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About Google Book Search Google's mission is to organize the world's information and to make it universally accessible and useful. Google Book Search helps readers discover the world's books while helping authors and publishers reach new audiences. You can search through the full text of this book on the web at |http: //books .google .com/I EFFICI ENCY ARITHMETIC ADVANCED BY CHARLES E. CHADSEY, Ph. D. SUPERINTENDEl^r' OF SCHOOLS DETROIT. MICH. • AND JAMES H. SMITH, A. M. INSTRUCTOR IN MATHEMATICS AND MANUAL TRAINING. SCHOOL OF EDUCATION. UNIVERSITY OF CHICAGO ATKINSON, MENTZER & COMPANY CHICAGO NEW YORK BOSTON ATLANTA DALLAS / 615124 C COPYRIGHT, 1917, BY' ATKINSON, MENTZER & COMPANY All rights reserved PREFACE This book has been prepared in the belief that work in Arithmetic in the seventh and eighth grades should emphasize drill upon fundamentals and their application to living, vital problems that the average child is almost sure to encounter in his individual experiences. At the same time, it is recognized that for the great majorit3;^^ing the l>ooks of this series certain topics will never receive %bf&ideration in the school training unless presented in this volume. Great care has been taken to present these topics in a simple, clear manner which ought to make their meaning and significance intelligible even to the younger pupils. The problems of the book, almost without exception, are actual problems taken from the various lines of business represented. Business men from all sections of the country have contributed problems, furnished definite and accurate information upon which to base problems, and have criticized the work from the standpoint of practical efficiency and reliability. Acknowledgment is hereby made to these gentle- men for their invaluable assistance. The methods of presentation and explanation of topics new to the child have been carefully tested in the school room and their effectiveness is thereby assured. Simplicity, clearness, and the avoidance of unnecessary repetition we believe to be characteristic of this series, especially in the applications of percentage and practical measurements which so often unneces- sarily confuse the pupil. Many school systems are modifying their courses in mathe- mathics in order to permit elementary algebra to be commenced in the eighth grade. This volume permits, through its arrange- ment, a very simple omission of topics in Part I which will III IV PREFACE enable any teacher to cover the essential topics in less than the customary two years. The arrangement also enables those who prefer to postpone some of the topics found in Part I to combine the seventh- and eighth-grade topics in such a way as to give a more extended discussion of closely related subjects. The fact that there are in reality only a few mathematical principles involved in ordinary arithmetic is kept clearly in mind. Too often the pupil has been led to believe that each new topic has little in common with preceding topics and therefore fails to learn the greatest educational lesson that can be taught — ^the application of a known principle to a new condition. The effort in this book is to keep the relationship between mathematical facts constantly before the pupil. Teachers of arithmetic must never forget that accuracy and reasonable rapidity in manipulation of niunbers are one of the chief aims in this study. Pupils of the seventh and eighth grades need continued practice of this kind. Ample oppor- tunity for this drill is furnished, and from the beginning to the end of the course there should be recurrence to these exercises. While it is not possible, in the limited space, to make personal acknowledgment to the large number of educators who have rendered assistance of great value in the preparation of this volume, the authors desire to express their indebtedness especially to Miss Katherine L. McLaughlin of the Elementary School of the School of Education, University of Chicago, to Mr. Warren E. Hicks, Assistant for Industrial Education, Department of Public Instruction, Madison, Wisconsin, to Mr. Lewis A. Bennert, Principal of School No. 3, Patterson, New Jersey, and to Mr. James C. Thomas of the publishers' editorial department, for their invaluable criticisms and suggestions. CONTENTS PART I— SEVENTH YEAR CHAPTER I. REVIEW OF THE FUNDAMENTALS— 1-22 Training for Speed and Accuract. CHAPTER II. REVIEW OF FRACTIONS— 23-44 Three Meanings op Fractions, 23; Reduction op Fractions, 23, Addition and Substraction of Frachons, 25; Multiplication and Division op Fracteons, 29; Review op Decimals, 34; Appued Rbtiew Problems in Fractions, 41. CHAPTER III. PERCENTAGE— 46-76 • Explaining Per Cent, 45; The Decimal Point and Percentage, 45; Common Fractions and Their Equivalent Per Cents, 46; Equations Applied to Percentage, 48; Drill Problems in Percentage, 51; Problems Collected bt Pupils, 61; Applied PiiOBLBBis in Per- centage, 63. CHAPTER IV. APPLICATIONS OF PERCENTAGE— 77-112 Business Transactions, 77; Discounts, 79; Interest, 83; Partial Payments, 89; Commission, 92; Taxes, 95; Special Assessments, 98; Custom Duties, 100; Internal Revenue, 103; Income Taxes, 104; Insurance, 106. CHAPTER V BUSINESS FORMS AND ACCOUNTS— 113-132 Sales Sups, 113; Invoices, 115; Monthly Statements, 117; Receipts, 118; Cash Accounts, 119; Daybook or Journal, 121; Personal Accounts, 122; Inventories, 124; Pay Rolls, 125; Cashier's Memo- randum, 126; Agencies for Shipping Merchandise, 127. CHAPTER VI. PRACTICAL MEASUREMENTS— 133-154 Lines and Angles, 135; Rectangles, 137; Boy Scouts — Appued Problems, 140; Parallelograms, 142; Trapezoids, 144; Triangles, 145; Area of Triangles, 146; Appued Problems, 149. CONTENTS PART II— EIGHTH YEAR CHAPTER I. REVIEW EXERCISES— 155-178 Training for Efficibnct, 155; Chbcking Up, 155; Speed Tests in Multiplication, 159; Short Methods in Multiplication, 160; Speed Tests in Division, 164; Short Methods in Division, 164; Review of Fractions, 167; Review of Decimals, 169; Review of Percentage, 170. CHAPTER II. BANKS AND BANKING— 179-206 National and State Banks, 179; Federal Reserve Banks, 181; Savings Accounts, 186; Bank Discount, 188; Exchange, 190; Stocks AND Bonds, 194; Signatures and Seals, 199; Investbientb, 203. CHAPTER III. REMITTING MONEY— 207-218 Postal Money Orders, 207; Express Monet Orders, 208; Bank Drafts, 209; Checks, 210; Emergency Remittances, 212; Telegraph- ing Money, 212; Cabling Money, 213; Money by Wireless, 14. CHAPTER IV. PRACTICAL MEASUREMENTS— 219-254 • QUADRILATERAU3, 219; TRIANGLES, 220; SQUARES AND SqUARB RoOTS 221; Right Triangles, 226; Equilateral Triangles, 231; Circles, 233; Shop Problems, 235; Hexagons, 240; Solids, 241; Prisms, 242; Cylinders, 246; Silos, 247; Irrigation, 248; Good Roads, 250. CHAPTER V. GRAPHS— 255-261 Pictorial Graphs, 255; Line Graphs, 256; Bar Graphs, 258; Dis- tribution Graphs, 260; Circle Graphs, 261. CHAPTER VI. MEASURING INSTRUMENTS-262-279 Thermometer, 262; Barometer, 264; Hygrobceter, 265; Weather Reports, 266; Electric Meter, 270; Gas Meter, 272; Steam Gauge, 274; Surveyor's Chain, 275; Measurement of Time, 276; Standard Time, 277; International Date Line, 279. CHAPTER VII. THE METRIC SYSTEM— 280-287 Weights and Measures, 280; Lengths, 281; Square Measure, 282; Volume, 283; Capacity, 284; Weight, 285. CHAPTER VIII. EFFICIENCY IN THE HOME— 288-299 Building a HoifE, 289; Furnishing a HoiiE, 290; Expenses of a Home, 292; Camppire Girls, 293; The Family Budget, 294; Efficiency IN Business, 296; Supplement, 300; Index, 313. ADVANCED ARITHMETIC PART I Ttaining for Speed and Accurate Several weeks before the opening of the regular baseball season, the players of the big leagues go soutli for a spring training trip. The players, with their lack of exercise during the winter's vacation, would not be in proper condition to go into the opening game of the season without this sort of preparation. You are just returning from a sunmier's vacation, during which you have lost some of your speed and accuracy in the various processes of arithmetic. It is therefore wise for you to take a preliminary trainii^ trip by reviewing the f uudamentfd When asked what the new workers in his firm needed most in arithmetic, the head of the school for training workers in one of the largest mercantile firms in the country replied: "Teach them to add, subtract, multiply and divide." He emphasized what all business men want — speed and accuracy in those four fundamental processes. CHAPTER I REVIEW EXERCISES Exercise 1. Reading Numbers In your studies and in reading the magazines and daily papers you are frequently called upon to read numbers. For convenience in reading, large numbers are pointed off into periods as in the following illustration: . g - (=3 5 » goo ts 3 -3 3 § g i 2 • g -3 § I •§ I i -a » & c ■*» M o ^ a 6,069,000,000,000,000,000,000. The number above represents the estimated weight of the earth in tons. Read it. In the following table the diameter and average distance from the sun is given for each of the planets in our solar system. Read these distances. Naiue of planet Diameter in miles Average distance from the sun in miles 1. Mercury 2,962 35,392,638 2. Venus 7,510 66,131,478 3. Earth 7,925 91,430,220 4. Mars 4,920 139,312,226 6. Jupiter 88,390 475,693,149 6. Saturn 77,904 872,134,583 7. Uranus 33,024 1,753,851,052 8. Neptune 36,620 2,746,271,232 A rapid review of this chapter should be given, followed by a systematic use of one or more of the standardized drill exercises at the beginning of each recitation period. REVIEW EXERCISES Exercise 2. Writing Numbers Occasionally one is called upon to write difficult numbers, and he should be able to do so when the need arises. Write the following numbers: 1. Ten thousand ten. 2. One hundred fifty thousand fifteen. 3. Two million two hundred thousand. 4. Sixteen million sixteen thousand sixteen. 6. Twenty-eight million four hundred fifteen thousand. 6. Two billion one million two hundred thousand seventy. 7. Four trillion four hundred billion two million. 8. Sixteen billion sixty million fifteen thousand. 9. Twenty-four billion sixty million sixty thousand. 10. Seventy million seventeen thousand six. 11. Twenty-nine billion six million twenty thousand. 12. Fifty million one hundred fifty thousand thirteen* 13. Forty billion one hundred seventy million. 14. Eight hundred thousand nine hundred sixty-four. 16. Twenty-four million twenty-six thousand two hundred. Exercise 3. Roman Notation It is customary to express chapters of books and often dates on important buildings in Roman numerals. Read the following numbers: 1. IV 6. XIX 11. XLIV 16. D 2. VI 7. XX 12. LXVI 17. M 3. XIV 8. XXII 18. XC 18. MDC 4. XVI ». XXXIV 14. XCVII 19. MDCCCXCVII 6. XVIII 10. XL 16. C 20. MDCCCCXVII Express in Romaii numerals: 1. 9 S. 29 6. 47 7. 72 9. 1492 2. 14 4. 33 «. 58 8. 96 10. 1918 4 SEVENTH YEAR EXERCISES FOR SPEED AliD ACCURACY Addition! Subtractioni Multiplication and Division^ To THE Teacher: The following exercises have been ar- ranged to assist pupils to develop accuracy and speed in the fundamental operations. The exercises have been organized so that the same time should be given for each exercise. For the seventh grade allow two minutes for each exercise. If the teacher finds that the previous preparation of the class makes this standard too high, or too low, she should adjust the time limit to suit her class. The best results can be secured if it is possible to have these exercises hektographed or mimeographed for drill purposes. Some of the exercises can be conveniently done by placing a sheet of paper under the examples in the book and writing the answers on this sheet of loose paper. Every exercise should be jsiccurately timed with a watch. These exercises may be used in two ways: (1) All pupils may practice on each exercise together. After time is called, the pupils should exchange papers and correct them as the teacher reads the answers. Keep individual records of the number of examples right for each exercise. (2) Start all of the pupils on Exercise 4. As soon as the pupil has finished correctly all the examples in one exercise within the time allowed, have him try the next exercise. Under this plan a pupil can progress at his own pace. Individual differences in pupils are thus recognized and provided for by this method. The papers of those who have finished should be collected and corrected before the next drill period. Some reliable pupil may be appointed by the teacher to help in this work. ^These exercises were arranged by Charles L. Spain, Assistant Supt. of Schools, Detroit, Michigan. EXERCISES FOR SPEED AND ACCURACY ] Sxercis ie 4. Addition 6 9 7 6 2 3 6 1 4 9 6 6 7 1 2 3 1 7 9 7 4 4 6 7 7 3 3 8 7 2 4 9 2 9 2 6 9 6 7 2 1 6 1 6 3 3 8 7 6 7 8 4 4 9 6 2 6 6 6 9 7 8 7 6 9 2 6 4 8 8 9 6 1 1 4 9 4 9 2 4 4 4 6 1 6 8 3 3 1 7 7 6 3 3 7 2 4 1 6 3 6 2 Exercise 6. Subtraction 17 66 98 77 19 34 76 68 49 46 49 66 647674683463 66 76 97 88 49 83 66 99 89 67 28 36 3 4 6 6 7 2 6 16 6 4 3 23 76 83 72 66 67 43 69 66 66 69 J 2 1 2 6 7 3 9 6 _6 4 Exercise 6. Addition 4 7 4 1 2 2 6 7 6 3 2 4 9 1 4 1 4 9 1 3 3 3 8 6 1 3 6 3 2 6 2 1 1 2 1 8 6 6 8 3 2 6 7 8 1 8 9 2 6 6 7 8 1 3 1 1 6 1 9 8 7 6 1 9 6 4 4 8 6 2 8 7 4 8 9 6 7 2 3 1 1 6 6 9 6 6 9 3 8 6 SEVENTH YEAR Exercise 7. Addition 56 31 47 24 14 24 32 70 32 48 61 62 15 33 36 18 17 43 20 20 26 81 42 22 72 21 13 50 73 13 27 16 48 33 52 75 32 17 12 26 31 33 41 21 23 62 26 61 Exercise 8. Multiplication 26 46 68 94 87 53 85 67 26 49 2 3 7 5 6 7 4 8 9 5 24 19 28 91 87 39 83 16 54 57 4 2 6 3 7 4 9 7 6 3 Exercise 9. Addition . 