 48.7 cc. of water ? 
What is the weight in kilograms of 43.9 1. of water? 

21. Mercury weighs 13.6 times as much as water ; what is 
the weight of 87.5 cc. of mercury ? Of 5 1. of mercury ? 

22. A tank is 7.9 m. by 4.3 m. by 3.1 m. How many grams 
of water will it hold ? 

23. What is the weight of 874 cc. of copper, the density of 
which is 89 g. per cubic centimeter ? 

24. What is the capacity of a bottle that holds 5 kg. of 
alcohol, the density of which is 0.8 g. per cubic centimeter ? 

25. What is the weight in grams of 56.8 cc. of alcohol? 
What is the weight in kilograms of 7 1. of alcohol ? 

26. What part of a liter is 1.7 cc. ? 



ORAPHS 

A SHEET of paper, ruled with horizontal and vertical lines 
that are equally distant from each other, is called a sheet of 
cross-section, or coordinate, paper. Every tenth line is very 
distinct so that it is easy for one to measure off the horizontal 
and vertical distances without the aid of a ruler. Ruled or 



ORAFB SHOWIHa TUB VaBUTIOH in PrICB OT COTTON Y&lUr FOB A 

Skbibs of Yeabs 

coordinate paper is used to record the rise and fall of the 
price of any commodity, or the rise and fall of the barometer 
or thermometer. 

Trade papers and reports frequently make use of coordinate 
paper to show the results of the changes in the price of com- 
modities. In this way one can see at a glance the changes 



GRAPHS 323 

and condition of a certain commodity, and can compare these 
with the results of years or months ago. He also can see 
from the slope of the curve the rate of rise or fall in price. 

If similar commodities are plotted on the same sheet, the 
effect of one on the other can be noted. Often experts are 
able to prophesy with some certainty the price of a commodity 
for a month in advance. The two quantities which must be 
employed in this comparison are time and value, or terms 
corresponding to them. 

The lower left-hand corner of the squared paper is generally 
used as an initial point, or origin, and is marked 0, although 
any other corner may be used. The horizontal line from this 
corner, taken as a line of reference or axis, is called the db- 
scissa. The vertical line from this corner is the other axis, 
and is called the ordinate. 

Equal distances on the abscissa (horizontal line) represent 
definite units of time (hours, days, months, years, etc.), while 
equal distances along the ordinate (vertical line) represent 
certain units of value (cost, degrees of heat, etc.). 

By plotting, or placing points which correspond to a certain 
value on each axis and connecting these points, a line is ob- 
tained that shows at every point the relationship of the line 
to the axis. 

EXAMPLES 

1. Show the rise and fall of temperature in a day from 
8 A.M. to 8 P.M., taking readings every hour. 

2. Show the rise and fall of temperature at noon every day 
for a week. 

3. Obtain stock quotation sheets and plot the rise and fall 
of cotton for a week. 

4. Show the rise and fall of the price of potatoes for two 
months. 

. 5. Show a curve giving the amount of coal used each day 
for a week. 



FORMULAS 

Most technical books and magazines contain many formulas. 
The reason for this is evident when we remember that rules 
are often long and their true meaning not comprehended until 
they have been reread several times. The attempt to abbre- 
viate the length and emphasize the meaning results in the 
formula, in which whole clauses of the written rule are ex- 
pressed by one letter, that letter being understood to have 
throughout the discussion the same meaning with which it 
started. 

To illustrate : One of the fundamental laws of electricity is that the 
quantity of electricity flowing through a circuit (flow of electricity) is 
equal to the quotient (expressed in amperes) obtained by dividing the 
electric motive force (pressure, or expressed in volts, voltage) of the 
current by the resistance (expressed in ohms). 

One unfamiliar with electricity is obliged to read this rule over several 
times before the relations between the different parts are clear. To show 
how the rule may be abbreviated, 

Let / = quantity of electricity through a wire (amperes) 
E = pressure of the current (volts) 
B = resistance of the current (ohms) 

Then /= jrH-i?=:? 

B 

It is customary to allow the flrst letter of the quantity to represent it in 
the formula, but in this case I is used because the letter C is used in an- 
other formula with which this might be confused. 

Translating Rules into Formulas 

The area of a trapezoid is equal to the sum of the two parallel 
sides multiplied by one half the perpendicular distance between 
them. 

824 



FORMULAS 325 

We may abbreviate this rule by letting 

A = area of trapezoid 

L = length of longest parallel side 

3f = length of shortest parallel side 

JV= length of perpendicular distance between them 

Then A= (^L + M) x—, or 

The area of a circle is equal to the square of the radius 
multiplied by 3.1416. When a number is used in the formula 
it is called a constant, and is sometimes represented by a letter. 
In this case 3.1416 is represented by the Greek letter ir (pi). 

Let A = area of circle 
B. = radius of circle 
Then A — kx i^, or (the multiplication sign is usually left out between 
letters) 

Thus we see that a formula is a short and simple way of 
stating a rule. Any formula may be written or expressed in 
words and is then called a rule. The knowledge of formulas 
and of their use is necessary for nearly every one engaged in 
the higher forms of mechanical or technical work. 

* When two or more quantities are to be multiplied or divided or other- 
wise operated upon by the same quantity, they are often grouped together 
by means of parentheses ( ) or braces { }, or brackets [ ] . Any number 
or letter placed before or after one of these parentheses, with no other 
sign between, is to multiply all that is grouped within the parentheses. 

In the trapezoid case above, — is to multiply the sum of L and Jf, hence 

the parentheses. To prevent confusion, different signs of aggregation 
may be used for different combinations in the same problem. 
For instance, 

r= iir^r5(ra + r'2) + :^1 which equals 



326 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Abbreviate the following rules into formulas : > 

1. One electrical horse power is equal to 746 watts. 

2. One kilowatt is equal to 1000 watts. 

3. The number of watts consumed in a given electrical 
circuit, such as a lamp, is obtained by multiplying the volts by 
the amperes. 

4. The number of volts equals the watts divided by the 
amperes. 

5. Number of amperes equals the watts divided by the 
volts. 

6. The horse power of an electric machine is found by mul- 
tiplying the number of volts by the number of amperes and 
dividing the product by 746. 

7. The speed at which a body travels is equal to the ratio 
between the distance traveled and the time which is required. 

8. To find the pressure in pounds per square inch of a 
column of water, multiply the height of the column in feet by 
0.434. 

9. The amount of gain in a business transaction is equal to 
the cost multiplied by the rate of gain. 

10. The selling price of a commodity is equal to the cost 
multiplied by the quantity 100 % plus the rate of gain. 

11. The selling price of a commodity is equal to the cost 
multiplied by the quantity 100 % minus the rate of loss. 

12. The interest on a sum of money is equal to the product 
of the principal, time (expressed as years), and the rate (ex- 
pressed as hundredths). 



FORMULAS 327 

13. The amount of a sum of money may be obtained 
by adding the principal to the quantity obtained by multi- 
plying the principal, the time (as years), and the rate (as 
himdredths). 

14. To find the length of an arc of a circle: Multiply the 
diameter of the circle by the number of degrees in the arc and 
this product by .0087266. 

15. To. find the area of a sector of a circle : Multiply the 
number of degrees in the arc of the sector by the square of the 
radius and by .008727; or, multiply the arc of the sector by 
half its radius. 

Translating Formulas into Rules 

In order to understand a formula, it is necessary to be able 
to express it in simple language. 

1. Oue of the simplest formulas is that for finding the area 
of a circle, A^^ir B? 

Here A stands for the area of a circle, 

B for the radius of the circle. 

IT is a constant quantity and is the ratio of the circumference of a 
circle to its diameter. The exact value cannot be expressed in figures, 
but for ordinary purposes is called 3.1416 or 3f . 

Therefore, the formula reads, the area of a circle is equal to 
the square of the radius multiplied by 3.1416. 

2. The formula for finding the area of a rectangle is 

^ = Xx W 

Here A = area of a rectangle 
L = length of rectangle 
W = width of rectangle 

The area of a rectangle, therefore, is found by multiplying 
the length by the width. 