32 24 31 25 70 42 50 36 16 13 22 33 17 31 30 20 31 62 11 10 11 16 19 32 20 42 25 62 17 10 23 60 19 13 20 16 51 55 61 16 30 22 4^ 12 20 32 14 12 Exercise 10. Subtraction 68 57 79 32 61 89 76 78 39 48 59 36 27 34 26 21 20 65 60 18 22 36 54 16 44 62 76 63 67 31 44 89 74 42 80 33 31 41 74 33 20 11 22 67 63 32 60 21 The order of the examples in each of these exercises should be fre- quently changed to prevent memorizing of answers. EXERCISES FOR SPEED AND ACCURACY Exercise 11. Division 8)48 7)66 9)81 6)46 7)84 4)36 7)63 6)64 6)66 8)66 9)63 7)36 6)60 9)90 4)36 9)46 4)20 7)42 7)70 9)36 8)40 6)36 6)36 6)48 9)99 8)64 9)64 9)27 3)24 6)42 6)66 8)80 7)77 6)72 6)60 3)21 7)28 4)40 s 6)40 6)26 4)24 3)27 8)98 4)48 3)33 3)30 6)24 8)32 6)16 6)18 7)28 3)36 4)44 2)22 4)16 Exercise 12. Addition 36 17 63 48 27 13 1 37 > 16 67 26 38 32 69 26 62 67 18 26 42 29 49 42 17 36 66 IE 1 27 ; 64 36 26 64 26 34 48 39 66 22 18 24 28 Exercise 13. Addition 6 3 6 1 6 7 7 7 6 4 7 6 8 3 6 1 3 4 9 6 4 • 9 4 8 6 6 9 1 9 6 7 9 6 1 7 7 7 4 9 3 7 1 1 1 7 8 9 4 4 1 1 6 6 7 6 4 2 9 7 6 2 9 6 4 8 2 6 7 6 4 7 8 8 6 9 6 7 9 7 7 6 4 4 6 1 8 6 7 8 8 SEVENTH YEAR Exercise 14. Subtraction 66 39 61 46 76 31 92 99 48 28 43 32 64 17 67 76 76 92 29 68 67 44 87 46 26 68 16 49 16 36 68 23 21 74 46 88 62 63 77 66 19 36 12 69 22 34 24 61 Exercise 16. Addition 2 6 6 4 13 2 6 3 4 4 12 7 5 1 24763239 11379757 44337816 14228447 22 6 6 6 2 2 5 66342633 32243361 Exercise 16. Multiplication 168 672 327 689 216 379 4 7 9 3 8 6 427 626 917 669 637 329 3 _6 _* _2 _8 8 Exercise 17. Addition 76 77 86 96 66 89 66 47 38 36 39 34 79 46 64 95 37 46 26 36 32 68 96 34 86 68 76 77 99 47 46 77 EXERCISES FOR SPEED AND ACCURACY 9 Exercise IB. Division 23)698 • 17)306 72)864 38)466 36)736 27)729 Exercise 19. Addition 68 16 18 22 16 12 S2 19 13 47 29 11 26 29 20 32 • 20 20 66 37 14 28 60 40 26 26 13 14 22 29 37 17 34 22 28 27 17 14 36 14 36 ^ Exercise 20. Subtraction 63 41 74 p 63 81 70 84 27 26 36 19 17 29 46 30 43 78 66 42 63 67 22 39 49 37 17 44 48 48 41 64 47 40 22 63 39 33 66 38 39 16 44 Exercise 21. Addition 22 69 36 61 76 37 29 41 36 64 37 64 70 60 67 37 22 71 67 27 63 37 90 31 43 22 76 26 79 67 61 96 27 87 88 68 10 SEVENTH YEAR Exercise 22. Mttltiplication 48 67 72 86 92 83 60 76 30 40 60 20 60 70 80 40 84 36 48 63 71 38 93 90 60 40 80 90 20 30 Exercise 23. Addition 38 67 32 21 36 30 74 72 64 67 64 43 29 63 44 78 34 43 76 97 60 76 61 61 78 86 89 66 83 27 20 66 96 96 64 10 40 81 67 36 These exercises axe continued on page 14. Exercise 24 Not only does one need to know how to work examples rapidly in addition, subtraction, multiplication and division, but he also needs to know how to apply these processes rapidly and accurately in solving problems. The time limit set for the abstract drill exercises is not to be used for this exercise. The teacher may have the pupils complete the solutions of these exercises for seat work. In the following exercise merely indicate the processes used in solving each problem: 1. A real estate dealer owns a farm of 142 acres worth $125 an acre; 6 city lots worth $1500 each and a store valued at $8750. Find the value of all of his property. Suggestions for solution: 142 acres are worth 142 times as much as 1 acre, hence multipHcation is the process necessary for finding the value of the farm. The next statement says: "5 city lots worth $1500 each.** The word each is the key word in that statement. 6 lots are worth 5 times as much as 1 lot, hence multiplication is used to find the value of the 5 lots. To find the value of the farm, the five city lots and the store, we must find the sum of all their values, hence addition is the last process. PRACTICE PROBLEMS 11 Indicating the soMion:^ (142 X $125) + (5 X $1500) +$8750 = value of all of his property. 2. A farmer sold 6 jars of butter containing respectively 24 lb., 26 lb., 29 lb., 28 lb., and 31 lb. Find the total num- ber of pounds that he sold. Indicating the sohdion: 24+26+29+28+31 =no. of lb. sold. 8. A boy bought a pony for $55. His expenses for the month amounted to $6. He sold the pony for $58. Did he gain or lose and how much? 4. The cost of drilling a well was 40|4 per foot for drilling and 80^ per foot for the iron tubing. If the well was drilled 150 ft. and 100 ft. of tubing was used, how much did it cost? 5. The distance from Chicago to St. Louis is 282 miles. What will a round-trip ticket cost at 2^ per mile? 6. A man bought a lot for $1250. He built a house on it that cost $5275 and then sold the property for $7000. How much did he gain? 7. In 1917, the House of Representatives had a membership of 435. If the population of the United States was approxi- mately 100,000,000 at that time, what was the number of people to one representative? 8. A farmer exchanges 36 bushels of apples at $1 per bushel for coal at $8 per ton. How many tons does he receive? 9. Mr. Brown bought a house for $8000. He paid $2000 down and agreed to pay the balance in 8 equal yearly payments. How large was each payment? 10. A real estate man trades 40 front feet of city ground at $240 a front foot for a Western farm of 80 acres. How much is the farm worth per acre? ^Parentheses should be used to separate the various steps in the problem in order to eliminate the necessity for teaching the law of signs. 12 SEVENTH YEAR 11. K, as computed, the water area of the earth is approxi- mately 144,500,000 square miles and the total surface of the earth is approximately 196,907,000 square miles, how much more water surface than land is there? 12. If the flow of water through the Chicago Drainage Canal is 360,000 cubic feet per minute, how much water passes through it in 24 hours? 18. A building worth $400,000 was damaged to the. amount of $75,000 by fire. The owners received from an insurance company $60,000 damages. What was the net loss to the owners of the building? 14. A falling body drops 144 feet in three seconds and 256 feet in four seconds. How far does it drop in the fourth second? 16. The product of four numbers is 10,920; three of the num- bers are 7, 8 and 15. What is the fourth number? 16. A gallon contains 231 cubic inches. How many gallons are there in a cubic foot (1728 cubic in.)? • 17. A man had $1275.45 on deposit in a bank. He gave checks for the following amounts: $110.00; $25.00; $222.50; $8.75 and $76.25. What was his balance in the bank after those checks had been cashed? 18. 15 acres of potatoes yielded 4125 bushels. What was the average yield per acre? 19. Mr. Jones bought 79 acres of land for $5530. How much did he pay per acre? 20. A speculator bought wheat in the fall of 1916 for $1.59 per bushel and sold it for $1.73 per bushel. How much did he make if he handled 600,000 bushels in the deal? 21. A man earns $1200 a year. His expenses per year are $975. In how many years can he save $1800 under those conditions? ' PRACTICE PROBLEMS 13 22. Mrs. Klein bought 2 dozen eggs at 28 cents per dozen, 2 pounds of butter at 38 cents per pound and 10 pounds of sugar for 63 cents. How much change should she receive from a ten-dollar bill? 23. A grocer bought 300 sacks of flour at 75^ per sack and paid $12.00 freight on the whole amount. He is selling the flour at $1.00 per sack. How much profit does he make on each sack? 24. A man bought three houses. He paid $5500 for the first; $4565 for the second and $7750 for the third. He sold the three houses for $18,500. How much did he gain? 25. A farmer sold 1600 bushels of rutabagas at 35^ per 100 pounds (1 bu. of rutabagas weighs 52 lb.). How much did he receive for them? 26. A dealer bought 3726 bushels of wheat at $1.03 per bushel and sold it at $1.07 per bushel. How much did he make on the transaction? 27. A grocer bought a box containing 100 apples for $2.00. Ten of them spoiled. He sold the remainder at 6 cents each. How much did he gain on the box of apples? 28. John has 45 marbles. Harry and James each have 9 times as many as John. How many marbles do they all have? 29. If the daily pay of a railroad conductor is $4.80 for an 8-hour day, what is his salary for a year of 330 working days if his overtime amounts to 320 hours and is paid at the regular daily rate? 30. A man's estate amounted to $15,630. His wife received $6000 and the rest was divided equally among his three children. How much did each receive? 31. 11,161,000 bales (500 pounds each) of cotton were raised in the U. S. in 1916. Find the production in pounds. 14 SEVENTH YEAR Exercise 26. Division 2)430 6)896 3)171 2)642 6)474 9)766 4)372 2)198 3)622 9)468 7)269 3)147 6 )326 8 )472 6)888 111 222 362 426 631 226 621 420 Exercise 26. Addition 636 326 784 340 362 216 441 236 726 262 673 316 160 228 796 203 436 323 666 132 438 361 726 262 869 120 262 626 661 326 622 176 Exercise 27. Subtraction 746 473 763 394 223 48 61 86 62 68 624 260 416 432 848 66 30 97 21 69 421 666 • 317 690 600 38 36 68 60 73 Exercise 28. Addition 127 423 377 266 188 177 609 346 369 208 127 606 718 306 223 361 746 462 119 227 148 647 329 136 228 239 136 226 EXERCISES FOR SPEED AND ACCURACY 15 427 12 Exercise 29. Multiplication 342 872 27 36 961 27 Exercise 30. Subtraction 678 364 466 123 646 124 388 236 394 181 189 146 867 640 311 200 386 362 618 303 621 611 786 463 157 133 141 120 • 383 202 468 367 124 114 • Exercise 31. Addition 34 73 29 19 22 26 23 29 28 • 77 43 Y2 26 93 36 81 46 84 11 68 16 62 24 20 63 64 93 61 70 12 17 13 20 30 83 64 56 16 47 48 21 27 Exercise 32. Division 20)600 30)900 40)120 60)660 70)490 60)300 80)240 20)800 40)280 70)630 60)420 80)400 30)270 80)480 80)640 60)260 20)140 90)810 70)360 20)120 50)700 70)280 60)300 60)660 80)800 90)630 50)760 16 SEVENTH YEAR 679 446 227 106 449 228 34 17 91 63 49 30 62 74 83 Exercise 33. Subtxaction 856 634 756 687 312 667 472 186 883 360 696 244 200 326 186 222 Exercise 34. 42 86 88 24 89 66 28 67 29 96 44 70 20 85 88 60 92 37 Addition 791 693 69 83 14 22 47 98 73 26 40 384 272 786 665 327 207 86 36 43 33 66 67 36 20 46 Exercise 36. Addition 764 843 697 634 488 886 668 488 397 636 927 848 368 456 543 384 163 646 844 567 Exercise 36 t. Multiplicati on . 462 672 147 121 251 362 EXERCISES FOR SPEED AND ACCURACY 17 Exercise 37. Addition 288 le? 472 144 263 321 326 221 149 186 176 490 281 482 201 214 199 129 161 266 221 186 246 178 127 Exercise 106 38. Diviidon 102 89)8722 84)7644 37)2442 21)2626 84)6804 Exercise 39. Addition 624 249 190 462 309 318 676 607 166 346 234 169 646 266 192 488 262 413 Exercise 40. Subtraction 763 228 374 386 169 186 823 912 973 337 864 699 433 741 277 666 249 626 462 267 318 « 199 607 496 346 606 169 619 ction 783 831 299 664 211 243 186 178 266 666 167 478 18 SEVENTH YEAR Exercise 41. Addition 971 466 998 878 246 761 783 326 876 717 202 344 HI 411 602 616 116 661 888 600 761 136 494 228 438 812 209 802 787 794 Exercise 42. Multiplication 2344 688 3271 689 75 422 Exercise 43. Addition 422 492 ' 666 862 667 836 122 646 896 976 263 636 361 624 962 • 262 227 327 166 213 426 831 447 991 772 991 887 .104 • Exercise 44. Divii sdon 33)792 72)16992 21)378 Exercise 46. Addition 467 717 617 913 308 297 124 890 434 718 383 466 323 262 913 ' 444 999 363 422 363 424 802 660 232 282 791 78i9 666 416 346 671 EXERCISES FOR SPEED AND ACCURACY 19 Exercise 46. Subtntctton 11 723697 683121 896762 33 83701 76243 69863 400271 38106 31)868 Exercise 47. Division Exercise 48. Subtractioa 976432186 78523321 934106626 66687810 773642 6&666 Exercise 49 Most stores now have cashiers to make change for their customers. This ia much more economical be- cause the cashier by constant prac- tice becomes much more efficient than would be possible for the many clerks whose attention is mainly devoted to selling goods. The modem method of making chai^ for a purchase is by addition. For example, if you seli goods to the amount of $1,73 and recrave a five-dollar bill from the purchaser, instead of subtractii^ $1.73 from $5.00 you start with the amount $1.73 and take 2^, 25(i and 3 one-dollar bills from the change drawer and say to the purchaser $1.73, $1.75, $2.00, $3.00, $4.00, $5.00. This method is not only quicker, but saves the purchaser 20 SEVENTH YEAR the trouble of counting his change. Practice making change in this way for the following purchases. Amount of money Amount of purchase presented to the cashier 1. $ 0.12 A dollar bill 2. $ 3.48 Ten-dollar bill 3. $ 1.06 Two dollar bills 4. $ 5.28 Two five-dollar bills 6. $ .08 A dollar bill 6. $11.27 A ten- and a five-dollar bill 7. $12.39 Three five-dollar bills 8. $ 7.33 Ten-dollar bill 9. $ .65 Five-dollar bill 10. $ 2.48 Three dollar bills 11. $ .42 A half-dollar SUPPLEMENTARY EXERCISES These exercises are provided for pupils who finish the regular practice exercises. They are purposely made more difficult in order to offer a special incentive to rapid workers. The same time limits should be used for these exercises that are used in the preceding exercises. 1 i Exercise 60. Addition 2 6 2 1 7 8 8 7 3 3 2 3 6 8 9 6 4 4 6 8 1 2 6 6 9 2 4 6 7 3 6 9 3 1 2 8 6 2 1 2 4 4 1 7 9 3 3 3 8 9 6 1 3 6 7 8 7 6 4 1 7 9 9 6 3 7 7 6 4 6 6 7 9 4 1 7 2 3 2 8 6 6 9 8 4 3 1 1 SUPPLEMENTARY EXERCISES 21 Exercise 61. Subtraction 8346 4206 9378 6600 6237 2973 6763 1828 2176 4266 » 8836 7000 1642 1961 4996 6284 5803 • 6082 3734 8312 2768 4766 1887 3123 Exercise 62. Multiplication 6328 1976 5836 8219 2 9 7 3 6786 3628 9163 7668 8 5 6 4 3784 2178 6639 6689 9 3 8 7 Exercise 63. Addition 667 913 422 308 457 717 637 416 492 836 124 383 232 286 772 991 896 976 718 890 363 408 426 831 661 624 323 262 927 873 4% 999 807 673 768 926 Exercise 64. Multiplication 6293 3829 4673 8166 27 64 38 96 22 SEVENTH YEAR Exercise 66. Division 2)7662 9)82603 7)26992 8)46288 6)31416 6)36834 3)3834 2)4906 9)46324 Exercise 66. Subtraction 937462 483692 267634 362183 217926 108926 871039 668372 783219 714826 219387 Exercise 67. 438478 Division 3)8673 4)24728 7)4893 632000 371483 693042 217662 72)30816 44)1684 68)36366 Exercise 68. Addition 8073 3468 7604 2936 3884 6846 6921 2836 6846 1649 1279 8706 9648 1906 6331 6331 2499 6342 2783 6276 7628 6674 7807 6619 9746 CHAPTER II REVIEW OF COMMON FRACTIONS Exercise 1. Three Meanings of a Fraction The fraction f may have any one of three meanings. (1) It may mean 3 of the 4 equal parts of a thing; (2) ^ of 3 equal things; or (3) 3 divided by 4. For example: an inch is divided into fourths, f of an inch may mean 3 of the 4 equal parts of an inch; J of 3 inches; or the quotient of 3 inches divided by 4. 3 of the 4 equal parts of an inch. H I I J of 3 inches. 1 '- 1 13 inchest- 4. The above diagram shows the three meanings of the fraction f . Work these three meanings out on your ruler. Exercise 2. Reduction to Lowest Terms The denominator 4 of the fraction indicates the size of the equal parts by showing into how many equal parts the whole has been divided. The numerator 3 shows the number of these equal parts which form the fraction. 