328 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

Express the facts of the following formulas as rules : 

1. Electromotive force or voltage of electricity delivered by 
a current, when current and resistance are given: 

E = RI 

2. For the circumference of a circle, when the length of the 
radius is given : 

C-2irR0VirD 

3. For the area of an equilateral triangle, when the length 
of one side is given: ^ a*V3 

4. For the volume of a circular pillar, when the radius and 
height are given: 

5. For the volume of a square pyramid, when the height 
and one side of the base are given : 

3 

6. For the volume of a sphere, when the diameter is given : 



F= 



irD" 



6 

7. For the diagonal of a rectangle, when the length and 
breadth are given : 

8. For the average diameter of a tree, when the average 
girth is known : n _ ^ 

IT 

9. For the diameter of a ball, when the volume of it is 
known. 8/6« 



FORMULAS 329 

10. The diameter of a circle may be obtained from the area 
by the following formula : 

D = 1.1283 X VA 

U. The number of miles in a given length, expressed in 
feet, may be obtained from the formula 

M= .00019 X F 

12. The number of cubic feet in a given volume expressed 
in gallons may be obtained from the formula 

C = .13367 X G 

13. Contractors express excavations in cubic yards; the 
number of bushels in a given excavation expressed in yards 
may be obtained from the formula 

C = .0495 X Y 

14. The circumference of a circle may be obtained from the 
area by the formula 

(7=3.5446 xV3 

15. The area of the surface of a cylinder may be expressed 
by the formula u4 = (0 X X) + 2 a 

When C = circumference 

L = length 
a = area of one end 

16. The surface of a sphere may be expressed by the formula 

S^D'x 3.1416 

17. The solidity of a sphere may be obtained from the 
formula 

S^D'x .5236 

18. The side of an inscribed cube of a sphere may be ob- 
tained from the formula 

S = Bx 1.1547, where S = length of side, 

B = radius of sphere. 



330 VOCATIONAL MATHEMATICS FOR GIRLS 

19. The solidity or contents of a pyramid may be expressed 

by the formula 

F 
S = Ax—, where A = area of base, 

F = height of pyramid. 

20. The length of an are of a circle may be obtained from 
the formula 

L= Nx .017453 R, where L = length of arc, 

N= number of degrees, 
B = radius of circle. 

21. The loss in a transaction may be expressed by the 
formula 

X = c X r, where L = loss, 

c = cost, 
r = rate of loss. 

« 

22. The rate of loss in a transaction may be expressed by 
the formula 

— = r. 

c 

23. The cost of a commodity may be expressed by the 
formula 

c = -— , where S = selling price, 

100 + r' . 

' c = cost, 

r = rate. 

24. The volume of a sphere when the circumference of a 
great circle is known may be determined by the formula 

25. The diameter of a circle the circumference of which 
is known may be found by the formula 



FORMULAS 331 

26. The area of a circle the circumference of which is known 
may be found by the formula 



Coefficients and Similar Terms 

When a quantity may be separated into two factors, one of 
these is called the coefficient of the other ; but by the coefficient 
of a term is generally meant its numerical factor. 

Thus, 4 & is a quantity comi>osed of two factors 4 and & ; 4 is a coef- 
ficient of 6. 

Similar terms are those that have as factors the same letters 
with the same exponents. 

Thus, in the expression, 6 a, 4 &, 2 a, 5 a&, 5 a, 2 &. 6 a, 2 a, 5 a are 
similar terms ; 4 &, 2 & are similar terms ; 5 ah and 6 a are not similar 
terms because they do not have the same letters as factors. 3 a&, 5 a&, 
1 a6, 8 ah are similar terms. They may be united or added by simply 
adding the letters to the numerical sum, 17 ah. 

In the following, 86, 56, 8 a6, 4 a, a6, and 2 a, 8 6 and 56 are similar 
terms ; 3 a6 and a6 are similar terms ; 4 a and 2 a are similar terms ; 8 6, 
8 a6, and 4 a are dissimilar terms. 

In addition the numerical coefficients are algebraically added ; 
in subtraction the numerical coefficients are algebraically sub- 
tracted ; in multiplication the numerical coefficients are alge- 
braically multiplied ; in division the numerial coefficients are 
algebraically divided. 

EXAMPLES 

State the similar terms in the following expressions : 

1. 5 0?, 8 aa;, 3 aj, 2 ax. 6. 16 abCy 2 ahCy 4 abc, 2 ah, 

2. 8a6c, 7c, 2a6, 3c, 8a6, 3a6. 

9a6c. 7. 8a;, 6a?, 13a;y, 5aj, 7y. 

3. 2 j9g, 5 j9, 8 g, 2p, 3 g, 5^. a 7y,2y,2xy,Sy,2xy. 

4. 4:y, 5 yz, 2 y, 15 z, 5 z, 2 yz. '^ ^ o^ 

5. 18 mn, 6 m, 5 w, 4 mn, 2 m, ^ 



332 VOCATIONAL MATHEMATICS FOR GIRLS 

Equations 

A statement that two quantities are equal may be expressed 
mathematically by placing one quantity on the left and the 
other on the right of the equality sign (=). The statement 
in this form is called an equation. 

The quantity on the left hand of the equation is called the 
left-hand member and the quantity on the right hand of the 
equation is called the right-hand member. 

An equation may be considered as a balance. If a balance 
is in equilibrium, we may add or subtract or multiply or divide 
the weight on each side of the balance by the same weight and 
the equilibrium will still exist. So in an equation we may 
perform the following operations on each member without 
changing the value of the equation : 

We may add an equal quantity or equal quantities to each memr 
her of the equation. 

We may subtract an equal quantity or equal quantities from 
each member of the equation. 

We may multiply each member of the equation by the same or 
equal quantities. 

We may divide each member of the equation by the same or 
equal qvxintities. 

We may extract the square root of each member of the equation. 

We may raise each member of the equation to the same power. 

The expression, A = irB? is an equation. Why ? 

If we desire to obtain the value of B instead of A we may do 
so by the process of transformation according to the above 
rules. To obtain the value of B, means that a series of opersr 
tions must be performed on the equation so that B will be left 
on one side of the equation. 

(1) A = irB^ 

(2) - = J?2 (Dividing equation (1) by the coefficient of iP.) 

TT 

(8) ^— = B (Extracting tlie square root of each side of the equation.) 



FORMULAS 333 

Methods of Representing Operations 
Multiplication 

The multiplication sign ( X ) is used in most cases. It should 
not be used in operations where the letter (x) is also to be em- 
ployed. 

Another method is as follows ; 

2.3 a. 6 2a. 36 4aj.6a 

This method is very convenient, especially where a number 
of small terms are employed. Keep the dot above the line, 
otherwise it is a decimal point. 

Where parentheses, etc., are used, multiplication signs may 
be omitted. For instance, (a + 6) x (a — b) and (a + b){a — b) 
are identical ; also, 2'{x — y) and 2(x —y). 

The multiplication sign is very often omitted in order to 
simplify work. To illustrate, 2 a means 2 times a ; 5 xyz means 
5 • a; • y • « ; x(a — b) means x times (a — 6), etc. 

A number written to the right of, and above, another (ic*) is 
a sign indicating the special kind of multiplication known as 
involution. 

In multiplication we add exponents of similar terms. 

Thus, iB* . aj» = aj2+' = a^ 

dbc • ab • d?h = a*b*c 

The multiplication of dissimilar terms may be indicated. 

Thus, a-6»c«a?«y-2; = abcxyz. 

Division 

The division sign (-^) is used in most cases. In many 
cases, however, it is best to employ a horizontal line to indicate 

division. To illustrate, — i— means the same as (a + b) -i- 

x-y 

(x — y) in simpler form. The division sign is never omitted. 



334 VOCATIONAL MATHEMATICS FOR GIRLS 

A root or radical sign (V^> \/^ is a sign indicating the special 
form of division known as evolution. 

In division, we subtract exponents of similar terms. 

Thus, a^-5.a^ = ^ = a»-2^a? 

The division of dissimilar terms may be indicated. 

dbc 



Thus, (abc) -i- xyz = 



Qcyz 



Substituting and Transposing 

A formula is usually written in the form of an equation. 
The left-hand member contains only one quantity, which is 
the quantity that we desire to find. The right-hand member 
contains the letters representing the quantity and numbers 
whose values we are given eithjer directly or indirectly. 

To find the value of the formula we must (1) substitute for 
every letter in the right-hand member its exact numerical 
value, (2) carry out the various operations indicated, remem- 
bering to perform all the operations of multiplication and 
division before those of addition and subtraction, (3) if there 
are any parentheses, these should be removed, one pair at a 
time, inner parentheses first. A minus sign before a parenthesis 
means that when the parenthesis is removed, all the signs of 
the terms included in the parenthesis must be changed. 

Find the value of the expression 

3a + 6(2a — 6 + 18), wherie a = 5, 6 = 3. 

Substitute the value of each letter. Then perform all addition or 
subtraction in the parentheses. 

3x5 + 3(10 -3 + 18) 
15 + 3(28-3) 
15 + 3(26) 
15 + 75 = 90 



FORMULAS 335 

EXAMPLES 

Find the value of the following expressions : 

1. 2u4x(2 + 3^)x8, when^ = 10. 

2. 8 a X (6 — 2 a) X 7, when a = 7. 

3. 86 + 3c + 2a(a + & + c)-8,whena = 9; 6 = 11; c=:.13. 

4. 8(aj + y), when a? = 9; y = ll. 

5. 13 (a?— y), when a? = 27 ; 2^ = 9. 