1. Show the three meanings that the fraction -3^ may have. 2. In the fraction ^ what is the denominator? What is the numerator? 3. This fraction shows that the whole has been divided into how many equal parts? 4. How many of these parts have been taken to form the fraction? 23 24 SEVENTH YEAR 6. Answer the same questions for the following fractions T^> "g"' 6> 3> 8> li"' 6. Divide both the numerator and the denominator of the fraction -^ by 4. What is the result? 7. Compare the fraction f with the fraction -j^, using the above diagram. Show that the two fractions are equal by using your ruler. 8. Divide both terms of the fraction ^ by 3. Use your ruler to compare the result with ^. 9. Divide both terms of the fraction ^ by 2. Compare the result with ^. 10. Multiply both terms of the fraction f by 3. Use your ruler to compare the result with f . 11. Multiply both terms of the fraction ^ by 2. Compare the result with -J. Use other examples, if necessary, to make clear the following: PRINCIPLE: When the numerator and denominator of a frac- tion are both multiplied by or both divided by the same ntmiber, the value of the fraction is not changed. When the numerator and denominator of a fraction are both divided by the same number, the fraction is said to be reduced to lower terms. When both terms are multiplied by the same number, the fraction is said to be reduced to higher terms. EEVIEW OF FRACTIONS 25 12. Change ^ to higher terms by multiplymg both terms by 2 ; by 3; by 5. Reduction to higher terms is used in reducing fractions to a common denominator. 13. Which is shorter: To divide both terms of ^ by 5, and then both terms of the result by 3, or to reduce to lowest terms by dividing both terms of ^ by 15? Reduce to lowest terms: 1. f 7. M 13. if 19. u S6. U 2. T^ 8. U 14. ft 20. u 26. U 8. t 9. if 16. if 21. u 27. u 4. A 10. U 16. U 22. ?2 3d 28. M 6. H 11. H 17. if 23. If 29. m 6. n 12. M 18. U 24. u 30. m Exercise 3. Addition and Subtraction of Similar Fractions Similar fractions are fractions having the same denominator. 1. $3 +$4 are how many dollars? 2. 3 books+4 books are how many books? 8. 3 fourths+4 fourths are how many fourths? The form f +^ means the same as 3 fourths+4 fourths. Which is more quickly written? Which form occupies the least space? If we use the more convenient form f for 3 fourths, we must not forget that the denominator merely indicates the name or size of the equal parts. The numerator shows how many of these equal parts compose the fraction. In adding the frac- tions l+f, we are merely adding two numbers of fourths, making -J. How shall we proceed, then, in subtraction of similar fractions? 26 SEVENTH YEAR Add or subtract the foUowii^: 1. i + f 2. ^ + f 3. 7 3 1 1 1 1 4. i + f 6. l + i 6. l-t 7. f-f 8 9 10 11 12 13 14 5 I 2 _ T -h T - it T3 — 5 2. ~~ 6 "" 6 "" 1 I 2 _ 3 T^ 3 — 4 5 9 TT I 11 3 _ 5 "" 4 _ 16. 2 I 5 -f = ri 1 — 16. A+A-A 17. f-f + i 18. 3 1 2 _ 1 5 T^ 5 5 19. l-f-f 20. H+A-A 21. l + l + l Exercise 4. Addition and Subtraction of Dissimilar Fractions Dissimilar fractions are fractions not having the same denom- inators. Can you add $3 and 4 books together? You can not unless you say 3 things and 4 things are 7 things; or 3 articles+4 articles are 7 articles. Only like numbers can be added or subtracted. The term thing or article might be called the common denominator of the two numbers. Can we add f+f? What must be done before we can add them? What is the least common denominator of these two fractions? The following form will be found very convenient for adding dissimilar fractions: 2 I 3_8+9_17«l 5. 3"r4 — j2 — 12 "■•^1^ The advantages of writing the denominator once as ir '^* . form above are (1) it is shorter; (2) it indicates the commit denominator more clearly and (3) shows that only the numer- ators are to be added. The expression ^^^ should be read REVIEW OF FRACTIONS 27 Add or subtract as indicated: 1. f + i = 7. t+A = 13. A+l = 19. f-! = 2. ii-l = 8. 7 3 _ 5 - 5 = 14. l + f = 20. i + l- 3. l + f = 9. T^+t = 16. f-l = 21. i-f = 4. il-f = 10. f-A= 16. ^-4 = 22. i+A= 6. ii+f = 11. 1 3 _ 4 14 17. 4 + 1 = 23. H-^ = 6. f-A= 12. |-f = 18. f + f = 24. n-^= After the pupils understand these problems, put the work on a time basis and give a drill exercise. 8 minutes is suggested as a suitable time limit for the average class. Exercise 6. Addition and Subtraction of Mixed Numbers In addition and subtraction of mixed numbers the form shown below is one of the most convenient: Example; Add 3|, 12f , 7^, 15^. As shown in the illustration, the least common denominator is found and written below the line. The numerators are then placed to the right of the vertical line, the sum being -|t or Iff. This sum is then added to the integers, making 38ff . q3 ^8 9 12f 18 7A •3 8 15| 12 38ff M Add: 1. 13f 8f 27| 431 2. 25| H 38f 3. 48| 62f 95| 86f 4. Subtract: 6. 9 8 o-g 7. 25^—85 8. 16|- 9i 9. 17|-10| 5f S. 21^ 7f 36^ H 48i 6| 9f .0. 7-}- -4| .1. 12 - -81 28 SEVENTH YEAR 12. A box of scouring brick weighed 60f lb. The box itself weighed 4^ lb. How much did the scouring brick weigh ? 13. The sum of two numbers is 28 J. One of the numbers is 17f. What is the other? 14. In two bins of potatoes there are 128^ bu. In one there are 62 J bu. How many are there in the other? 16. A flagstaff 62^ ft. high was made of two poles spliced together. The lower pole was 28 f ft. tall. How mtich did the upper pole add to its height? 16. A kite string 286^ ft. long broke at a distance of 127^ ft. from the lower end. What length of string went with the kite? 17. A clerk earned $90 per month. His expense for board, for this period, was $30 i; for laundering, $5 J; for articles of clothing, $14 J; for life insurance, $3^; for incidentals, $14 f. What was the surplus for the month? 18. A boy sawed a piece of board exactly 20 inches long from a board 26^ inches long. Allowing -^ of an inch for the cut of the saw, find the length of the piece that was left. 19. Four boards were glued together for a table top. When planed for the glue joints, they measured 6f in., 7§ in., 7 J in. and 6^ in. respectively. Find the width of the table top. How much would have to be planed off this top to make it 27 in. in width. 20. A school room is 12 ft. high. The picture molding is 3f ft. from the ceiling. How far is the molding from the floor? 21. How wide must a strip of goods be cut to make a ruffle 3 in. wide when finished if ^ in. is turned under for the heading and f in. is used for the lower hem? 22. A room is 12^ ft. long and 11 f ft. wide. How many feet of base board are required to go around the room, deducting 3§ ft. for the door? REVIEW OF FRACTIONS 29 Ezerdse 6. Multiplicatioii of Fracti<ni8 Example: 4X3 = ? Take a foot ruler. What is ^ of a foot in inches? What is ^ of f of a foot in inches? Show, then, that ^ of ^ of a foot ^-^ of a foot, i of f of a foot =YS ^^ ^ foot? j- of f of a foot --j^ of a foot? In multiplication of fractions the word of may be replaced by the sign X. Therefore: f Xf = A- Ck>mpare the product of the numerators of the fractions with the num- erator of the result, -f^. Ck>mpare the product of the denominators of the fractions with the denominator of Uie result, ■^. Reduce -^ to its lowest terms. Cancellation is the process of reducing to lower terms before multiplying by dividing any numefator and any denominator of the fractions by the same number: 1 1 ^X^=^ < 3 2 2 1 We see, then, that in the multiplication of fractions the product of the numerators of the fractions becomes the numerator of the result and the product of the denominators the denominator of the result, cancellation being used to shorten the process. Multiply the following fractions: Use cancellation. 1- l^X f = 9. i^X I = 17. i X I X A= 18. "§■ X "5 X"5^= 19« "2 X 3X7*^ ao. fxfxii= ai. MxM xH= aa. MxMx i = 28. MxMx I = 84. MxHxU^ 2. ixf = 10. HxA= 8. f X^- 11. |xM= 4. T«WX f = : 18. if Xt%= 6. Jxi= 3 18. 1 X 1 - 6. ^Xf= : I*. Mx||= V |xf = 18. fxf = 8. ixi- 16. ixi = 30 SEVENTH YEAR 26. A boy glued 5 maple strips and 4 walnut strips together to make a pen tray. If each of the strips was -^ in. wide, how wide was the piece for the tray? 26. A teacher asked a boy to make him a book case for a set of encyclopedias consisting of 30 volumes. How long must the boy make each of the two shelves if the books average 2| in. in thickness? 27. How many yards of ruf9ing must be made to put 5 ruffles around a dress skirt three yards in girth if ^ extra is allowed for the gathering? 28. How much will f of a yard of ribbon cost at 22 cents per yard? 29. A piece of goods containing 6 quarter-inch tucks and a 1-in. hem is 20 in. when finished. How wide was it before being tucked and hemmed? 30. How wide must a piece of goods be, to be 24 in. wide when complete, if we allow for 6 "one-eighth'' inch tucks; 6 "one-fourth" inch tucks and a 2-in. hem? Exercise 7. Division of Fractions In division of fractions we may use two methods: (1) reduce to a conunon denominator and divide the numerators; (2) invert the divisor and multiply. (1) Example: |-.f =g^l2=^=^or if Note that you are dividing 12 fifteenths by 10 fifteenths, giving as a result \% times — the denominator being eliminated in the division. (2) Example: |4-§ = ? Take a sheet of paper and fold it into thirds as in the illustration. How many times will the shaded portion representing f be contained in the whole sheet? _-_J_ , J. ^_ ..,I.T..— — . ■ . ' ' . , . , . ■ '•-' \ ■ ' ■^■l : ■'. \ ■'. ^ . • !•■ J ,_\ REVIEW OF FRACTIONS 31 Since a whole sheet contains f of a sheet 1^ or ^ times, f of a sheet contains f of a sheet ^ of -f times. 2 Therefore: 4 2^36 1 -+-«-X-=-or 1- 5 3 5 2 5 5 1 ■| is the divisor. We see that the f- has heen inoerted, beooming -f when we multiply. By using the above method with other examples you wiU find that the divisor is always inverted before you multiply. « PRINCIPLE: To divide one fraction by another, invert the divisor and multiply. This method is preferred to reducing to a oonomon denominator because the division example is converted into a multiplication example, which is the easiest of all the processes in fractions. Divide the following fractions: 1. 8. f + f- 10. J -5- i = 1. 8. f 3 J. 5 ^ 1 7 16. f -i- i 17. M 8. H- I = A= 18. f 18. H 20. f 22 __ Ezerdse 8. Multiplication and Division of Mixed Numbers How do you change a mixed number to an improper fraction? Which is easier: to divide 2f by if or to divide |- by |-? In multiplication ai^d division of mixed nmnbers, then, it is easier first to reduce the mixed numbers to improper fractions and then perform the operation of multiplying or dividing. Multiply or divide: 1. 3fX2f 2. 6§Xlf 8. 12f ^2| 4. 5f4-3^ 6. 3iX8f 6. 2-3-5-3-j- 7. 2|xlf 8'7X • o3. • • 3 "^"^4 9. lfX2| = 10. 6iX6| = 11. 6|-J^3^ = 12* V7g"~r"03"=^ 32 SEVENTH YEAR 13. 4iX2| = 17. 6|X1VV= 21. lfX3i = 14. 9fxiH= 18. 4jX3| = 22. 8|-5-li = 16. 19. ll-i-lf = 28. 2fX2j = 16. 3i-Mi = 20. 4f-5-3i = 24. 2|-f-3j = 26. How many times can 1 J gallons of oil be drawn from a barrel holding 31^ gallons? 26. How many bushels of apples at Slf can be bought for $7i? 27. If nine hogsheads would hold 50f bu., what would 1 hogshead hold? 28. How many pounds of bacon at $J per pound can be bought for $i? 29. At $lf per crate, how many crates of peaches can be bought for $17^? 30. A railway section of 8^ miles cost for construction $246,504 J. What did it cost per mile? 31. A banker bought a tract of timber for $7490, at $53^ per acre. How many acres did he buy? 32. If I pay $5f for books at $f per volume, how many volumes do I buy? 33. At $f per basket, how many baskets of fruit can be bought for $27? 34. At 3^ miles an hour, how long does it take a person to walk 8f miles? 36. A teacher has a desk book rack 21 in. long. How many text books averaging ^ in. thick will it hold? 36. A class bought two strips of ribbon of diflferent colors for class colors. They divided the strips, which were 2lJ yards in length, into 32 equal parts. How long was each piece? REVIEW OF FRACTIONS 33 87. A girl making a base for a letter rack wished to locate the central line. If the base board is 3^ in. wide, how far will the center line lie from each edge? 38. When sugar is selling at 7§ cents per pound, how many pounds are sold for a dollar at that rate? Exercise 9. Drill on the Four Processes in Fractions Solve the following: 10. |xt= 12. t+l- 13. f Xf = i-4. 3 '2 15. J -1 = 16. |+f = 26. Find the cost of a lOf -lb. turkey at 28 cents a pound. 26. How much will a 4^-lb. chicken cost at 24§ cents a pound? 27. A roast weighing 4§ lb. costs 81 cents. How much was the cost per pound? 28. A barrel of flour weighs 196 lb. How many pounds are there in a J-bbl. sack? In a |-bbL sack? 29. Obtain local prices at a butcher shop and find the cost of 2f lb. of round steak; 5^ lb. of rib roast; and 1^ lb. of pork chops. 30. A man owned f of a mill and sold f of his share. What part of the total value of the mill did he sell? What part of the mill did he still own? 1. fxf = 2. 5 8 6 IT- 3. 1 + 1 = 4. 1-^1 = 6. A-f- 6. Hxn= 7. i^f= 8. 1 + 1 = 17. ixj= 18. i+i = 19. f -i= 20. f^i= 21. 1+1= 22. ix^= 38. 1-^1= 24. UH= 34 SEVENTH YEAR Exercise 10. Review of Decimal Fractions A fraction, whose denominator is ten or some product of tens, is called a decimal. The value of a figure in a decimal is shown by its position with regard to the decimal point. o a I I I ® 8 £ S S S s 1 •a JS d ^ n & § u 'i s s § 5 45 p 'o ^ ua ■*» s S s -*? ■ O 0) a rS -5? o a s 1 1 1 1,1 1 1 . 1 1 1,1 1 1 In the above number how does the 1 in tenths place compare in value to the 1 in units place? How does the 1 in units place compare in value to the 1 in hundreds place? How does the 1 in units place compare in value with the 1 in tenths place? How does the 1 in units place compare in value with the 1 in thousandths place? Start at the 1 in hundred thousands place and go to the right. How do the values of the I's change? Start at the 1 in millionths place and go to the left. How do the values of the I's change? The number above is read one hundred eleven thousand, one hundred eleven, and one hundred eleven thousand one hundred eleven millionths. Read the following decimals: 1. .001 2. 19.02 3. .0005 4. 50.001 5. .00125 6. .375 7. 3.1416 8. 1.4142 9. 2150.42 10. .866 11. .7584 12. .5236 13. 1.732 14. 8.75 16. .875 16. .0875 17. .00875 18. .000875 19. .005 20. .000005 REVIEW OF DECIMALS 35 How many decimal places are needed to write tenths; thousandths; hundredths; ten-thousandths; millionths; hun- dred-thousandths? Practice on this question until you can give the answers instantly, because it will help you in writing decimals. Write in figures:^ !• One hundredth. 2. Two hundred and five ten-thousandths. 3. Sixty-three thousandths. 4. Twenty-five hundredths. 6. Seven hundred fifteen thousandths. 6. Eighty-seven thousandths. 7. Nine hundred forty thousandths. 8. Sixty-three hundredths. 9. Sixty-seven thousandths. 10. Eight thousandths. 11. Five ten-thousandths. 12. One hundred twenty-five hundred-thousandths 13. Twenty-five millionths. 14. Twenty-five and five ten-thousandths. 16. One hundred and forty-three thousandths. 16. One hundred forty-three thousandths. 17. Four hundred one and four hundred one thousandths. 18. Three and twenty-five ten-thousandths. 19. Eight hundred and s6ven millionths. ^In writing decimals, it is a good plan to have no erasers at the black- board and require the pupils to be sure of the number of places before they be|^ writing each decimal that you read to them. 36 SEVENTH YEAR Exercise 11. Addition and Subtraction of Decimals Decimals are added and subtracted in the same manner as whole numbers. The decimal points must be kept in a vertical line and the other figures in their proper columns. Add: 1. 2.7; .3; 37.1; 2.04; .0033;. 16.125; 105.06. 2. 15.03; 325.075; 18.0025; 15.005; 87.08. 8. .0025; .009; .00125; .875; .05. 4. .425; 3.1416; 1.4142; 15.375; 8.8736; 5.75. 5. 45.375; 37.525; 29.65; 86.245; 18.0005; 57.075. 6. .0075; 5.0035; .2508; .025; 2.1754; .7856. 7. 3.006; 61.375; 25.025; 7.75; .0725; 15.7. 8. 25.5; 5.78; .375; 2.14; 37.45; 4.806; 8.6. 9. .625; .375; .875; .125; .75; .25; .075. 10. 4.5; 67.34; 8.054; .4862; 325.8; .755. Subtract: . 1. 4.312 from 7.505. 6. 87.45 from 148.1. 2. 1.4142 from 3.1416. 7. 29.802 from 32. 3. 23.075 from 28.008. 8. .25 from 25.1. 4. 1.387 from 2.025. 9. 2.62 from 4.875. 6. 6.76 from 11.025. 10. 27.51 from 30. Note: Practice should be rriven in reading decimals as follows: 1.4142 — read: one, point, four, one, four, two. Exercise 12. Multiplication of Decimals Express the decimal .05 as a common fraction. Also the decimal .5 as a common fraction. REVIEW OF DECIMALS 37 If we multiply TDirXtV without cancelling, what is the product? How do we express yMu ^ * decimal? Therefore: If we multiply .05 by .5, the product is .025. How does the number of decimal places in the product compare with the number of decimal places in both the multi- plicand and multiplier? PRINCIPLE: In multiplication of decimals as many places are pointed off in the product as there are decimal places in both multiplicand and multiplier. Multiply: 1. 25.5X4.025 2. .005 X. 25 8. 3.75X3.78 4. 4.002 X. 32 6. .866X1.4 6. 273.5X1.64 7. 352.x. 0175 8. .0002 X. 0021 9. 62.5X7.05 10. .21 X. 3 11. $145.50X.375 12. $257.75 X. 06 18. $1250. X. 055 14. 2.72 X. 08 16. .0385 X. 55 16. 6.45X3.83 17. $250. X. 055 18. 275.5 X. 039 19. $272.75X.0275 20. 7.5X3.1416 21. 2.54X2.54 22. .5326X175.65 28. .0375 X. 0025 24. 855.x 0075 26. A cubic foot of water weighs approximately 62.5 pounds. Copper is 8.93 times as heavy as the same volume of water. How much will a cubic foot of copper weigh? 26. Gold is 19.3 times as heavy as the same volume of water. Find the weight of a cubic foot of gold. 27. How much heavier is a cubic foot of gold than a cubic foot of copper? 28. A gallon of water weighs 8.34 pounds. Kerosene is .8 as heavy as the same volume of water. What is the weight of a gallon of kerosene? 38 SEVENTH YEAR Exercise 13. Applied Problems XT. S. Army Daily (Garrison) Ration per Man Beef, fresh 20. oz. Milk, evap. unsweetened . 0.5 oz. Flour 18. oz. Vinegar^ 0.64 oz. Baking powder 0.08 oz. Salt 0.64 oz. Beans 2.4 oz. Pepper, black 0.04 oz. Potatoes 20. oz. Cinnamon 0.014 oz. Primes 1.28 oz. Lard 0.64 oz. Coffee,roasted and ground 1.12 oz. Butter 0.5 oz. Sugar 3.2 oz. Syrup 1.28 oz. Flavoring extract, lemon . .0.014 oz. 1. Copy in column form and find the total weight, in pounds and ounces, of the seventeen items given in this table. 2. Find the total required for one week. For thirty days. 3. Find the daily amount required for a company of 95 men. For two companies of 85 men each. 4. Find the daily amount that would be needed for a regi- ment of 972 men. 6. Five Signal Corps men were stationed 21 days at Mt. View. Find the total amount of rations they required. 6. It took 47 Army engineers 14 days to build a certain bridge. What amount of rations did they require? 7. A batallion of three companies aggregating 270 men was stationed at a certain point for two weeks. What amount of beef, flour and potatoes was required for that period? 8. What amount of beans, prunes, coffee and sugar was needed during that time? 9. Find the amount required of the other ten items for the same period for these 270 men. 10. Find from local prices what the daily ration would amount to for 100 men for 30 days for beef, beans and coffee. 'Approximate reduction to ounces. The government standard gives vinegar 0.16 gill and syrup 0.32 gill. REVIEW OF DECIMALS 39 Exercise 14. Division of Dedmals 1. Divide .025 by .05. Express as common fractions and divide. What is the quotient? Express this quotient as a decimal. Divide the following decimals by using common fractions: 2. .626 -^ 12.5. 3. .625-^.125. Check your results secured by dividing with common frac- tions with the quotients expressed in the decimal form as shown below: .5. .05 5 .05) .02 5 12. 5). 6 25 .125). 625 25 6 25 625 Answer the following questions for each of the above prob- lems: 4. How many decimal places are there in the divisor? 6. How many decimal places is the decimal point in the quotient to the right of the decimal point in the dividend? 6, Can you tell from the above problems how the quotient should be pointed oflf in the division of decimals? PRIKCIPLE: In division of decimals, as many decimal places are pointed off in the quotient to the right of the decimal point in the dividend as there are decimal places in the divisor. Caviion: Be sure that you place the figures of the quotient exactly where they belong or you will introduce an error in the result when you point oflf the decimal places in the quotient. Divide the following (carry out three decimal places if they do not come out even) : 40 SEVENTH YEAR 1. 30. by 7.5 6. 31.042 by 8.3 11. 26.52 by 3.4 2. 1.2 by .6 7. 8.2 by .0041 12. 20.5 by 8.2 3. 36. by 2.4 8. 46.875 by .375 18. 8.5 by 3.4 4. 61.165 by 37.9 9. .0003 by .5 14. 6.3 by .18 6. .008 by .04 10. .4 by .002 16. 3. by 8 Exercise 15. Changing a Common Fraction to a Decimal On page 23 it was shown that one meaning of a fraction is: the numerator divided by the denominator. This is the simplest method to use in reducing a common fraction to a decimal. Reduce f to a decimal. Divide 3 by 8. .375 8)3.000 Therefore : | = .375 Reduce the following fractions to decimals: • 1. i 6. f 11. i 16. ^ ^•i 7.1 ". 1 17. i O. 3 8.1 13. f 18. f *.i A £ 14. 1 19. tV R 1 0. 8 10. i 16. f • 20.^ Exercise 16. Ch andne a Decii nal to a Common Fr Express the decimal .375 as a common fraction. Reduce this fraction to its lowest terms. Example : 1^7^ = ^^ = f . Reduce to common fractions: 1. .50 6. .6 11. .125 16. .05 2. .626 7. .875 12. .2 17. .075 8. .75' 8. .03125 13. .33§ 18. .025 4. .8 9. .0125 14. .66f 19. .02 6. .25 10. .0375 16. .16| 20. .35 APPLIED PROBLEMS IN FRACTIONS Applied Problems Involving Fractions The following problems were supplied by one of the largest stores in the United States. They are practical problems, representing selections from admd sales slips, involving frac- tions. Many of the great commercial bouses find it necessary to tnun their applicants in such problems as these in order to make them proficient in fractions. One young man graduated from a school for training em- ployees in a half-day. Why? Simply because he had mastered his arithmetic before applying for a position and so did not need the course of trmning. Exercise 17 Find the amount of the purchases in each of the following problems: 1. Mrs. H. A. Marshall purchased 9| yards broadcloth at $2.75 per yard. 3. Mrs. S. A. Thompson bought 1§ yards tulle at Jp.75 per yard. 3. Miss Myrtle Hanlon purchased if yards net at 55^; ij yards lace at 30fi; 1^ yards veiling at {1.75. 42 SEVENTH YEAR 4. Mrs. Harry Smith bought 2f yards lace at 65ff ; 2f yards edging at 3ff; 8f yards edging at 3ff; 1^ yards edging at 15^. 6. Mrs. C. P. Murray purchased 1 J yards velour at $2.50; 1^ yards velvet at $3.50. 6. Mrs. M. M. Spaulding bought 5^ yards dress goods at $2.65; 4f yards dress goods at $3.55; 2^ yards dress goods at $6.00; 3^ yards dress goods at $5.35. • 7. Mrs. E. F. Chatfield ordered 6^ yards lace at 45^; Ij yards veiling at 95ff; 1 J yards fillet at 55 ff; ^ yard net at 8. Mrs. R. F. Arnold purchased 5^ yards edging at 12ff; 2^ yards silk at 85ff ; 1^ yards cretonne at $1.50; ^ yard damask at 15ff. 9. Mr. C. P. Chase purchased the following: 31 J yards linoleum at $1.40; 81^ feet wood strips, laid, at 5§ff; 6f yards cork carpet at $1.25; 2f dozen f-inch Daisy pads at 80ff. 10. Mrs. R. H. Byron purchased ^ dozen tassels at $9.00 per dozen; 1^ yards braid at 60ff; 1 J yards guimpe at $1.75; 1^ yards trimming at 45ff. 11. Mr. S. E. Brown bought 1^ dozen stair pads at $2.00; 21^ yards china matting at 40ff; 6f yards Armstrong linoleum at $1.75. 12. Mr. H. H. Howard purchased 1^ yards linoleum at 80^; 1 Duchess rug at $7.50; 1 Bokhara rug at $35.00; 1 Smyrna rug at $7.00; 11^ yards velvet stair carpet at $1.35. 13. Mrs. F. A. Cornell made the following purchases: 6 J yards guimpe at 45(5; f dozen tassels at $2.25; 4f yards fringe at $1.75. • 14. Mrs. M. H. Gardner bought j dozen tassels at 75«f; 3 J yards trimming at $1.05; 5| yards braid at 50^; 1 J yards braid at $1.25. APPLIED PROBLEMS IN FRACTIONS 43 16. Mrs. J. C. Gibson gave the following order: 1^ yards fringe at lOff ; 2§ yards trimming at 25ff; 3^ yards braid at 50ff. 16. Mrs. E. S. Harding purchased 15^ yards cretonne at 60ff; f yard taffeta at $2.50; 1 velour remnant at $1.50. 17. Mrs. F. L. Black bought ^ yard braid at 75ff; 2| yards swansdown at $1.75; 1^ yards trimming at 18ff. 18. Mr. Frank Adams purchased J dozen rolls paper at 12ff ; f yards oil cloth at 30ff ; if yards art paper at 25^; ^ dozen Dutch Klenzer at 90ff. 19. Mrs. Chas. Madison made the following purchases: f yards oil cloth at 65 ff; 17^ yards lace at 5ff; ^ dozen bars Ivory Soap at 84ff; J dozen cans Kitchen Klenzer at 50ff. 20. Mrs. M. C. Nelson bought 2^ yards net at $2.50; 1§ yards muslin at $2.50; 16 f yards net at 35ff; if yards Sunfast at $2.25; f pair portieres at $21.50. 21. Mrs. Harry Newell bought the following items: 7| yards Sundour at $2.50; 4f yards edging at 10^; 12^ yards muslin at 40ff. 22. Mrs. D. D. Penfield gave the following order: f dozen towels at $3.00; f yards damask at $1.50; f dozen wash cloths at $1.00; § dozen dusters at $1.75. 23. Mrs. C. H. Van Buren bought the following: f yards sheeting at 75ff; f dozen towels at $6.00; f yard linen at 65ff; § yard linen at $1.25. 24. Mrs. C. P. Warren purchased as follows: f dozen broom bags at $2.40; 3f yards crash at 30^; 2\ yards huck at 65ff ; 3^ yards linen at 65ff. 26. Mrs. Harry S. Perry purchased the following: ^ pound candy at 40ff ; 2^ yards embroidery at 15ff ; 4f yards embroidery at 15ff; if yards embroidery at 18^. 44 SEVENTH YEAR 26. Mrs. Wm. Penn bought the following: ij yards silk at $2.00; 1 J yards silk crepe at $2.00; 1 J yards silk at $1.00; f yards silk net at $1.10. 27. Mrs. O. O. Morrison gave the following order: f yards silk at $1.75; 9 yards silk poplin at 50ff; 1^ yards silk at $1.75; f yards crepe at $1.50; 1 J yards silk at 75ff. 28. Mrs. S. S. Melrose bought as follows: 2 J yards ribbon at 28^; 2§ yards ribbon at 29fi; if yards ribbon at 7ff ; 4f yards ribbon at 14ff. 29. Mrs. Charles Mason purchased the following: 2 J yards ribbon at 25ff ; 3 J yards ribbon at 18ff; 1^ yards ribbon at 38ff; § yard ribbon at 38ff. 30. Mrs. Chas. P. Hulce ordered 2j yards trimming at 85ff; f yards trinmiing at $3.00; 2j yards braid at50ff;4^ yards braid at 7ff; 1^ yards cord at 8^4. 81. Miss T. E. Bennett made the following purchases: ij yards edging at 7^; 2§ yards lace at 4^; if yards lace at 60fi; 1 J yards lace at 25^. 82. Mrs. Harold P. Piatt bought the following: J yard dress goods at $3.10; f yards dress goods at 65ff ; J yard dress goods at $3.25; ^ yard dress goods at $3.50. 33. Mrs. C. F. Prince ordered the following: 1 J yards silver lace at $4.65; lOf yards lace at $2.95; 2f| yards lace at $3.50; 12 J yards lace at $1.50; | yards veiling at 50ff. 84. Miss S. A. Roberts bought 1§ yards braid at $1.65; 4^ yards braid at 15^; 4§ yards braid at 3^4; 8^ yards braid at lOji; 1 J yards braid at $1.50. 86. Mrs. C. F. Sheldon purchased 16 J yards net at 50ff; 3f yards muslin at 55^; 44f yards net at $1.00; 2§ yards net at $1.25; 2^ yards Sundour at $1.25. CHAPTER III PERCENTAGE Exercise 1 The expression per cent means hundredths. To say that 4 per cent of a certain cow's milk is butter fat means that xcir of the milk is butter fat. The sign % is usually used in place of the words per cent. The fraction twenty-five hundredths may be expressed in three ways: (1) as a common fraction, -^(p^; (2) as a decimal, .25; (3) as a per cent, 25%. The name hundredths is expressed in the first case by the denominator 100; in the second case by means of the decimal point and the two decimal places; and in the third case by the sign %. It is customary to omit the decimal point after whole numbers. The decimal point is placed in the expression 25.% to make clear the process of changing from decimals to per cent. How has the decimal point been moved in changing from the decimal 0.25 to the expression 25.