6. 24y + 82;(2 + y)-3y, when 2/ = 8; 2 = 11. 

7. Q(6J»f+3iV^)4-2 0, when JW=4, JV^=5, Q = 6, = 8. 

a Find the value of X in the formula X = ^(^•^+^\ 
when JW= 11, JV^= 9, P = 28. 

9. 0? = ?^^:^, when 71 = 5, m = 6,P=8, Q = 7. 

10. Find the value of T in the equation 

y^S(^4-y)+7(a:-hy) ^^ ^^^ ^g 

U. 3a+4(6 — 2a + 3c)-c, when a = 4, 6 = 6, c = 2. 

12. 5 j9 — 8 5 (|9 + r — /S) — g, when p = 5, g = 7, r = 9, /S = 11 

13. ^ + ^_p2--3(/S' + * + 2>), whenp = 5, /S=8, « = 9. 

14. a'-6'+c2, when a = 9, 6 = 6, c = 4. 

15. (a + 6) (a + 6 — c), when a = 2, 6 = 3, c = 4. 

16. (a^ - 6') (a* + 6^), when a = 8, 6 = 4. 

17. (c»+^)(c'-- (i*), c = 9, d = 5. 

18. Va« + 2a6 + 6^ when a = 7, 6 = 8. 

19. Vc* — 61, when c^6. 



336 VOCATIONAL MATHEMATICS FOR GIRLS 

PROBLEMS 

Solve the following problems by first writing the formula 
from the rule on page 326, and then substituting for the answer. 

1. How many electrical horse power in 4389 watts ? 

2. How many kilowatts in 2389 watts ? 

3. (a) Give the number of watts in a circuit of 110 volts 
and 25 amperes. 

(b) How many electrical horse power ? 

4. What is the voltage of a circuit if the horse power is 
2740 watts and the quantity of electricity delivered is 25 
amperes ? 

5. What is the resistance of a circuit if the voltage is 110 
and the quantity of electricity is 25 amperes ? 

6. What is the pressure per square inch of water 87 feet 
high? 

7. What is the capacity of a cylinder with a base of 16 
square inches and 6 inches high? (Capacity in gallons is 
equal to cubical contents obtained by multiplying base by the 
height and dividing by 231 cubic inches.) 

8. What is the length of a 30° arc of a circle with 16" 
diameter ? 

9. What is the area of a sector which contains an arc of 
40° in a circle of diameter 18" ? 

10. What is the amount of $ 800 at the end of 5 years at 5 %? 

11. What is the amount of gain in a transaction, when a 
man buys a house for $ 5000 and gains 10 % ? 

12. What is the selling price of an automobile that cost 
$ 896, if the salesman gained 33 % ? 

13. What is the capacity of a pail 14" (diameter of top), 
11" (diameter of bottom), and 16" in height ? 

14. What is the area of an ellipse with the greatest length 
16" and the greatest breadth 10" ? 



FORMULAS 



337 



Interpretation of Negative Quantities 

The quantity or number — 12 has no meaning to us according 
to our knowledge of simple arithmetic, but in a great many 
problems in practical work the minus sign before a number 
assists us in understanding the different solutions. 

To illustrate : 



Fahrinhbit Tbebmombtbb 



Boiling 
point of 
water 



Freezing 
point of ■ 
water 



212" 



a 

o 
a 



82» 



3 i«« 

OB i 



0" 



Cbntiobadb Thbbmomxtba 



Boiling 
point of 
winter 



Freeadng 
point of • 
water 



lOO* 



SB. 

o 
a 

m 



cr 



On the Centigrade scale the freezing point of water is marked 
0**. Below the freezing point of water on the Centigrade scale 
all readings are expressed as minus readings. 

— 30° C means thirty degrees below the freezing point. In 
other words, all readings, in the direction below zero are 
expressed as — , and all readings above zero are called -h. 
Terms are quantities connected by a j/lus or minus sign. 
Those preceded by a plus sign (when no sign precedes a quan- 
tity plus is understood) are called positive quantities, while 
those connected by a minus sign are called negative quantities. 



338 VOCATIONAL MATHEMATICS FOR GIRLS 

Let us try some problems involving negative quantities. 
Find the corresponding reading on the Fahrenheit scale cor- 
responding to — 18® C. 

F = I C + 32° 

F = |(-18°)H-82° 

Notice that a minus quantity is placed in parenthesis when it is to be 
multiplied by another quantity. 

F =- H29 4. 32" = _ 82f° H- 32° ; F =- i°. 

The value — J° is explained by saying it is | of a degree below zero 
point on Fahrenheit scale. 

Let us consider another problem. Find the reading on the Centi- 
grade scale corresponding to — 40° F. 

Substituting in the formula, we have 

C = f (- 40° - 82°) = K- 72°) = - 40°. 

Since subtracting a negative number is equivalent to adding 
a positive number of the same value, and subtracting a posi- 
tive number is equivalent to adding a negative number of the 
same value, the rule for subtracting may be expressed as fol- 
lows : Change the sign of the subtrahend and proceed as in 
addition. 

For example, 40 minus — 28 equals 40 plus 28, or 68. 

40 minus + 28 equals 40 plus — 28, or 12. 

— 40 minus + 32 equals — 40 plus — 82 = - 72. 

(Notice that a positive quantity multiplied by a negative quantity or 
a negative quantity multiplied by a positive quantity always gives a 
negative product. Two positive quantities multiplied together will give 
a positive product, and two negative quantities multiplied together will 
give a positive product.) To illustrate : 

5 times 6 = 5 x 6 = 26 

5 times - 6 = ^ X (- 6) =- 25 

(-5) times (-5) = + 25 

In adding positive and negative quantities, first add all the 
positive quantities and then add all the negative quantities 



FORMULAS 339 

together. Subtract the smaller from the larger and prefix the 
same sign before the remainder as is before the larger number. 

For example, add : 

2a, 5a, —6a, 8-a, —2a 
2a + 5a + 8a = 15a; — 6a-2a=-8a 
15 a — 8a = 7a 

EXAMPLES 

Add the following terms : 

1. 3 a?, — 05, 7 a?, 4 a;, — 2 a?. 

2. 6y,2y,9y, -Ty. 

3. 9 ab, 2dbf 6ab, — 4 ab, 7 ab, — 6 ab. 

Multiplication of Algebraic Expressions 

Each term of an algebraic expression is composed of one or 
more factors, as, for example, 2 ab contains the factors ^, a, and 
6. The factors of a term have, either expressed or understood, 
a small letter or number in the upper right-hand corner, which 
states how many times the quantity is to be used as a factor. 
For instance, ab\ The factor a has the exponent 1 understood 
and the factor b has the exponent 2 expressed, meaning that a 
is to be used once and b twice as a factor. oJb^ means, then, 
a X 6 X 6. The rule of algebraic multiplication by terms is as 
follows: Add the exponents of all like letters in the terms 
multiplied and use the result as exponent of that letter in the 
product. Multiplication of unlike letters may be expressed 
by placing the letters side by side in the product. 

For example : 2 aft x 3 62 = 6 ^fts 

4a X 36 = 12a6 

Algebraic or literal expressions of more than one term are 
multiplied in the following way : begin with the first term to 
the left in the multiplier and multiply every term in the multi- 
plicand, placing the partial products underneath the line. Then 



340 VOCATIONAL MATHEMATICS FOR GIRLS 

repeat the same operation, using the second term in the multi- 
plier. Place similar products of the same factors and degree 
(same exponents) in same column. Add the partial products. 

Thus, a-\- b multiplied by a — &. 

a + b 
a— b 



a2 4. a6 - 62 
~ ab 



Notice the product of the sum and difference of the quantities is equal 
to the difference of their squares. 

EXAMPLES 

1. Multiply a -f 6 by a -f 6. 

State what the square of the sum of the quantities equals. 

2. Multiply 05 — y by 05 — y. 

State what the square of the difference of the quantities equals. 

3. Multiply (i) + g)(p — g). 7. Multiply (a? — y)(aj — y). 

4. Multiply (i) + g)(i> + g). a (a? + y)«=? 

5. Multiply (r + «)(r - «). 9. {x - y)« = ? 

6. Multiply (a ± b){a ± b). 10. {x -f y)(x -y) = ? 



USEFUL MECHANICAL INFORBiATION 

There are certain mechanical terms and laws that every girl 
should know and be able to apply to the labor-saving devices 
and machines that are used in the home to-day. 

Time and Speed 

Two important terms are time and speed. Speed is the 
name given to the time-rate of change of position. That is, 

S-oeed — C/hange of position or distance ^ 

Time taken 

EXAMPLES 

1. A train takes 120 seconds to go one mile; what is its 
speed in miles per hour ? 

One hour contains 60 minutes, 1 minute contains 60 seconds, then 1 hour 

contains 

60 X 60 = 3600 seconds. 

If the train goes one mile in 120 seconds, in one second it will go y^ 
of a mile and in 3600 seconds it will go 

3600 X xl^ = 30 miles per hour. Ans, 

2. At the rate of 80 seconds per mile, how fast is a train 
moving in miles per hour ? 

In a second it will move ^ of a mile ; in 3600 seconds it will move 
3600 times as much. 

3. At the rate of 55 miles an hour, how many seconds will 
it require to travel between mile-posts ? 

4. A watch shows 55 seconds between mile-posts ; what is 
the speed in miles per hour ? 

341 



342 VOCATIONAL MATHEMATICS FOR GIRLS 

5. What number of seconds between mile-posts will corre- 
spond to a speed of 40 miles an hour ? 

6. The rim of a fly-wheel is moving at the rate of one mile 
a minute. How many feet does it move in a second ? 

7. If a train continues to travel at the rate of 44 feet a 
second, how many miles will it travel in an hour ? 

8. If a train travels at the rate of 3.87 miles in 6 minutes, 
how many miles an hour is it traveling ? 

Motion and Momentum 

Many interesting facts about the motion of bodies can be 
understood by the aid of a knowledge of the laws of motion 
and momentum. 

A body acted upon by some force,^ such as steam or elec- 
tricity, starts slowly, increasing its speed under the action of 
the force. To illustrate: — when an electric car starts, we 
often experience a heavy jarring ; this is due to the fact that 
the seat starts before our body, and the seat pushes us along. 
There is a tendency of bodies to remain in a state of rest or 
motion, which is called inertia, that is, the inability of a body 
itself to change its position, to stop itself if moving, or to start 
if at rest. 

The momentum of a body is defined as the quantity of 
motion in a body, and is the product of the mass 2 and the 
velocity in feet per second (speed). 

Example. To find the momentum of a body 9 pounds in 
weight, when moving with the velocity of 76 feet per second. 

If the mass of the body upon which the force acts is given in pounds, 
and the velocity in seconds, the force will be given in foot-pounds. 

Mass Velooitt Momentum 

9 X 76 = 676 foot-pounds. 

1 Force is that which tends to produce motion. 
3 Mass is the quantity of matter in a body. 



USEFUL MECHANICAL INFORMATION 343 

We may abbreviate this rule by allowing letters to stand for 
quantities. Let the mass be represented by M and the veloc- 
ity by F. 

EXAMPLES 

1. What is the momentum of a car weighing 16 tons, mov- 
ing 12 miles per hour ? 

2. What is the momentum of a motor-car weighing 3 tons, 
moving 26 miles per hour ? 

3. What is the momentum of a person weighing 135 pounds, 
moving 5 miles per hour ? 

4. A truck weighing 4 tons has a momentum of 620,000 foot- 
pounds. At what speed is it moving ? 

Work and Energy 

Work is the overcoming of resistance of any kind. Energy 
is the ability to do work. Work is measured in a unit called 
a foot-pound. It is the work done in raising one pound one 
foot in one second. One horse power is 33,000 foot-pounds in 
one minute. 

EXAMPLES 

1. A woman lifts a package weighing 15 lb. from the floor 
to a shelf 6 ft. above the floor in two seconds. How many 
foot-pounds of force does she use ? 

2. How much work does a woman weighing 130 pounds do 
in climbing a 13-story building in 20 minutes ? Each story 
is 16' high. 

3. If an engine is rated at 5 H. P.,^ how much work will it 
do in 8 seconds ? in 3 minutes ? 

^ Remember that 1 H. P. means 33,000 ft.-lb. in one minute. 



344 VOCATIONAL MATHEMATICS FOR GIRLS 

4. Find the horse power developed by a locomotive when it 
draws at the rate of 31 miles per hour a train offering a resist- 
ance of 130,000 lb. 

Machines 

Experience shows that it is often possible to use our strength 
to better advantage by means of a contrivance called a 
machine. Every home-maker is interested in labor-saving 
devices. 

The mechanical principles of all simple machines may be 
resolved into those of the lever, including the wheel and axle 
and pulley y and the inclined plane, to which belong the wedge 
and acreio. 

In all machines there is more or less friction} The work 
done by the acting force always exceeds the actual work 
accomplished by the amount that is transformed into heat. 
The ratio of the useful work to the total work done by the 
acting force is called the efficiency of the machine. 

Fffio'p o — ^^^^^^ work accomplished 

Total work expended 

• Levers. — The efficiency of simple levers is very nearly 
100 (fo because the friction is so small as to be disregarded. 

Inclined Planes. — In the inclined plane the friction is 
greater than in the lever, because there is more surface with 
which the two bodies come in contact ; the efficiency is some- 
where between 90 % and 100 %. 

Pulleys. — The efficiency of the commercial block and tackle 
with several movable pulleys varies from 40 % to 60 %. 

Jack Screw. — In the use of the jack screw there is neces- 
sarily a very large amount of friction so that the efficiency is 
often as low as 25 %. 

^ Friction is the resistance which every material surface offers to the slid- 
ing or moving of any other surface upon it. 



USEFUL MECHANICAL INFORMATION 345 

EXAMPLES 

1. Mention some instances in which friction is of advantage. 

2. If 472 foot-pounds of work are expended by a dredge in 
raising a load, and only 398 pounds of useful work are accom- 
plished, what is the efficiency of the dredge ? 

3. If 260 foot-pounds of work are expended at one end of 
a lever, and 249 pounds of useful work are accomplished, what 
is the efficiency of the lever ? 

4. If 689 foot-pounds of work are expended in raising a 
body on an inclined plane, and only 684 pounds of useful 
work are accomplished, what is the efficiency of the inclined 
plane ? 

5. If 844 foot-pounds of work are expended in raising a 
body by means of pulleys and only 612 pounds of useful work 
are accomplished, what is the efficiency of the pulley ? 

Water Supply 

The question of the water supply of a city or a town is very 
important. Water is usually obtained from lakes and rivers 
which drain the surrounding country. If a lake is located in 
a section of the surrounding country higher than the city 
(which is often located in a valley), the water may be obtained 
from the lake, and the pressure of the water in the lake may 
be sufficient to force it through the pipes into the houses. But 
in most cases a reservoir is built at an elevation as high as the 
highest portion of the town or city, and the water is pumped 
into it. Since the reservoir is as high as the highest point of 
the town, the water will flow from it to any part of the town. 
If houses are built on the same hill with the reservoir, a stand- 
pipe, which is a steel tank, is erected on this hill and the water 
is pumped into it. 

Water is conveyed from the reservoir to the house by means 



346 VOCATIONAL MATHEMATICS FOR GIRLS 

of iron pipes of various sizes. It is distributed to the differ- 
ent parts of the house by small lead, iron, or brass pipes. 
Since water exerts considerable pressure, it is necessary to 
know how to calculate the exact pressure in order to have pipes 
of proper size and strength. 




Water Supply 



"^mmmp^ 



The distribution of water in a city during 1912 is as follows : 



Months 




January 

February 

March 

April 

May 

June 

July 

August 

September 

October . 

November 

December 



167,866,290 
147,692,464 
146,933,054 
143,066,067 
161,177,486 
176,479,364 
189,063,260 
179,379,666 
169,394,758 
176,067,671 
153,484,712 
161,976,208 



H 

0. 

OD >< 

< 



5,092,461 
6,092,844 
4,739,776 
4,768,869 
5,199,274 
6,882,645 
6,098,816 
6,786,438 
5,646,492 
6,679,699 
5,116,167 
4,902,468 







H -4 09 


gs 


i: 


"•WW 

« -. * 


S IB 


^ 


as 09 




0. 




S fe. 


Pki 


^ 


W o 




^Q 


1-t 


1-t 




UO 


o 




CO 


-^ 




■^ 


^0 




1-t 


r^ 




1-t 


r^ 





^ V M 

S? "< s 

« ^ u 

^ ^ S 

3 5 » 



What is the number of gallons per day for each consumer ? 
What is the number of gallons per day for each inhabitant ? 



PLUMBING AND HYDRAULICS 



347 



EXAMPLES 

1. Water is measured by means of a meter. If a water 
meter measures for five hours 760 cubic feet, how many gal- 
lons does it indicate ? 

Note. — 231 cubic inches = 1 gallon. 

2. If a water meter registered 1845 cubic feet for 3 days, 
how many gallons were used ? 

3. A tank holds exactly 12,852 gallons ; what is the capacity 
of the tank in cubic feet ? 

4. A tank holds 3841 gallons and measures 4 feet square on 
the bottom ; how high is .the tank ? 

Rectangular Tanks. — To find the contents in gallons of a square or 
rectangular tank, multiply together the length, breadth, and height in 

feet; multiply the result by 7.48. 