%? A decimal, then, may be changed to a per cent by moving the decimal point two places to the right and attaching the % sign. Change the following decimals to per cents: 1. .25 6. .125 11. .75 16. .3 2. .35 7. .875 12. .005 17. .025 8. .01 8. .5 18. .00125 18. .0075 4. .2 9. .625 14. 2.5 19. .85 6. .16f 10. .375 16. 3.75 20. .20 45 46 SEVENTH YEAR We have already shown that 25.% = .25. In changing from % to a decimal^ how is the decimal point moved? Change the following per cents to decimals: 1. 20% 6. 25% 11. 250% 16. 50% 2. 33i% 7. .25% 18. 625% 17. 37i% 8. 376% 8. 75% 18. 10% 18. i% *. 12i% 9. 62|% 14. 66|% 1». lf% 5. .12^% 10. 40% 16. 60% 20. 3.9% Exercise 2 How do you change a common fraction to a decimal? Change the following fractions to decimals and then to per cents as follows : -^=-05 = 1. 2. 3. 4. 6. 1 2 1 3 1 4 1 5 1 6 0' 8. i 10. f 11. 12. 13. 14. 16. 1 8 3 J 2 5 3 5 4 5 16. 17. 18. 19. 20. 3. 4 2 3 5. 6 1 TF 1 From the results that you have secured in the above exercise, fill out a table similar to the form shown below. Leam all the % equivalents of the conmion fractions, for you will need this information in the following exercise. Common Fractions and Their Equivalent Per Cents ^=?% . i=?% !=?% i=?% i=?% 1- = ?% !=?% !=?% Have the teacher check this table before you leam it so that you will not leam any incorrect equivalents. PERCENTAGE 47 Exercise 3 Find 12^% of 64. 12 1% = what common fraction? If we know that 12^% = 5, which is easier, to take .12^X64 or i of 64? Find the following per cents by using fractional equivalents: 1. 33^% of 120 18. 76% of 320 2. 87^% of 160 14. 66f % of 300 8. 26% of 60 16. 16§% of 96 4. 20% of 45 16. 83|% of 36 5. 37i% of 200 17. 2% of 160 6. 50% of 1640 18. 80% of 60 7. 12 §% of 400 l«. 60% of 450 8. lli% of 81 20. 26% of 820 9. 62^% of 72 21. 14f % of 70 10. 40% of 75 22. 37 J% of 16 11. 10% of 160 " 28. 33^% of 63 12. 6|% of 32 24. 50% of 84 Since per cents may be expressed in equivalent decimals, it is often convenient to multiply by a decimal if the fractional equivalent is large. Find the following per cents, using decimal multipliers: 25. 17% of 153 81. 6% of 43 26. 23% of 90 82. 7% of 65 27. 52% of 83 88. 11% of 85 28. 37% of 135 84. 15% of 124 29. 29% of 105 85. 21% of 34 80. 16% of 38 86. .6% of 96 87. Find 5§% of $2000. 38. Which is larger, 17% of $35 or 15% of $39? 48 SEVENTH YEAR Exercise 4 Choose the most convenient equivalent and find the following per cents: 1. 25% of 1240 16. 21% of 825 2. 8% of 412 17. 40% of 150 8. 12% of 217 18. 60% of 842 4. 20% of 315 19. 16% of 124 6. 12§% of 720 20. 87^% of 128 6. 16f % of 96 21. 2% of 600 7. 22% of 121 22. 7% of 125 .8. 5% of 132 23. 60% of $80 9. 5% of 120 24. 33^% of $360 10. 80% of 250 26. 11^% of $450 11. 13% of 138 26. 75% of $480 12. 37^% of 88 27. 17% of $312 13. 66f % of 75 28. 6% of $450 14. 15% of 200 29. 5i% of $110 16. 62^% of 160 30. if % of $50 EQUATIONS Exercise 6 1. What is the product of 9X15? 9 and 15 are called the factors of the product, 135. 2. If the two factors are given, what process is used in finding the product? 3. If 8 times a certain number =128, what is the number? 4. If 5 times a certain number =55, what is the number? 6. If the product of two factors =48 and one of the factors is 6j what is the other factor? PERCENTAGE-THE EQUATION 49 6. If the product of two factors is 91 and one of the factors is 13, what is the other factor? 7. If the product of two factors and one of the factors are given, what process is used to find the other factor? Show how the preceding problems illustrate the principles: 1. Factor X factor = product. 2. Product -^ one factor ~ the other factor. The letter X is often used to stand for the unknown product ^ or the unknown factor. It is shorter and is not confusing if you remember that it always stands for the unknown number. Such expressions as 9X15 = X and 8XX=128 are called equations because the expressions on the left and right sides of the equality sign are equal. Any equaiion can be represented by a balance as shown in the illustration above, putting the expressions on the scale pans and thus showing their equality. The value of X in the equation 9 X 15 = X can be found by multiplying the two factors 9 and 15. The value X in the equation 8XX=128 is found by dividing the product 128 by the factor 8, giving the other factor X= 16. Find the values of X in the following equations: 1. 7XX=35 8. .06X300=X 2. X=9X25 4. .25XX=50 50 SEVENTH YEAR 6. XX15 = 75 9. 40 = XX500 6. X= 12X20 10. 6%X$150=X 7. 12XX = 240 11. 25%XX = $40 8. 240 = XX20 12. $16 = X%X$200 Exercise 6 Percentage problems may be easily solved by stating them in the form of an equation and then solving by the principles: 1. Factor X factor = product. 2. Product -^ one factor = the other factor. Remember that, in multiplying or dividing, per cents must be expressed either as decimals or as common fractions. 1. What is 6% of $200? This problem may easily be changed into an equation. X may stand for what, which merely stands for the unknown number. Is may be replaced by the equality sign ( = ) and the word of may be replaced by the sign X. The equation is: X=6%X$200. 6% and $200 are both factors of the unknown product X. The principle Factor Xf actor = prodiLct applies to this equation. Before we multiply, it will be necessary to change 6% to a decimal or a common fraction because the multiplier must be an abstract number. 6% = .06. Therefore: 6%XS200 = .06XS200=S12.00. 2. What is 25% of $80? Equation: X=25%XI80. 25% = i Then 25% X|80 =i X$80 =$20. State the equations for the following problems and then solve them: 3. What is 5% of $300? 8. What is 15% of $25? 4. What is 10% of $120? 9. What is 60% of $350? 6. What is 33^% of $90? 10. What is 8% of $110? 6. What is 50% of 22 pounds? 11. What is 16f % of 48 hogs? 7. What is 20% of 84 miles? 12. What is 12^% of 24 cents? PERCENTAGR-THE EQUATION 61 Exercise 7 1. A boy bought a motorcycle for $70 and sold it at a gain of 20%. How much did he gain? This problem can be changed into the simple form of the preceding exer- cise. The question is: How much did he gain? The problem states that he gained 20%. Since gain is alivaya figured on the cost, he gained 20% of $70. In short form the problem really means: What is 20% of $70? Equation: X=20%X$70. X = .20 X $70 = $14.00, the gain. Remember that the number of per cent must be changed to a decimal or a common fraction before multiplying, because the multiplier must be an abstract nimiber. 8. A merchant sold a suit costing $15 at a profit of 40%. What was his profit on the suit? By studying this problem as we did problem 1, we see that it can be put in the shortened form: What is 40% of $15? Equation: X =40% X$15. 40%=f . Then X=fX$15 =$6.00, the profit. 3. A firm recently announced an increase of 15% in the salaries of all of its employees. How much increase would a man receive whose salary had been $100 per month? 4. On a loan of $250 for a year, I receive 6% of that sum for the use of the money. How much do I receive for the use of the money? 6. A real estate dealer sold a lot costing $1500 at a gain of 33|%. What was his gain? Exercises 6 to 13 have been arranged according to the three t3rpes of percentage problems for the convenience of the teacher who prefers to use a different method from the one developed in the text. 52 SEVENTH YEAR 6. A fanner planted 40% of his farm of 240 acres in com. How many acres did he plant in com? 7. A ranch owner had 648 cattle and marketed 12 J% of them. How many cattle did he market? 8. An agent sold an automobile costing him $1200 at a profit of 33^%. Find the amount of his profit. 9. My neighbor sold a cow costing him $75 at a gain of 20%. Find the amount of his profit. 10. I have a balance of $150 on deposit in the bank. If I give Ja tailor a check for 20% of this amount to pay for a suit of clothes, how much does my suit cost me? 11. A grocer sells eggs costing 24 cents per dozen at a profit of 25%. How much profit does he make on each dozen of eggs? 12. A farmer takes a can containing 100 pounds of milk to 4 a creamery. A test is made of the milk and it shows that the milk contains 3.9% of butter fat. How many pounds of butter fat are there in the can of milk? 13. A family pays 30% of their income of $1200 for rent. How much do they pay for rent? 14. At what price must a horse costing $125 be sold to gain for its owner 20%? 16. If a suit marked at $25 is reduced 20% in price, what is the reduced price mark? 16. A man bought 4 suburban lots for $700 each. On two of them he made a gain of 25% when he sold them and on the others he lost 10%. What was his loss or gain on the four lots? The last three problems in this exercise may be more conveniently solved by using the method shown in the next exercise. PERCENTAGE— THE EQUATION 53 Exercise 8 1. What will be the result if 200 is increased 12% of itself? 200 is already 100% of itself. If it is increased 12%, the result will be 112% of 200. Equation: X«112%X200. X = 1.12 X200 =224.00, the new result. 2. What will be the result if $125 is decreased 20%? $125 « 100% of itself. 100% -20% (decrease) =80%. The new result will be only 80% of $125. X=80%X$125. X=iX$125=$100. What will be the result if 3. 300 is increased 30%? 13. $30 is decreased 33 J%? 4. $500 is increased 6%? 14. $250 is decreased 20%? 6. 180 lb. is increased 10%? 16. 360 is decreased 10%? 6. $240 is increased 16f %? 16. $75 is decreased 20%? 7. 80 is increased 20%? 17. 40 is decreased 40%? 8. 36 is increased 33 J%? 18. 240 bu. is decreased 12§%? 9. 1601b. is increased 12 1%? 19. 140 lb. is decreased 10%? 10. 20 bu. is increased 25%? 20. $120 is decreased 16f %? 11. $500 is increased 8%? 21. $80 is decreased 37|%? 12. 32 is increased 25%? 22. 8 bu. is decreased 50%? 23. K a suit of clothes marked at $30 is reduced 16f % in price, what is the reduced price mark? 24. A certain brand of shoes, retailing at $5 per pair, advanced 20% in price in a year. What was the increased price of a pair of these shoes? 26. A man paying a rental of $408 per year finds that his rent is to be increased 12% on account of improvements on the property. What is his new rent per year? 54 SEVENTH YEAR 26. K $1640 worth of groceries have advanced 25% in price since they were purchased, what is their new valuation? 27. A man has $14,000 invested in a lumber business and ! $26,000 in an artificial stone enterprise. In the lumber business, he loses 8% of his investment. What amount must he gain on the other investment to yield him a profit of 10% on both investments? Exercise 9 !• 24 is what % of 30? This type of problem may easily be changed into the equation form: 24=X%X30. In this equation we have the product (24) given and also one of the factors (30). The other factor is unknown. This equation involves the principle: Product-:- one factor = the other factor. .S or 80% 30)24.0 240 Therefore: 24=80% of 30. 2. 16 is what % of 24? Equation : 16 = X% X24. The unknown factor X% =the product 16-^the factor 24. Since a fraction may stand for an indicated division, we may indicate this division in the form of the fraction, -J^. Then X%=M = 1^661%. Therefore : 16 is 66f % of 24. 8. 6 is ?% of 18? 9. $80 is ?% of $120? 4. 20 is ?% of 25? 10. 24 bu. is ?% of 40 bu.? 6. 15 is ?% of 18? 11. 48 is ?% of 64? 6. 25 is ?% of 40? 12. $120 is ?% of $2400? 7. 48 is ?% of 80? 18. $16 is ?% of $200? 8. 27 is ?% of 36? 14. 20 bu. is ?% of 24 bu.? PERCENTAGE— PRACTICE PROBLEMS 55 16. 80 is ?% of 160? 22. $400 is ?% of J1200? 16. 81 is ?% of 90? 28. $63 is ?% of $1260? 17. 21 is ?% of 63? 24. $7 is ?% of $140? 18. 24 is ?% of 240? 26. $15 is ?% of $300? 19. 16 is ?% of 96? 26. $12 is ?% of $240? 20. 75 is ?% of 125? 27. 320 acres is ?% of 480 acres? 21. $60 is ?% of $75? 28. 10 gaUons is ?% of 80 gallons? Work of this type is valuable in giving experience in solving equations before attempting to solve concrete problems in which such equations are involved. Exercise 10 1. A newsboy bought 50 Sunday papers and sold 48 of thena. What per cent of his papers did he sell? Since he sold 48 out of 50, the question is: 48 is what % of 50? Equation: 48=X%X50. PRINCIPLE : Product -^ one factor = the other factor. Then X% =48^50 = .96 or 96%. 2. A farmer bought a carloaxi of steers averaging 930 lb. When the farmer sold them, they averaged 1240 lb. What was the per cent of increase in their weight? 1240 lb. -930 lb. =310 lb., the increase. 310 lb. is what % of 930 lb.? 3. If the farmer bought the steers for $7.00 per hundred and sold them for $9.45 per hundred, what was his per cent of gain in the selling price per hundred over the buying price? 4. If a grocer buys eggs at 24 cents per dozen and sells them at 28 cents per dozen, what is his per cent of profit? 6. During the season of 1916, the Boston American League ball team won 91 games out of a total of 154. What per cent of its games did Boston win? 56 SEVENTH YEAR 6. During the same season, Brooklyn in the National League won 94 games out of 154. Find the per cent of games won by Brooklyn. 7. In the Worid's Series between Boston and Brooklyn, Boston won 4 out of the 5 games played. What per cent of games did Boston win in this series? 8. A lumber firm increased its capital from $30,000 to $45,000. What was the per cent of increase in its capital? 9. A laboratory test showed that a white potato, weighing 16 oz., contained 10 oz. of water. What is the per cent of water in potatoes as shown by this test? 10. The same kind of a test on a sweet potato, weighing 15 oz., showed that it contained 8.25 oz. of water. What per cent of water is there in a sweet potato? 11. If the per cent of refuse is the same in both white and sweet potatoes, which of these vegetables contains the more nutritive material? 12. If sweet potatoes are selling at 4 cents per pound and white potatoes at 2 cents per pound, which is more economical, considering the amount of nutritive material in each? 13. What per cent of profit must be made on the sale of goods costing $50,000 to cover an expense of $7500 and a net gain of the same amount? 14. A certain grade of canned peas advanced in price from 12 cents to 15 cents per can. Find the per cent of increase. 