I = length of tank in feet 
b = breadth of tank in feet 
h = height of tank in feet 
Contents = Ibh cubic feet x 7.48 = 7.48 Ibh 
gallons 

(Note. — 1 cu. ft. = 7.48 gallons.) 

If the dimensions of the tank are in inches, multiply the length, 
breadth, and height together, and the result by .004329. 

5. Find the contents in gallons of a rectangular tank having in- 
side dimensions (a) 12' x 8' x 8'; (b) 15" x 11" X 6"; (c) 3' 4" 
X 2' 8" X 8"; (d) 5' 8" x 4' 3" x 3' 5"; (e) 3' 8" x 3' 9" x 2' 5", 

Cylindrical Tank. — To find the contents of a cylin- 
drical tank, square the diameter in inches, multiply 
this by the height in inches, and the result by .0034. 

d = diameter of cylinder 
h = height of cylinder 
Contents = d^h cubic inches x .0034 = d^h .0034 gallons 



6. Find the capacity in gallons of a cylindrical tank (a) 14" 
in diameter and 8' high; (b) 6" in diameter and 6' high; 




348 VOCATIONAL MATHEMATICS FOR GIRLS 

(c) 15" in diameter and 4' high; (d) V 8" in diameter and 
6' 4" high ; (e) 2' 2" in diameter and 6' 7" high. 

Inside Area of Tanks. — To find the area, for lining purposes, of a 
square or rectangular tank, add together the widths of the four sides of 
the tank, and multiply the result by the height. Then add to the above 
the area of the bottom. Since the top is usually open, we do not line 
it. In the following problems find the area of the sides and bottom. 

7. Find the amount of zinc necessary to line a tank whose 
inside dimensions are 2' 4" x 10" x 10". 

8. Find the amount of copper necessary to line a tank 
whose inside dimensions are 1^9" x 11" x 10", no allowance 
made for overlapping. 

9. Find the amount of copper necessary to line a tank 
whose inside dimensions are 3' 4" x 1' 2" x 11", no allowance 
for overlapping. 

10. Find the amount of zinc necessary to line a tank 
2' 11" X 1' 4" X 10". 

Capacity of Pipes 

Law of Squares. — The areas of similar figures vary as the 
squares of their corresponding dimensions. 

Pipes are cylindrical in shape and are, therefore, similar 
figures. The areas of any two pipes are to each other a& the 
squares of the diameters. 

Example. — If one pipe is 4" in diameter and another is 2" 
in diameter, their ratio is J^, and the area of the larger one is, 
therefore, 4 times the smaller one. 

EXAMPLES 

1. How much larger is a section of 5" pipe than a section 
of 2" pipe ? 

2. How much larger is a section of 2y pipe than a section 
of 1" pipe ? 

3. How much larger is a section of 5" pipe than a section of 
3" pipe ? 



PLUMBING AND HYDRAULICS 



349 



Atmospheric Pressure 

The atmosphere has weight and exerts .pressure. The pres- 
sure is greatest at sea level, because here the depth of the 
atmosphere is greatest. In mathematics the pressure at sea 
level is taken as the standard. Men have learned to make 
use of the principles of atmospheric pressure in such devices 

as the pump, the barometer, the vacuum, etc. 
Atmospheric pressure is often expressed as a 

certain number of "atmospheres." The pressure 

of one " atmosphere " is the weight of a column of 

air, one square inch in area. 
At sea level the 

average pressure of 

the atmosphere is 

approximately 15 

pounds per square 

inch. 

The pressure of 

the air is measured 

by an instrument 

called a barometer. 

The barometer con- 
sists of a glass tube, 

about 3H inches 

long, which has 

been entirely filled 

with mercury (thus 

removing all air from the tube) and inverted in 

a vessel of mercury. 

The space at the top of the column of mercury 

varies as the air pressure on the surface of the 

mercury in the vessel increases or decreases. The 
Basomstbb pressure is read from a graduated scale which indi- 




Barombteb Tube 



350 VOCATIONAL MATHEMATICS FOR GIRLS 

cates the distance from the sor&ce of the mercuiy in the 
vessel to the top of the mercoiy oolomn in the tube. 

QUESnOHS 

1. Four atmospheres would mean how many poonds ? 

2. Give in pounds the following pressures: 1 atmosphere; 
^ atmosphere ; f atmosphere. 

3. If the air, on the average, will support a column of 
mercury 30 inches high with a base of 1 square inch, what 
is the pressure of the air ? (One cubic foot of mercury weighs 
849 pounds.) 

Water Pressure 

When water is stored in a tank, it exerts pressure against 
the sides, whether the sides are vertical, oblique, or horizontal. 
The force is exerted perpendicularly to the surface on which it 
acts. In other words, every pound of water in a tank, at a 
height above the point where the water is to be used, possesses 
a certain amount of energy due to its position. 

It is often necessary to estimate the energy in the tank at 
the top of a house or in the reservoir of a town or city, so as 
to secure the needed water pressure for use in case of fire. In 
such problems one must know the perpendicular height from 
the water level in the reservoir to the point of discharge. This 
perpendicular height is caUed the head. 

Pressure per Square Inch. — To find the pressure per square 
inch exerted by a column of water, multiply the head of water 
in feet by 0.434. The result will be the pressure in pounds. 

The pressure per square inch is due to the weight of a column of 
water 1 square inch in area and the height of the column. Therefore, 
the pressure, or weight per square inch, is equal to the weight of a foot of 
water with a base of 1 square inch multiplied by the height in feet. Since 
the weight of a column of water 1 foot high and having a base of 1 square 
inch is 0.434 lb., we obtain the pressure per square inch by multiply- 
ing the height in feet by 0.434. 



PLUMBING AND HYDRAULICS 



351 



EXAMPLES 

What is the pressure per square inch of a column of water 
(a) 8' high? (6) 15' 8" high? (c) 30' 4'' high? (d) 18' 9'' 
high ? (e) 41' 3" high ? 

Head. — To find the head of water in feet, if the pressure 

(weight) per square inch is known, multiply the pressure by 

2.31. 

Let p = pressure 

h = height in feet 
Then p=:h x 0.434 lb. per sq. in. 



0.434 0.434 



Xp=2.Slp 



EXAMPLES 

Find the head of water, if the pressure is (a) 49 lb. per 
sq. in.; (b) 88 lb. per sq. in.; (c) 46 lb. per sq. in.; (d) 
28 lb. per sq. in. ; (e) 64 lb. per sq. in. 

Lateral Pressure. — To find the lateral 
(sideways) pressure of water upon the 
sides of a tank, multiply the area of the 
submerged side, in inches, by the pressure 
due to one half the depth. 

Example. — A tank 18" long and 12" 
deep is full of water. What is the lateral 
pressure on one side ? 



length depth 

18" X 12" =216 square inches = area of side 

depth 

1' X 0.434 = .434 lb. pressure at the bottom of 

the tank 
= pressure at top 
2) .434 lb. 
.217 lb. average pressure due to one half the 

depth of the tank 
.217 X 216 = 46.872 pounds = pressure on one 
side of the tank 






— Preanire 
is zero 



^— — — — PreMure 
is half that at 
base 






Lateral Pj^essubb 



352 VOCATIONAL MATHEMATICS FOR GIRLS 

Water Traps 

The question of disposing of the waste water, called sewage, is of 
great importance. Various devices may be used to prevent odors from 
the sewage entering the house. In order to prevent the escape of gas 





B 





T 



Water Traps 



from the outlet of the sewer in the basement of a house or building, a 
device called a trap is used. This trap consists of a vessel of water 
placed in the waste pipe of the plumbing fixtures. It allows the free pas- 
a3ge of waste material, but prevents sewer gases or foul odors from enter- 
ing the living rooms. The vessels holding the water have different forms ; 
(see illustration). These traps may be emptied by back pressure or by 
siphon. It is a good plan to have sufficient water in the trap so that it 
will never be empty. All these problems belong to the plumber and in- 
volve more or less arithmetic. 

To determine the pressure which the seal of a trap will resist : 
Example. — What pressure will a l|-inch trap resist ? 

If one arm of the trap has a seal of 1} inches, both arms will make a 
column twice as high, or 8 inches. Since a column of water 28 inches 
in height is equivalent to a pressure of 1 pound, or 16 ounces, a column 
of water 1 inch in height is equivalent to a pressure of |^ of a pound, or 
^} = ^ ounces, and a column of water 8 inches in height is equivalent to 
8 X ^ = "V* = 1.7 ounces. 

Therefore, a IJ-inch trap will resist 1.7 ounces of pressure. 



PLUMBING AND HYDRAULICS 353 

EXAMPLES 

1. What back pressure will a |-iiich seal trap resist ? 

2. What back pressure will a 2-inch seal trap resist ? 

3. What back pressure will a 2^inch seal trap resist ? 

4. What back pressure will a 4J-inch seal trap resist ? 

5. What b^ck pressure will a 5-inch seal trap resist ? 

Water Power 

When water flows from one level to another, it exerts a 
certain amount of energy, which is the capacity for doing 
work. Consequently, water may be utilized to create power 
by the use of such means as the water wheel, the turbine, and 
the hydraulic ram. 

Friction, which must be considered when one speaks of 
water power, is the resistance which a substance encounters 
when moving through or over another substance. The amount 
of friction depends upon the pressure between the surfaces in 
contact. 

When work is done a part of the energy which is put into 
it is naturally lost. In the case of water this is due to the 
friction. All the power which the water has cannot be used 
to advantage, and efficiency is the ratio of the useful work done 
by the water to the total work done by it. 

Efficiency. — To find the work done upon the water when a 
pump lifts or forces it to a height, multiply the weight of the 
water by the height through which it is raised. 

Since friction must be taken into consideration, the useful 
work done upon the water when the same power* is exerted 
will equal the weight of the water multiplied by the height 
through which it is raised, multiplied by the efficiency of the 
pump. 

Example. — Find the power required to raise half a ton 



354 VOCATIONAL MATHEMATICS FOR GIRLS 

(long ton, or 2240 lb.) of water to a height of 40 feet, when 
the efficiency of the pump is 75 %. 

Total work done = weight x height x efficiency counter 
1120 X 40 X W = 59,733.8 ft. lb. 

H. P. required = 5M§M = 1.8. Ans. 
^ 33000 



EXAMPLES 

1. Find the power required to raise a cubic foot of water 
28', if the pump has 80 % efficiency.^ 

2. Find the power required to raise 80 gallons of water 15', 
if the pump has 75 % efficiency. 

3. Find the power required to raise 253 gallons of water 
18', if the pump has 70 % efficiency. 

4. Find the power required to raise a gallon of water 16', if 
the pump has 85 % efficiency. 

5. Find the power required to raise a quart of water 25', if 
the pump has 70 % efficiency. 

Density of Water 

The mass of a unit volume of a substance is called its 
density. One cubic foot of pure water at 39.1° F. has a mass 
of 62.425 pounds ; therefore, its density at this temperature is 
62.425, or approximately 62.5. At this temperature water 
has its greatest density. With a change of temperature, the 
density is also changed. 

With a rise of temperature, the density decreases until at 
212° F., the boiling point of water, the weight of a cubic foot 
of fresh water is only 59.64 pounds. 

When the temperature falls below 39.1° F., the density of 
water decreases until we find the weight of a cubic foot of ice 
to be but 57.5 pounds. 

1 Consider the time 1 minute in all power examples where the time is not giyen. 



PLUMBING AND HYDRAULICS 355 

EXAMPLES 

1. One cubic foot of fresh water at 62.6** F. weighs 62.365 lb., 
or approximately 62.4 lb. What is the weight of 1 cubic inch ? 
What is the weight of 1 gallon (231 cubic inches) ? 

2. What is the weight of a gallon of water at 39.1** F. ? 

3. What is the weight of a gallon of water at 212** F. ? 

4. What is the weight of a volume of ice represented by a 
gallon of water ? 

5. What is the volume of a pound of water at ordinary 
temperature, 62.5** F. ? 

Specific Gravity 

Some forms of matter are heavier than others, Le, lead is 
heavier than wood. It is often desirable to compare the 
weights of different forms of matter and, in order to do this, 
a common unit of comparison must be selected. Water is 
taken as the standard. 

Specific Gravity is the ratio of the mass of any volume of a 
substance to the mass of the same volume of pure water at 
4** C. or 39.1** F. It is found by dividing the weight of a known 
volume of a substance in liqui(J by the weight of an equal 
volume of water. 

Example. — A cubic foot of wrought iron weighs about 
480 pounds. Find its specific gravity. 

Note. — 1 cu. ft. of water weighs 62.425 lb. 

Weight of 1 cu. ft. of iron __. 480 __ 7 7 Ang 
Weight of 1 cu. ft. of water ~ 62.426 ~ * * 

To find Specific Gravity. — To find the specific gravity of a 
solid, weigh it in air and then in water. Find the difference 
between its weight in air and its weight in water, which will 
be the buoyant force on the body, or the weight of an equal 
volume of water. Divide the weight of the solid in air by its 
buoyant force, or the weight of an equal volume of water, and 
the quotient will be the specific gravity of the solid. 



356 VOCATIONAL MATHEMATICS FOR GIRLS 

Tables have been compiled giyjng the specific gravity of different solids, 
so it is seldom necessary to compute it. 

The specific gravity of liquids is very often used in the 
industrial world, as it means the " strength " of a liquid. In 
the carbonization of raw wool, the wool must be soaked in 
sulphuric acid of a certain strength. This acid cannot be 
bought except in its concentrated form (sp. gr. 1.84), and it 
must be diluted with water until it is of the required strength. 

Tbe simplest way to determine the specific gravity of a liquid is with 
a hydrometer. This instrument consists of a closed glass tube, with a 
bulb at the lower end filled with mercury. This bulb of mer- 
cury keeps the hydrometer upright when it is immersed in a 
liquid. The hydrometer has a scale on the tube which can 
be read when tbe instrument is placed in a graduate of the 
liquid whose specific gravity is to be determined. 

But not all instruments have the specific gravity recorded 
on the stem. Those most commonly in use are graduated 
with an impartial scale. 

In England, Twaddell^s scale is commonly employed, and 
since most of the textile mill workers are English, we find the 
same scale in use in this country. The Twaddell scale bears a 
marked relation tQ specific gravity and can be easily converted 
into it. 

Another scale of the hydrometer is the Beaume, but these 
readings cannot be converted into specific gravity without 
the use of a complicated formula or reference to a table. 

Htdrombtkr Scale Formula for Gontbrtino into S. G. 

1. Specific gravity hydrometer Gives direct reading 

2. Twaddell S. G. = O^xyiOO 

100 

8. Beaume S. G. = ^^'^ 




146.8 - N 
iV= the particular degree which is to be converted. 

Example. — Change 168 degrees (Tw.) into S. G. 

(.6x168) + 100 ^13^ ^^ 
100 



PLUMBING AND HYDRAULICS 357 

Another formula for changing degrees Twaddell scale into specific 
gravity is : (^ ^ ^^ ^^^ = specific gravity. 

In Twaddell^s scale, P specific gravity = 1.006 

2° specific gravity = 1.010 
8° specific gravity = 1.016 

and so on by a regular increase of .005 for each degree. 

To find the degrees Twaddell v^rhen the specific gravity is given, multi- 
ply the specific gravity by 1000, subtract 1000, and divide by 5. Formula : 

(S. G. X IWO) - 1000 ^ j^g^ TwaddeU 

ExAMPi.a. — Change 1.84 specific gravity into degrees Twad- 

deU, 

(1.M X 1000) - 1000 ^ jgg j^g^ TwaddeU 
5 

EXAMPLES 

1. What is the specific gravity of sulphuric acid of 116** Tw.? 

2. What is the specific gravity of acetic acid of 86** Tw. ? 

3. What is the specific gravity of a liquid of 164** Be. ? 

4. What is the specific gravity of a liquid of 108** Be.? 

5. What is the specific gravity of a liquid of 142** Tw.? 

Heat 

Heat Units. — The unit of heat used in the industries and 
shops of America and England is the British Thermal Unit 
(B, T. U.) and is defined as the quantity of heat required to 
raise one pound of water through a temperature of one degree 
Fahrenheit. Thus the heat required to raise 5 lb. of water 
through 15 degrees F. equals 

6 X 16 = 75 British Thermal Units (B. T. U.) 
Similarly, to raise 86 lb. of water through J° F. requires 
86 X i = 43 B. T. U. 

The unit used on the Continent and by scientists in America 
is the metric system unit, a calorie. This is the amount of 
heat necessary to raise 1 gram of water 1 degree Centigrade. 



358 VOCATIONAL MATHEMATICS FOR GIRLS 

EXAMPLES 

1. How many units (B. T. U.) will be required to raise 
4823 lb. of water 62 degrees ? 

2. How many B. T, U. of heat are required to change 365 
cubic feet of water from 66° F. to 208° F.? 

3. How many units (B. T. U.) will be required to raise 785 
lb. of water from 74° F. to 208° F.? 

(Consider one cubic foot of water equal to 62^ lb.) 