16. An owner of a bungalow costing $3000 rents it for $25 per month. His expenses are $60 for repairs, taxes and insur- ance. Find the per cent of profit each year on his investment. 16. A farmer applied fertilizer to a field yielding an average of 48 bushels of corn per acre and secured 66 bushels per acre. Find the per cent of increase due to the fertilizer. PERCENTAGE— FRACTIONAL EQUIVALENTS 57 Exercise 11 1. 24 is 75% of what number? Equation: 24=75%XX. X, the unknown f actor , =24 -5- .75 =32. Care must be taken in this type of problem to reduce the per cent to a decimal or a conmion fraction before dividing. 2. 16 is 25% of what number? Equation: 16=25%XX. In this problem, we see that 16 =25% or ^ of the number. The number —A times 16, or 64. Fractional equivalents are much shorter in solving some equations thaii decimals. Practice using both in solving equations and then choose the more convenient method for each equation. 8. 18 is \2\% of ? 12. $15 is 6% of ? 4. 21 is 75% of ? 18. $21 is 6% of ? 6. 48 is 80% of ? 14. $14 is 4% of ? 6. 40 is 62|% of ? 16. $12.80 is 8% of ? 7. 8 is 16f % of 7 16. 11 lb. is 4% of ? 8. 64 is 50% of ? 17. 9 is 2^% of ? 9. 12 is 25% of ? 18. 12 is 3% of ? 10. 63 is 87 f% of ? 19. 245 is 20% of ? 11. 9 is 16f % of ? 20. 81 is 37|% of ? Exercise 12 1. If a man sells a house for $2760, which is 92% of what he paid for it, what was the original purchase price? In short form this problem means: $2760 is 92% of ? (cost). Equation: $2760 =92% XX. Find the value of X. 58 SEVENTH YEAR 2. I wrote a check for an insurance premium for $52.24 and found that it would take out 42% of the money I had on deposit in the bank. How much money did I have on deposit? 3. After losing 18% of his investment in a gold mine, a man has $6192.60 left. How much did he have invested in the mine? 4. A farmer sold a cow for $84, thereby gaining 20%. How much did the cow cost? Suggestions: The cost of the cow = 100% of the .cost. If the farmer gained 20%, he sold the cow for how many % of the cost? 5. The present enrollment of a school of 486 pupils is 20% more than its last year's enrollment. What was the last year's enrollment? 6. The circulation of a certain newspaper is now 39,875. This is an increase of 10% over that of last year. What was last year's circulation? 7. If a railway line has been extended 18% of its original length and is now 554.6 miles long, what was its original length? 8. If I add to my bank deposit $120, which is 60% of what I already have on deposit, what was my balance before making the deposit? 9. I paid $5 for a pair of shoes. This was 16f % of what I paid for a suit. How much did I pay for the suit? 10. A bank distributes dividends amounting to $4800. This sum is 12% of its capital stock. Find its capital stock. 11. A banker gained 8% on an investment. If his profits were $202, what was the amount of his investment? « 12. A boy gained 6 lb. during his summer vacation. This was 6 J% of his weight at the beginning of the vacation. How much did he weigh at the close of the vacation? PERCENTAGE— REVIEW PROBLEMS 59 REVIEW PROBLEMS IN PERCENTAGE^ Exercise 13 1. Mr. Brown lost 15% on an investment of $1800. What was his loss? 2. A boy who weighs 77 lb. has gained 10% since his last birthday. What was his weight then? 3. An owner of a farm worth $175 an acre wishes to get a return of 4^% on his investment. What rent must he charge? 4. If you have 12 problems to solve for home work and work 10 correctly, what should your grade be, considering the prob- lems of equal value in grading? 6. 23 pupils in a class of 25 were promoted. What per cent of pupils failed? 6. A man has an annual income of $1500 and pays $420 a year for rent. What per cent of his income does he pay for rent? 7. A liveryman bought a team of horses for $350. After using them for two years, he sold them at a- loss of 40%. What did he receive for the team? 8. A contractor figured a house to cost $4375 and secured the contract for $5500. What was his per cent of profit if his estimate was correct? 9. An abandoned beach hotel which cost $80,000 is sold for $48,000 at what per cent of loss? The purchaser reopens it for a new class of patronage and sells it to a company for the original cost. What was his per cent of profit? 10. A boy gave his playmates 75% of his apples and had 4 left. How many had he at first? ^This list of problems is designed to give practice in stating equations for the three types of percentage problems. 60 SEVENTH YEAR 11. A teamster paid $100 each for 2 horses, $60 for a wagon, anci $20 for a second-hand set of harness! At what price must he sell the outfit to gain 10%? 12. The sales of a certain store were $72,000 for the year and the profit made was $8000. What was the per cent of profit? 13. A mill is sold for $856,000 at an advance of 14^% on its cost price. How much did it cost? 14. A man's expenses in a year are $1200. His salary is 133f % of that amount. How much money can he save in a year out of his salary? 15. A grocer buys eggs at wholesale for 24f!^ and sells them for 32f! per dozen. What is his per cent of profit? 16. I paid my rent with a check for $37.50, which was 5% of my deposits in the bank. What was the balance remaining in the bank? 17. A collector charged $60 for collecting a debt of $1200. What per cent did he charge for collecting? 18. The engine in my automobile is 40 H. P. My neighbor's engine is 60 H. P. His engine is how many per cent as powerful as mine? 19. A factory employing 40 equally paid operators of machines, reduces its force by 25% and increases by 25% the wages of those that remain. Does it pay more or less in wages than before? 20. Helen spent 35% of her Christmas money on one shop- ping trip and 28% on the next trip. What per cent of her money was left? If she had $7.40 left, how much money had she at first? 21. A merchant sold goods for which he paid $30,000 at an average of 30% higher price, but lost 5% from the failure of certain debtors. What was the amount of his profit? PERCENTAGE— PUPILS' OWN PROBLEMS 61 22. If one cow yields 15 quarts of milk each day, the milk containing 3.6% of butter fat, and another cow yields 12 quarts of milk per day, containing 4.5% of butter fat, which cow is the more profitable for butter making? 23. A house and lot were purchased for $4000. The house was moved and sold for S2000 and the cost of moving. At what price must the lot be sold to realize a total gain of 25% on the investment? 24. The sales in a store were $960 for one day, which would have meant a profit of 20% but for the unfortunate acceptance of a counterfeit 20-dollar bill which could not be traced to the payer. What was the net per cent of gain? 25. Standard milk is 87% water, 4% fat, .7% ash, 3.3% protein and the remainder is made up of carbohydrates. What per cent of standard milk is carbohydrates? 26. A merchant marks a suit of clothes costing $20 at an increase of 60%. Later he discounts the marked price 20%. What was the cost to the purchaser? What was the merchant's per cent of profit on his cost? 27. After grooving, a 4-inch floor board is only 3 J inches on its face. If you figure the number of board feet for a floor, what per cent must you add to allow for the grooving? Exercise 14 PROBLEMS COLLECTED BY PUPILS The following problems were gathered by a seventh grade class from their experiences and consultations with their parents. See how many of these problems you can solve. 1. I have done 8 of the 50 arithmetic drill cards. What per cent have I yet to do? 2. My father received an order from the army for $85,900 worth of goods. He receives 4% commission. How much does he receive? 62 SEVENTH YEAR 3. I bought a share of stock last year for $114. I have just sold it for $181. What was my per cent of gain? 4. Last year flour was $6.75 per bbl. and this year (1916) it is $10.00 per bbl. What is the per cent of increase? 6. A bill of lumber was sold, the price being $864, but an allowance of 10% was made for poor grade. There was also a discount of 2% for prompt payment. Find the net amount of the bill. 6. A manufacturer makes and sells an article for $24.00 per dozen. His overhead charges^ are 20% of this and he allows a cash discount of 7%. What is the net amount of his profit per dozen, after deducting $15.00 for materials and cost of manufacturing? a 7. A wholesale dealer buys a boiler from the manufacturer at the list price of $24.00 less 40% discount. He sells it to his retail customer at 30% discount from the list price. How much profit does he make on the sale? 8. A corporation is capitalized at $50,000. How much busi- ness will they have to do yearly to pay a dividend of 10% on their capital stock, provided their profit is 5% of their total sales? 9. During 1915 a manufacturer employed 206 men at $2.00 per day. In 1916 he employed 175 men and his total daily wage bill was $395.00. By what per cent had the daily per capita wage increased? 10. In 1900, $100 would buy a certain number of articles of goods. In 1910, it took $120 to buy the same articles and in 1916 it took $160 to buy the same goods. By what per cent should wages have increased between 1910 and 1916 to have enabled the laborer to purchase the same quantity of goods in 1916 as he had been able to purchase in 1910? ^Overhead charges cover all expenses of a factory except cost of material and cost of labor. PERCENTAGE— DAIRY PRODUCTS 63 16 Prepare a list of percentage problems based on the business conditions in your community. Each pupil should bring in at least two problems from which the teacher can select a list for review work in percentage. Try to get actual transactions to use in your problems. Exercise 16 MILK AND CREAM Efficient dairymen are now testing the milk of each cow to see which are the most productive. Those which are not profitable are sold and others secured in their places which produce a higher per cent of butter fat. The amount of butter fat is ascertained by means of the Babcock test. 1. Some pupil in the class should make a careful study of the Babcock test and make a full report to the class. 2. Standard milk is 87% water, 4% fat, 3.3% protein, .7% ash, and the remainder is made up of carbohydrates. What per cent of standard milk is carbohydrates? 3. Cream is 74% water, 2.5% protein, 4.5% carbohydrates, .5% ash and the remainder fat. What per cent of the cream is fat? The test for butter fat is made in bottles similar to the one shown in the illustration. The butter fat accumulates in^ the neck of the bottle and can be measured on the scale with a pair of dividers. The bottle in the illustration shows a test yielding 4% of butter fat. 64 SEVENTH YEAR 4. A farmer took a can of milk weighing 275 lb. to the creamery. The test for this milk showed 3.8% of butter fat. How much did he receive for this butter fat at 26 cents per pound? 5. A certain recorded Jersey cow yielded 17,557 pounds of milk in one year. From this amount of milk, 998 pounds of butter fat were obtained. What per cent of the milk was butter fat? 6. A certain recorded Guernsey cow yielded in one year 910 pounds of butter fat in 17,285 pounds of milk. What was the per cent of butter fat in her milk? 7. A Shorthorn cow yielded 18,075 pounds of milk in a year. The milk of this cow contained 735 pounds of butter fat. What was the per cent of butter fat in her milk? 8. A cow's milk was tested by a dairyman with a view to purchasing the cow. He found her milk to test 3.2% butter fat. If the price was satisfactory, would you buy the cow to add to a dairy herd? 9. A certain Holstein cow yielded an average of 14,134 pounds of milk per year for five years. If her milk tested 3.7% butter fat, how many pounds of butter fat did this cow produce in the five years? 10. How much was this butter fat worth at 28 cents per pound? 11. If one cow yields 30 lb. of milk per day testing 3.4% of butter fat and another cow yields 25 lb. of milk testing 4.4% of butter fat, which cow is the more profitable and how much per week? If whole milk is sold for city consumption, the quantity of milk is a more important consideration than the per cent of butter fat, providing that the percentage of butter fat does not fall below a minimum of about 3.4%. PERCENTAGE— DAIRY PRODUCTS 65 12. A dairymaD tested ten cows for butter fat with the following resulte : Pounds of milk Per cent of Cow per day butter f&t 1 30 3.9 2 28 3.4 3 24 4.0 4 35 4.1 6 26 3.3 6 32 3.9 7 22 3.8 8 29 4.2 9 21 3.5 10 28 4.0 Which cows would you recommend that he keep and which ones would you recommend that he sell and buy others to take their places? Give ■ easoos for your decisions. Duchess Skylark Ormsby, a Holstein-Friesian cow, has the record of being the world's champion butter producer. She produced 27,761 lb. of milk in a year, yielding 1205 lb. of butter fat. 15. Find the per cent of butter fat in the milk of the champion cow. 14. At 35 cents a pound, how much was that amount of butter fat worth? 16. How much would the whole milk from this cow have brought at $2.00 per hundred pounds? Counuy of Uw iDtenutioDal HsrvegCer Co. 66 SEVENTH YEAR THE MEAT ZHDUSTRY {Applied percentage problems) The meat industry is one of the moat important enter- prises in our country. In a recent year the production of beef, veal, mutton and pork amounted to 22,378,000,000 lb., an average of about 220 lb. for each person in the United States. Not all of this immense production of meat was consumed in tbb country, however, for a large portion of it was exported to foreign countries. Exercise 17 1, A farmer sold a carload of 20 steers avera^ng 1250 lb. in weight for Sll.OO per hundred pounds. How much did he receive for them? 3. If one of these steers loses 40% in being dressed, what is the weight of the dressed beef in a steer weighing 1250 lb.7 3. If a steer weighing 1093 pounds alive weighs 632 pounds when dressed, what per cent did this steer lose in being slaugh- tered? 4. The two loins of a hog weigh about 10% of the weight of a live hog. How much would each of the loins from a 220- Ib. hog weigh? 6. A farmer ships a carload of 95 hogs aver^ng 225 pounds in weight, receiving $12.35 per hundred. How much did he receive for the carload of hogs? 6. Find the broker's commission at $10.00 per carload of 19,000 lb. and 5 cents [>er hundred in excess of that weight. PERCENTAGE— THE MEAT INDUSTRY 67 J Bound 24.00% ZJLoin JC.60' 3%FIatat 2^3 ■ 4Jtib 9.64 - A'MwBi 9.46- OBridM e.oo 7'Chadt 22.05 SSJfkin/t 0,ZS 9^uei In slaughtering a beef, the waste materials are all used. From these waste materials or by-products are made leather, glue, oleo oil, soap and fertilizers. The carcass of a beef is divided into 8 different cuts as shown in the illustration at the left. The percentage of the dressed weight included in each cut of the beef is also shown. 7. A dressed carcass of a steer weighs 670 lb. Find the weight included in each of the different cuts for one-half of the carcass, using the percentages in the illus- tration. 8. If the by-products of a steer costing $132 were estimated as worth $36, what per cent of the original cost of the steer was obtained from the by-products? 9. A hog loses 25% to 35% of its weight in being dressed. How much will a 200-lb. hog lose in weight if the loss is 33%? 10- How much will the 200-lb. hog weigh when dressed? 11. How much will a 175-lb. hog weigh, dressed; shrinking 35%? 12. The two short cut hams of a hog are about 13f % of the live weight of a hog. How much do the two short cut hams of a 230-lb. hog weigh? Oleomargarine is one of the most important products made by the packing industry. It is made from a mixture of oleo oil, neutral, vegetable oil, milk and cream, and butter. The oleo oil is made from the fat of cattle. Neutral is made from the finest leaf fat of hogs. The vegetable oils include such oils as cottonseed oil and peanut oil. 68 SEVENTH YEAR 15. The wholesale price on a certain brand of oleomargarine was 24ff per pound in December of a recent year. The cheapest brand made by the same firm was selling at only 75% of that price. What was the price of the cheaper grade? 14. The retail price of the best brand of oleomargarine mentioned in problem 11 was 28f!S at a certain grocery store. The retail price was how many per cent greater than the whole- sale price? 16. A certain meat packing firm states that 80% of their sales go for the purchase of live stock, 8% for labor, 5% fo^- freight and 4f % for other expenses. What per cent of their sales is left for dividends for the stockholders? 16. If their total sales amounted to $500,000,000 per year^ compute the amount paid for live stock, the amount paid for labor and the amount left for dividends. . The receipts at the nine principal live stock markets in the United States for the years ending October 1 are as follows: Cattle Sheep Hogs 1911 9,416,374 13,530,833 19,217,506 1912 8,861,404 14,148,096 21,035,035 1913 9,188,500 14,146,284 19,997,656 1914 8,193,856 14,702,889 19,366,263 1915 8,464,185 11,994,851 21,366,263 17. What has been the percent of decrease in the number of cattle from 1911 to 1915? 18. What has been the per cent of decrease in the number of sheep received from 1914 to 1915? 19. What was the per cent of increase in the supply of hogs from 1911 to 1915? 20. The average wholesale price of dressed beef in New York in 1911 was $8.77 and in 1915 it was $11.64. What has been the per cent of increase in the wholesale price of beef in that period? PEECENTAGE— THE COTTON INDUSTRY 69 COTTON When picked, cotton is first pnned,' and then packed into bales weighing approximately 500 pounds. To economiae space in ship- ping long distances these bales usually are com- pressed by powerful mar chines into the smallest possible compass. The illustration shows one of Hi«h 0.0,1*1- Cotton C«np«>a. these machines compressing a bale of cotton. The following table gives the number of bales produced in the leading cotton-producing states. No. of bales No. of bales No. of bales 1913 1914 1915 Toms 3,945,000 4,692,000 3,175,000 . Georgia 2,317,000 2,718,000 1,900,000 South Carolina 1,378,000 1.634,000 1,190,000 Alabama 1,495,000 1,751,000 1,050,000 Miesisaippi 1,311,000 1,246,000 940,000 Arkansas 1,073,000 1,016,000 786,000 North Carolina 793,000 931,000 708,000 Oklahoma 840,000 1,292,000 630,000 Louisiana 444,000 449,000 360,000 Tennessee 379,000 384,000 296,000 Missouri 67,000 82,000 52,000 Florida 59,000 81,000 B0,000 Vii^inia 23,000 25,000 16,000 All other states 32,000 64,000 40,000 United States 14,156,000 16,136,000 11,161,000 Total Value of Crop. $885,350,000 1591,030,000 $602,393,000 ■Qinning is the process of removing the seeds from the cotton- 70 SEVENTH YEAR Exercise 18 1. What was the per cent of increase in the number of bales of cotton from 1913 to 1914? (See preceding page.) 2. Find the price per pound for cotton in 1913; for 1914 and for 1915. The large crop and the outbreak of the great European War in 1914 were responsible for the low price in 1914. Com- pute the prices per bale. 3. Note the decreased production in 1915. What was the per cent of decrease from the jrield for 1914? 4. What per cent of the total production of the United States was the production of Texas in 1914; in 1915? 6. The production of Oklahoma in 1915 was what per cent of its production in 1914? 6. The total production of the United States for 19 14. was what per cent greater than the total production for 1915? 7. The total exports of cotton for 1913 was 4,562,295,675 lb. What was the value of our cotton exports in 1913 at 12.2 cents per pound? 8. Cotton constitutes about 53% of our total agricultural exports. From the data given in problem 7, compute the value of our total agricultural exports for 1913. 9. It is estimated that cotton forms 63% of the total crop production in Texas. From the data in the table and the cost per pound in problem 2, find the value of the total crop pro- duction of Texas in 1915. This offers a valuable type of work — getting information from a table of statistics. Additional exercises of this type may be made from tables of statistics such as those found in the Statesman's Year Book or other similar pubhcations. PERCENTAGE— FOOD PRICES 71 FOOD PiaCES Exercise 19 The following table, originally published in a large daily newspaper, shows the advances in the wholesale prices of certain food supplies during a recent year. 1. Find the per cent of increase for each food product given in the table. Food Products. 1915. Hams, fresh $0.16 Bacon 24 Beef, No. 1, ribs 17 Sbeep, whole 00^ Leg of muttoD 12 Chickens, broilers 20^ Turkeys 20 Eggs, No. 1 24% Butter 27 Potatoes .* 48 Onions, green 07 Cabbage (barrel) 86 Lettuce, leaf (box) .35 Celery (bunch) 26 Com, small cans (dozen) 78 Tomatoes, fresh 90 Nayy beans (bushel) 3.15 Peas, 2-lb. cans (dozen) 85 Apples, green (barrel) 3.25 Raspberries (No. lO's) 5.50 Peaches 2.86 Lemons, crate 3.00 Tea 36 Flour (barrel) 6.25 Sugar, granulated (100 lb.) 5.50 Cornstarch 03 Rolled oats 03 Spaghetti 06 Sardines 07% Soap, kitchen 02% 1916. $0.20 .26% .19 .14% .16 .24% .30 .33 .34% 1.60 .10 1.90 .55 .30 .90 1.25 6.65 1.05 4.76 6.25 3.75 7.25 .40 7.95 6.40 .03% .04 .07% .12 .03% 2. Find the average per cent of increase in all these food products. 8. Ascertain if pos- sible the present whole- sale prices on the food products listed and de- termine the per cents of increase or decrease since the last year shown in the table. 4. If you can get the prices, prepare a list of prices on farm products and determine the per cents of increase or decrease for two recent years. Compare com, oats, hay, cotton, cattle, hogs, rice, sheep, horses, tobacco, and other such farm products. Local Prices Secure at a local grocery store the retail prices on a list of at least 10 articles for this year and also the prices for last year on the same quality of goods. 6. Find the per cent of increase or decrease on each of the articles that you have listed. Ask the grocer to tell you the causes for the increases or decreases on the various articles. 73 SEVENTH YEAR FOOD VALUES There are four principd food substances in the foods that we eat : (1) protein (pro'-te-in) (2) corbo- % hydrate; (3) fat; (4) mirieral Tnatter. R Water is also an important con- stituent of food products. Differ- ^ ent food products contain different ij- proportions of these food substances. Eggs, as shown in the illustration, are composed of 73.7% water, 14.8% protein, 10.5% fat and 1% ash or mineral matter. The protein compounds not only build up the tissues of the body but they also furnish enei^ to enable us to do our work. The carbohydrates and fats supply enei^ for the body. Exercise 20 1. Usii^ the percentages given in the illustration above, find the number of ounces of each of the constituents in a pound of eggs. 2. The average composition of 1 pound of beef is as follows: water 10.72 oz.; protein 3.04 oz.; fat 2.08 oz.; and mineral matter .16 oz. Find the per cent of each substance in the average pound of beef. 8, A white potato is composed of 1.8% prot«in, .1% fat, 14.7% carbohydrates, .8% ash, 62.6% water and 20% refuse. Find the number of ounces of each constituent in 1 lb. of pota- toes. (Refer to page 312 for additional data for problems.) 4. White bread is composed of 9.2% protein, 1.3% fat, 53.1% carbohydrates, 1.1% ash, 35.3% water. How many ounces ore there of each food substance in a pound loaf of bread? 5, Compare amounts of various food substances in bread and potatoes. PERCENTAGE PROBLEMS— FOOD VALUES 73 6. If cereals and their products supply 62% of the carbo- hydrates, and vegetables and fruits together 16% of the carbohydrates, what per cent of the total carbohydrates do both of these classes supply? 7. If meat and poultry supply 16% of the total food material in the average American home, and dairy products 18%, cereals and their products 31%, vegetables and fruits, together, 25%, how much of the total food materials do these items constitute? 8. If meat and poultry supply 30% of the protein, the dairy products 10% of it, cereals and their products 43% of it, and vegetables and fruits together 9% of it, how much of the protein is supplied by these four kinds of food? 9. If meat and poultry supply 59% of the fat, dairy prod- ucts 26% of the fat, cereals and their products 9% of the fat, and fruits and vegetables together 2% of the fat, what per cent of the total fat do these four kinds of food supply? Domestic science courses not only teach how to cook foods but also what kinds of foods to prepare in order to secure a proper proportion of the various food substances. When coal is burned, it supplies heat which may be converted into the energy of steam and run a steam engine. In a similar manner the food which we eat is consumed by our bodies, supplying heat and energy to do our work. Experiments have been made to show the amount of energy which each food product yields. These amounts of energy are expressed in terms of calories (kal'-o-ries). A calorie is used in this connection to mean the amount of heat required to raise 1 pound of water 4° Fahrenheit. The number of calories per day needed by any person varies with his weight and the amount of work which he does. A man at hard work or an active growing boy may require as 74 SEVENTH YEAR much as 5000 calories of food energy per day. An average man requires about 2500 calories when engaged in an occupation where he is sitting most of the day. The problem of the scientific cook is to serve foods which will contain the proper food substances and at the same time supply a sufficient number of calories each day. The following table^ shows the amount of each food product which will yield 100 calories: Milk f cup, whole; 1^ cups, skim ^ream J cup, thin; 1 J tablespoons, very thick Butter 1 tablespoon Bread 2 slices S^xS^^xJ' Fresh fruit 1 large orange or apple Eggs 1 large, 1^ medium Meat (beef, mutton, chicken, etc.) About 2 oz. lean Bacon (cooked crisp) About ^ oz. (very variable) Potatoes 1 medium Sugar 1 tablespoon Cocoa, made with milk -f of a cup Cooked or flaked breakfast foods f to 1 J cups Dried fruit 4 or 5 prunes or dates Exercise 21 1. A man requiring 25(X) calories per day eats the following breakfast: 1 cup of breakfast food with J cup of thin cream, 1 cup of cocoa made with milk, 2 slices of bread, 1 tablespoon of butter, 2 small slices of bacon and 1 egg (large). Find the* nmnber of calories supplied by this breakfast. 2. What per cent of the total requirement for a day is furnished by that breakfast? 3. It is desirable that a family of five consume 3 quarts of milk per day. If they consume 17 quarts per week, what per cent of the desirable quantity have they used? ^See Rose, Feeding the Family. PERCENTAGE PROBLEMS— FOOD VALUES 75 4. From the preceding table, prepare a menu for breakfast that will furnish between 700 and 900 calories. 6. Prepare a menu for lunch to furnish approximately 1000 calories. 6. Which will furnish the largest number of calories, a large orange or a medium sized egg? (See table, page 74.) 7. How many calories will a dozen medium sized eggs supply? 8. How many calories are there in a quart of milk? (2 cups make a pint.) 9. How many calories are there in a pound of prunes (40 to the pound)? 10. A man requiring 3000 calories per day eats a breakfast furnishing 700 calories, a lunch furnishing about 900 calories and a dinner furnishing about 1400 calories. Find the per cent of the total furnished by each meal. 11. If the meals for a family for a week cost $5.60 and the meat costs $1.40, the vegetables 70 cents and the butter 48 cents, what per cent of the total was spent for each group? 12. What per cent of the weekly expense was left for other materials? IS. If it takes 1 hour to prepare an entire meal and 20 min- utes to make the dessert, what per cent of the whole time is given to the dessert? The following table shows the number of calories supplied by a pound of each food product: Beef, fresh lean 709 Beans 1564 Beef, fat 1357 Oatmeal 1810 Bacon (average) 2836 Lettuce 87 Butter 3488 Cabbage 143 Apples 285 Sugar 1814 Potatoes, white 378 Bread - 1174 Milk, whole 314 Eggs 672 76 SEVENTH YEAR Exercise 22 1. The food value of a pound of fresh lean beef is what per cent of the food value of a pound of butter? 2. A pound of white potatoes furnishes what per cent as many calories as a pound of butter? 3. How does the food value of a pound of lettuce compare with the food value of a pound of white potatoes? (Express in per cent.) 4. In the same way compare the food values of fat beef and bacon. 