4. How many B. T. U. of heat are required to change 1825 
cu. ft. of water from 118° to 211° ? 

5. How many heat units will it take to raise 484 gallons of 
water 12 degrees ? 

6. How many heat units will it take to raise 5116 gallons 
of water from 66° F. to 198° F.? 



f{ f( 



100 



213' 



Temperature 

The ordinary instruments used to measure temperature 
are called thermometers. There are two kinds — Fahren- 
heit and Centigrade. The Fahrenheit ther- 
mometer consists of a cylindrical tube filled 
with mercury with the position of the mercury 
at the boiling point of water marked 212, and the 
position of mercury at the freezing point of 
water 32. The intervening space is divided into 
180 divisions. The Centigrade thermometer has 
the position of the boiling point of water 100 
and the freezing point 0. The intervening space 
is divided into 100 spaces. It is often necessary 
to convert the Centigrade scale into the Fah- 
renheit scale, and Fahrenheit into Centigrade. 

nTo convert F. into C, subtract 32 from the F. 
degrees and multiply by f , or divide by 1.8, or 
C. = (F. - 32°) I, where C. = Centigrade reading 
Thermometers and F. = Fahrenheit reading. 







17^ 






I 



32' 



0' 



HEAT AND TEMPERATURE 359 

To convert C. to F., multiply C. degrees by f or 1.8 and add 
32°. 

5 

Example. — Convert 212 degrees F. to C. reading 

5(212^ - 32-) ^ 5(180°) ^ 900'^ ^ ^^p ^ 
9 9 9 * 

Example. — Convert 100 degrees C. to F. reading. 

^ ^ ^^° H- 32° = ?52! + 32° = 180° + 32° = 212° F. 
6 6 

If the temperature is below the freezing point, it is usually 
written with a minus sign before it : thus, 15 degrees below the 
freezing point is written — 15°. ^n changing — 15° C. into F. 
we must bear in mind the minus sign. 

. Thus, \p = —-1-32° j?T_ - 15° X 9 ^ 3^o ^_27° + 32° =6° 

6 6 

Example. — Change — 22° F. to C. 

C. = 5 (F. - 32) 

C. =1 (-22°-32°) =5 (-64°) =-30° 

EXAMPLES 

1. Change 36° F. to C. 6. Change 225° C. to F. 

2. Change 89° F. to C. 7. Change 380° C. to F. 

3. Change 289° F. to C. 8. Change 415° C. to F. 

4. Change 350° F. to C. 9. Change 580° C. to F. 
^ 5. Change 119° C. to F. 

Latent Heat 

By latent heat of water is meant that heat which water ab- 
sorbs in passing from the liquid to the gaseous state, or that 
heat which water discharges in passing from the liquid to the 



360 VOCATIONAL MATHEMATICS FOR GIRLS 

solid state, without affecting its own temperature. Thus, the 
temperature of boiling water at atmospheric pressure never 
rises above 212 degrees F., because the steam absorbs the 
excess of heat which is necessary for its gaseous state. Latent 
heat of steam is the quantity of heat necessary to convert a 
pound of water into steam of the same temperature as the 
steam in question. 



COMMERCIAL ELECTRICITY 

Amperes. — What electricity is no one knows. Its action, 
however, is so like that of flowing water that the comparison is 
helpful. A current of water in a pipe is measured by the 
amount which flows through the pipe in a second of time, as 
one gallon per second. So a current of electricity is measured 




Water Analogy of Fall op Potbntdll 

by the amount which flows along a wire in a second, as one 
coulomb per second, — a coulomb being a unit of measurement 
of electricity, just as a gallon is a unit of measurement of 
water. The rate of flow of one coulomb per second is called one 
ampere. The rate of flow of five coulombs per second is five 
amperes. 

Volts. — The quantity of water which flows through a pipe 
depends to a large extent upon the pressure under which it 
flows. The number of amperes of electricity which flow along 
a wire depends in the same way upon the pressure behind it. 



COMMERCIAL ELECTRICITY 361 

The electrical unit of pressure is the voU. In a stream of 
water there is a difference in pressure between a point on the 
surface of the stream and a point near the bottom. This is 
called the difference or drop in level between the two points. 
It is also spoken of as the pressure head, " head '' meaning the 
difference in intensity of pressure between two points in a body 
of water, as well as the intensity of pressure at any point. 
Similarly the pressure (or voltage) between two points in an 
electric circuit is called the difference or drop in pressure or 
the potential. The amperes represent the amount of electricity 
flowing through a circuit, and the volts the pressure causing 
the flow. 

Ohms. — Besides the pressure the resistance of the wire 
helps to determine the amount of the current : — the greater 
the resistance, the less the current flowing under the same 
pressure.. The electrical unit of resistance is called an ohm. 
A wire has a resistance of one ohm when a pressure of one volt 
can force no more than a current of one ampere through it. 

Ohm's Law. — The relation between current (amperes), 
pressure (volts), and resistance (ohms) is expressed by a law 
known as Ohm^s Law, This is the fundamental law of the 
study of electricity and may be stated as follows : 

An electric current flowing along a conductor is equal to 
the pressure divided by the resistance. 

Currera (amperes) = ^e^^"'-^ ijo^^) 

Resistance (ohms) 

Letting /= amperes, E = volts, R = ohms, 

J=^-f-i?or/ = =| 

R 

E==IR 

"-1 

Example. — If a pressure of 110 volts is applied to a re- 
sistance of 220 ohms, what current will flow ? 



362 VOCATIONAL MATHEMATICS FOR GIRLS 



Example. — A current of 2 amperes flows Ina circuit the resist- 
ance of which is 300 ohmB. What is the voltage of the circuit ? 



ExAMPLR. — If a current of 12 amperes flows in a circuit 
and the voltage applied to the circuit is 240 volts, find the 
resistance of the circuit. 

^ = B — =20oUms. Am. 
I 12 

Ammeter and Voltmeter. — Ohm's Law may be applied to a 

circuit as a whole or to any part of it. It is often desirable to 

know how much current is flowing 

in a circuit without calculating it by 

Ohm's Law. An instrument called 

an ammeter is used to measure the 

current. This instrument has a 

low resistance so that it will not 

cause a drop in pressure. A volt- 

Toeter is used to measure the voltaga 

This instrument has high resistance 

so that a very small current will 

flow through it, and is always placed in shunt, or parallel 

(see p. 235) with that part of the circuit the voltage of which 

is to be found. 

Example. — What is the resistance of wires that are carry- 
ing 100 amperes from a generator to a motor, if the drop or 
loss of potential equals 12 volts ? 

Drop in voltage — IE / = 100 amperes 

Drop Id volU =12 11= ? obms 

It=- B= — = 0.12ohai. Atu. 

I 100 

Example. — A circuit made up of incandescent lamps and 
conducting wires is supplied under a pressure of 115 volts. 



COMMERCIAL ELECTRICITY 



363 



The lamps require a pressure of 110 volts at their terminals 
and take a current of 10 amperes. What should be the resist- 
ance of the conducting wires in order that the necessary cur- 
rent may flow ? 

Drop in conducting wires = 115 — 110 = 6 volts 

Current through wires = 10 amperes 

E 6 
jB= — = — = 0.6 ohm resistance. -4ns. 

/ 10 



EXAMPLES 

1. How much current will flow through an electromagnet 
of 140 ohms' resistance when placed across a 100-volt circuit ? 

2. How many amperes will flow through a 110-volt lamp 
which has a resistance of 120 ohms ? 

3. What will be the resistance of an arc lamp burning 
upon a 110-volt circuit, if the current is 5 amperes ? 

4. If the lamp in Example 3 were to be put upon a 150-volt 
circuit, how much additional resistance would have to be put 
into it in order that it might not take more than 5 amperes ? 




Motor 

Electric Road System 

5. In a series motor used to drive a street car the resistance 
of the field equals 1.06 ohms ; the current going through equals 
30 amperes. What would a voltmeter indicate if placed 
across the field terminals ? 

6. If the load upon the motor in Example 5 were increased 
so that 45 amperes were flowing through the field coils, what 
would the voltmeter then indicate ? 



i^ 



INDEX 



Addition, 3 

Compound numbers, 46 

Decimals, 33 

Fractions, 21 
Aliquot parts, 39 
Alkalinity of water, 298 
Ammeter, 362 
Ammonia, 296 
Amount, 53 
Amperes, 169, 360 
Angles, 66 

Complementary, 66 

Right, 66 

Straight, 66 

Supplementary, 66 
Annuity, 192 
Antecedent, 37 
Apothecary's weights, 276 
Apothem, 72 

Approximate equivalents between 
metric and household measures, 
281 
Approximate measures of fluids, 277 
Arc, 64 

Area of a ring, 65 
Area of a triangle, 69 
Atmospheric pressure, 349 
Avoirdupois weight, 43 



Bacteria, 294, 298 
Banks, 178 

Cooperative, 179 

National, 178 

Savings, 179 
Baths, 292 
Bed linen, 161 
Beef, 118 
Bills, 243 

Blue print reading, 80 
Board measure, 131 
Bonds, 187 
Brickwork, 134 



Building materials, 133 
Buying Christmas gifts, 94 

Cotton, 229 

Rags, 229 
. Wool, 229 

Yarn, 229 



Cancellation, 13 
Capacity of pipes, 348 
Carbohydrates, 102 
Cement, 136 
Chlorine, 297 
Circle, 64 
Circumference, 64 
Civil Service, 268 
Claims, 196 
Clapboards, 138 
Clothing, 91 
Coefficients, 331 
Color of water, 296 
Common denominator, 20 

Fractions, 17 

Multiple, 15 
Comparative costs of digestible 
nutrients and energy in different 
food materials at average prices, 
114, 115 
Compound numbers, 42, 46 

Addition, 46 

Division, 47 

Multiplication, 47 

Subtraction, 46 
Computing profit and loss, 252 
Cone, 75 
Consequent, 57 
Construction of a house, 128 
Cooperative banks, 179 
Cost of food, 105 
Cost of furnishing a house, 146 
Cost of subsistence, 91 
Cotton, 217 

Yarns, 223 

365 



4 



366 



INDEX 



Counting, 44 
Credit account, 244 
Cube, 61 
Cube Root, 61 
Cubic measure, 42 
Cuts of Beef, 120 

Mutton, 122 

Pork, 121 
Cylindrical tank, 347 

Dairy Products, 310 

Debit, 244 

Decimal Fractions, 30 

Addition, 33 

Division, 36 

Mixed, 31 

Multiplication, 35 

Reduction, 32 

Subtraction, 34 
Denominate fraction, 45 

Number, 42, 45 
Denomination, 42 
Denominator, 17 
Density of water, 354 
Deodorants, 294 
Diameter, 64 

Distribution of income, 89 
Division, 9 

Compound numbers, 47 

Fractions, 25 

Income, 92 
Drawing to scale, 85 
Dressmaking, 198 
Dry measure, 43 

Economical marketing, 125 

Uses of Meats, 117 
Economy of space, 130 
Efficiency of water, 353 
Electricity, 360 
EUipse, 72 
En^ish system, 276 
Ensilage problems, 307 
Equations, 332 

Substituting, 334 

Transposing, 334 
Equiangular triangle, 68 
Equilateral triangle, 68 
Estimating distances, 86 

Weights, 87 
Evolution, 61 



Exchange, 193 

Expense account book, 95 

Factors, 13 

Farm measures, 307 

Problems, 305 
Filling, 217 
Flax, 217 
Flooring, 139 
Fluid measure, 277 
Food, 100 

Values, 110 
Formulas, 327 

For computing profit and loss, 253 
Fractions, 17 

Addition, 21 

Common, 17 

Decimal, 30 

Division, 25 

Improper, 17 

Multiplication, 24 

Reduction, 17 

Subtraction, 22 
Frame and roof, 132 
Free ammonia, 297 
Frustum of a cone, 76 
Furnishing a bedroom, 153, 154, 155 

Dining room, 156 

Hall, 146 

Kitchen, 162 

Living room. 149, 150. 152 

Sewing room, 161 

Germicides, 294 

Graphs, 322 

Greatest common divisor. 15 

Hardness of water. 298 
Heat, 357 

And Ught, 167 

Units, 357 
Hem, 200 
Hexagon, 72 
Horizontal addition, 237 
Household linens, 160 

Measures, 277 
How to make change, 266 

Solutions of various strengths from 
crude drugs or tablets of known 
strength, 286 



INDEX 



367 



How to read an electric meter, 169 

Gas meter, 168 
Hypodermic doses, 288 

Improper fractions, 17 
Inclined planes, 344 
Income, 89 

Inside area of tanks, 348 
Insurance, 188 

Fire, 188 

Life, 189 
Integer, 1, 17, 31, 45 
Interest, 53 

Compound, 56 

Simple, 53 
Interpretation of negative quantities, 

337 
Invoice bills, 243 
Involution, 61 
Iron in water, 298 
Isosceles triangle, 68 

Jack screw, 344 

Kilowatt, 169 

Kitchen weights and measures, 103 

Latent heat, 359 
Lateral pressure, 351 
Lathing, 141 
Law of squares, 348 
Least common multiple, 15 
Ledger, 244 
Levers, 344 
Linear measure, 42 
Linen, 217 

Yarns, 222 
Liquid measure, 43 
Lumber, 131 

Machines, 344 
Measure, of time, 43 

Length, 317 
Medical chart, 292 
Mensuration, 64 
Menus, making up, 113 
Merchandise, 243 
Methods of heating, 174 
Methods of solving examples, 87, 

88 
Metric system, 276, 279, 282, 317-319 



Millinery problems, 212 
Mixed decimals, 31 
Mohair, 217 
Momentum, 342 
Money orders, 194 
Mortar, 133 
Mortgages, 180 
Motion, 342 
Multiplication, 8, 242 

Algebraic expressions, 339 

Compound numbers, 47 

Decimals, 31 

Fractions, 24 
Mutton, 122. 123 

National banks, 178 

Nitrogen, 297 

Notation, 1 

Notes, 181 

Numerals, Roman, 2 

Numeration, 1 

Numerator, 17 

Nurses, arithmetic for, 276-303 

Nutritive ingredients of food, 101 

Octagon, 72 
Odor of water, 296 
Ohm, 361 
Ohm's Law, 361 
Oxygen consumed, 297 

Painting, 141 
Papering, 142 
Paper measure, 44 
Pay rolls, 255 
Pentagon, 72 
Percentage, 50 
Perimeter, 72 
Plank, 131 
Plastering, 133 
Polygons, 72 
Poultry problems, 312 
Power, 30 
Pressure, lateral, 351 

Per square inch, 350 

Water, 350 
Principal, 53 
Profit and loss, 246 
Promissory notes, 182 
Proper fractions, 17 
Proportion, 57, 58, 59 



368 



INDEX 



Protractor, 67 
Pulleys. 344 
Pyramid, 75 

Quadrilaterals, 71 

Radius, 64 

Rapid calculation, 233 

Rate (per cent), 50 

Ratio, 57 

Raw silk yams, 222 

Reading a blue print, 80 

Rectangle, 71 

Reduction, 42 

Ascending, 42, 44 

Descending, 42, 44 
Right triangles, 68, 69 
Roman numerals, 2 
Root, cube, 62 

Sqi^are, 61 
Ruffles, 201 
Rule of thumb methods, 88 

Savings bank, 179 

Interest tables, 56 
Scalene triangle, 68 
Sector, 64 

Sediment in water, 296 
Shingles, 137 
Shoes, 219 
Silk, 217 
Similar figures, 77 

Terms, 331 
Simple interest, 53 

Proportion, 59 
Slate roofing, 137 
Specific gravity, 355 
Specimen arithmetic papers, 272 

Sealers of Weights and Measures, 
273 

State visitors, 274 

Stenographers, 273 
Sphere, 76 
Spun silk yarns, 223 
Square measure, 42 
Square root, 62 
Stairs, 140 
Steers and beef, 118 
Stocks, 184 
Stonework, 135 
Strength of solutions, 224 



Studding, 132 

Substituting in equations, 334 

Subtraction 

Compound numbers, 46 

Decimals, 34 

Fractions, 22 
Supplement, 66 

Table linen, 161 

Table of metric conversion, 317 

Table of wages, 257 
Tanks, 347 
Taxes, 143 

Temperature, 290, 358 
Temporary loans, 259 
Terms used in chemical and bacterio- 
logical reports, 296 
Time and speed, 341 
Time sheets, 255 
Trade discount, 52, 207 
Transposing in equations, 334 
Trap)ezium, 71 
Trapezoid, 72 
Triangles, 68 

Equiangular, 68 

Equilateral, 68 

Isosceles, 68 

Right, 68, 69 

Scalene, 68 
Trust companies, 179 
Tucks, 199 

Turbidity of water, 296 
Two-ply yarns, 223 

Unit, 1 

United States revenue, 144 

Useful mechanical information, 341 

Use of tables, 88 

Uses of nutrients in the body, 102 

Value of coal to produce heat, 167 
Volt, 169, 360 
Voltmeter, 362 
Volume, 74 

Warp, 217 

Water, alkalinity of, 298 

Ammonia in, 296, 297 

Analysis of, 296 

Bacteria in, 298 

Chlorine in, 297 



INDEX 



369 



Water, ^ — continued. 
Color of, 296 
Hardness of, 298 
Iron in, 298 
Nitrogen in, 297 
Odor of, 296 

Oxygen consumed by, 297 
Power, 353 
Pressure, 350 

Residue on evaporation, 296 
Sediment in, 296 
Supply, 345 
Traps, 352 
Turbidity of. 296 



Watt, 170 
Wool, 211 
Woolen yarns, 220 
Work, 343 
Worsted yarns, 219 

Yarns, 217 
Cotton, 223 
Linen, 222 
Raw silk, 222 
Spun silk, 223 
Two-ply, 223 
Woolen, 220 
Worsted, 219 



1^-^ 



YB 0520C 



1