5. Which is cheaper, sugar at 7 cents per pound or beans at 10 cents per pound, considering the food values of each? 6. Which is cheaper, apples at 6 cents per pound or bacon at 28 cents per pound? 7. Which is cheaper, oatmeal at 5 cents per pound or eggs at 26 cents per dozen? (Figure eggs at 1§ lb. per doz.) 8. From the cost of milk and butter in your community, compute the cost of the amount of each necessary to supply 100 calories. 9. Find the cost of 100 calorie portions of cabbage, potatoes, lean beef, beans, sugar, bread, eggs and bacon in your commu- nity. 10. Prepare a menu for a lunch from the items listed on page 75, providing 900 calories for each of 4 persons. From local prices in your community, estimate the cost of this lunch for each person. 11. Prepare and present a problem on food values to the class for solution. 12. If you have a school lunch room, estimate the cost to the students of 100 calorie portions of as many of the dishes as you can find the data to compute. CHAPTER IV APPLICATIONS OF PERCENTAGE The subjects treated in this chapter do not involve any new principles of percentage but merely an application of the prin- ciples already mastered to new business situations. New terms and new business forms will have to be mastered in making the application of the principles already learned. The discussion, then, at the beginning of each list of problems should be thoroughly mastered in order to get a good knowledge of business terms and organization. BUSINESS TRANSACTIONS Exercise 1 The gross profit in any business transaction is the difference between the cost price and the selling price. The net profit is the gross profit less the expenses of the transaction. 1. A notion store sold 100 pairs of wooden knitting needles at 10 cents per pair, at a profit of 33^%. What was the cost of each pair of needles? 2. If the selling price of an article is 4 times the cost, what is the per cent of gain? 3. A fancy vest is sold for $7 at a profit of 40%. What was its cost price? 4. A village lot was purchased for $1000, but because of a decline in real estate values was sold for $750. What was the per cent of loss? 6. A man sold a horse for $120 at a loss of 25%. What did the horse cost him? 77 78 SEVENTH YEAR 6. A merchant bought goods listed at $1200 at a reduction of 40%. He sold them at a profit of 25%. What was the total selling price of the goods? 7. A merchant having goods worth $10,000 increased his stock 25% and sold the entire stock at an averagje profit of 20%. For what sum did he sell it? 8. When an article that cost $24 is sold at a profit of 10% and the purchaser sells it again at a loss of 20%, what is its last selling price? 9. A liveryman sold a horse for $175 at a profit of 25%. What was the cost of the horse? 10. A man sold two farms for $7500 each. On one he gained 20% and on the other he lost 20%. Did he gain or lose on the entire transaction and how much? 11. A farmer bought a herd of 20 steers, averaging 1100 lb. each, at $7.50 per hundred. He fed them 700 bu. of corn worth 65ji per bu., 15 tons of hay worth $12 per ton and roughage worth $60. If his pasture of 20 acres was worth $6 per acre, what was his profit on the herd of cattle if they weighed 1476 lb. and brought $10.50 per hundred when he sold them? 12. A farmer sold his neighbor a cow at an advance of 10% of what she cost him. His neighbor sold her to a dairyman at an advance of 25%, receiving $110 for the cow. Find the amount of profit made by each. 13. A manufacturer sold a hardware dealer a stove at a profit of 10% on the cost of manufacturing. The hardware dealer sold the stove to a customer for $61.60 at a profit of 40%. Find the cost to the manufacturer. 14. A dair3nnan sold two cows for $90 each. On one he gained 20% and on the other he lost 10%. Find his per cent of gain or loss on the entire transaction. APPLICATIONS OF PERCENTAGE— DISCOUNTS 79 DISCOUNTS Exercise 2 A discount is a sum deducted from the price of an article. Discounts are usually computed by per cents. To state that you will sell an article at a discount of 25% means that you will sell it for j off or 25% off the regular list price. Many firms give discounts for cash purchases. It is profitable for these firms to give small discounts for cash purchases because they can re-invest the money and be making additional profits. 1* A music dealer sold a piano which he had listed for $400 at a discount of 20%. How much did he receive for it? list price of the piano ==$400 20% of $400=i of $400= 80=the discount. He received $320 The amount that is left after the discount is subtracted from the list price is called the net proceeds. In problem 1, $400 is the list price, $80 is the discount and $320 is the net proceeds. Find the discounts and net proceeds of the following list prices at the stated discounts: 2. $100, 25%. 6. $1.00, 30%. 10. $20, 15%. 3. $ 25, 10%. 7. $1.50, 33j%. 11. $40, 25%. 4. $250, 20%. 8. $500, 2%. 12. $5.00, 10%. 5. $ 30, 40%. 9. $125, 20%. 13. $452.75, 2%. 14. After using a motorcycle, costing $150, for a month, a boy offered it for sale at a discount of 15% of the cost price* How much did he want for the motorcycle? 16. A merchant bought a bill of goods amounting to $1240 and received a cash discount of 2% for prompt payment. What was the net proceeds of his bill? 80 SEVENTH YEAR CLEARANCE SALES Exercise 3 Retail stores iiave clearance sales in order to dispose of old goods on hand and make room for new styles and up-to-date patterns. They often give reductions of 10%, 20%, 33 J%, or even as high as 50%. In order to dispose of goods left on hand in which the styles are likely to change, the merchant may offer the goods at cost in order to prevent a loss at a later date when the goods are out of style. 1. A merchant advertised a 20% discount sale on shirtSo How much was the price on a shirt listed regularly at $2.50? 2.. A clothier oiffers a discount of 15% on all suits and over- coats in his store. What is his sale price on suits listed at $25? 3. A furniture store advertised a closing out sale, offering a discount of 33f % on the regular prices. Find the cost of the following articles listed regularly as' follows: 1 library table — $30.00; 2 rocking chairs at $15.00 each; 1 davenport — $42.00; 1 brass bed— $24.00; 1 mattress— $12.00; 1 set of springs — $9.00; and 1 dresser— $24.00. 4. In a clearance sale, a merchant gave a discount of 40% on novelty dress goods and 20% on the staple weaves. Why could he afford to give a larger discount on the novelty goods? 6. One shoe store advertised a ceitain shoe that retails regularly at $4.00 for $3.45; another store advertised the same shoe at a discount of 15%. Which was the better offer and how much? * 6. A merchant advertised $2.00 silks at a discount of 20%. What was his sale pric6 on those silks? 7. Straw hats worth $3.00 early in the season were sold late in the season at $1.50. What was the per cent of discount? APPLICATIONS OF PERCENTAGE— DISCOUNTS 81 COMMERCIAL DISCOUNTS Exercise 4 * Wholesale dealers and manufacturers often offer two or more discounts off the list price. These discounts are called Irade or commercial discounts. There are several advantages in using this system of com- mercial discounts. In the first place, catalogues are expensive to issue. By making the list prices of the articles high, fluctua- tions in the cost of materials will not make it necessary to issue a new catalogue. Instead, the firm can merely send out a new discount sheet which gives the discounts allowed on the various classes of articles. This discount sheet costs very little compared with the original cost of the catalogue. Further- more a retail dealer can show his customer the catalogue and give him a discount on the list price without the customer knowing the extent of his profit. Can you think of any other advantages of commercial discounts? If a firm is selling goods at a certain discount, a decrease in the cost of production may enable them to add a second discount. A discount is also usually allowed for prompt payment. Consequently, we occasionally see goods listed subject to a series of three successive discounts. Commercial discoimts are computed in sucession. The first discount is taken from the list price and the second dis- count is then computed on the remainder and so on. 1. A bed room suite was listed at $80 less discounts of 20% and 10%. What was the net price? 20%X$80 =$16, the first discount. $80 —$16 =$64/the remainder. 10%X$64 =$6.40, the second discount. $64 -$6.40 =$57.60, the net price. The net price is the list price less the conmiercial discounts. 82 SEVENTH YEAR 2. A piano listed at $500 has discounts of 30% and 5%. Find the net price. 3. A hardware firm .quotes a certain grade of hammers at $12 a dozen, less discounts of 33j% and 25%. What is the cost of each hammer to a local dealer? What must he mark a hammer to make a profit of 50%? 4. A merchant buys sweaters from a factory at $24 per dozen at discounts of 20% and 5%. What must he sell them at in order to make a profit of 60%? 5. Stoves are quoted by a manufacturer at $40 each, subject to discounts of 25%, 10% and 5%. What is the net price to the retail dealer if he is allowed a further discount of 2% for cash? 6. Find the net price on a dining table and set of six chairs listed at $80 if discounts of 20% and 15% are allowed. 7. A music cabinet is listed at $65 with discounts of 25%, 10% and 5%. Find the net price. List price Discount Net price 8. $175 20%, 10% and 5% ? 9. $150 25% and 5% ? 10. $400 30%, 10% and 5% ? 11. $40 20% and 3% ? 12. $75 25% and 2% ? In order to save computation, firms have tables showii^ a single discount which is equivalent to the series of successive discounts. 13. What single discount is equivalent to successive discounts of 20% and 10%? 20% X 100% =20% 10% X 80% =8% 100%- 20% =80% 80%- 8% = 72%, net price. APPLICATIONS OF PERCENTAGE— DISCOUNTS 83 100% -72% = 28%. Therefore, 28% is equivalent to successive discounts of 20% and 10%. 14. What single discount is equivalent to successive discounts of 30% and 20%? 16. Find the single discount equivalent to commercial dis- counts of 25%, 10% and 5%. 16. Which is better, a single discount of 40% or successive discounts of 25% and 20%? How much better? 17. Find the net price of a bill of goods amounting to $280 with discoimts of 25% and 10% with an additional discount of 2% for cash. 18. Find the net price on a set of harness listed at $60, subject to discoimts of 20% and 10%. Note: Bank DiscqurU will be treated under the topic Banks. INTEREST Exercise 6 Much of the business of the world is carried on with borrowed money. Men of ability and industry often do not have enough money of their own to supply the capital necessary for estab- lishing or conducting their business enterprises. On the other hand there are men who prefer to loan their money rather than attempt to run a business of their own. Thus money is loaned, in the business world, not as a matter of personal favor or accommodation, but as a matter of busi- ness based on benefits to both lender and borrower. The person who lends the money receives pay for the use of it from the borrower. Money paid for the use of money is called inte/^esL 84 SEVENTH YEAR The borrower in receiving money loaned to him, gives a dated and signed promise to return the money loaned (or the principal) with a certain interest at a stated date. Such a paper is called a note. Here is a note of simple form: „ afterdate ^ Cf. promise to pay to ..-.i§?^fw.f^56:. •r orrierQnf^Ji/n^^ with interest at .^ ^-^/.— /or value received, ^^^cAa/^ In a new conmiunity, where capital is greatly needed, money would often command a much, higher rate of interest than the law would allow. Most states provide penalties for charging a higher rate of interest than the legal rate fixed by law. The laws of the different states are not uniform as to the rate of interest that will be permitted. Interest that is unlawful in rate is called usury. Find what is the legal rate of interest in your state by inquiring at the bank. In ordinary transactions involving interest any month is considered one-twelfth of the year and thirty days constitute a month. In the case of large amounts of money, where exactness as to time is very important, the time of the loan is often stated in days and is reckoned according to agreement or custom. In exact interest 365 days are considered a year. Since banks consider 360 days a year in computing bank discount, it is customary to figure interest on that basis. The following form is very convenient for computing simple interest because it allows one to use cancellation: APPLICATIONS OF PERCENTAGE— INTEREST 85 Find the interest on $300 for 1 year, 3 months and 15 days at 6%. 3 93 Z00 300 4 00 20 4 In the above problem, the rate is used as a common fraction Y^'y the time 1 year (360 days) +3 months (90 days) +15 days =465 days which is |^ of a year. The interest for 1 year ($300 Xt^) must therefore be multiplied by |^ to find the interest for the given time. When the time is expressed in years and months, the form can be shortened by expressing the years and months as twelfths of a year. Find the interest on $200 for 1 year, 6 months at 6%. 6 18 «00Xj-^X^ = $18. i Find the interest on: 1, $500 for 6 months at 6%. 2. $350 for 1 year at 7%. 8. $1000 for 2 years at 6%. 4. $2000 for 2 years at 5|%. 5. $250 for 2 years, 6 months at 7%. 6. $6500 for 5 years, 6 months at 5%. 7. $325 for 2 years, 9 months at 6%. 8. $480 for 1 year, 8 months, 15 days at 6%. 86 SEVENTH YEAR 9. $2000 for 2 years, 8 months, 20 days at 5%. 10. $500 for 1 year, 5 months, 18 days at 6%. 11. $425.50 for 1 year, 3 months, 21 days at 6%. 12. $218.50 for 2 years, 10 months, 12 days at 6%. 18. $350.75 for 2 years, 8 months, 19 days at 6%. 14. $875.25 for 1 year, 3 months, 27 days at 6%. 16. $5000 for 4 years, 7 months, 18 days at 5%. 16. $150 for 1 year, 3 months, 20 days at 7%. 17. $200 for 6 months at 3%. 18. $175 for 1 year, 2 months, 15 days at 6%. 19. $300 for 2 years, 4 months at 6%. 20. $2500 for 1 year, 9 months, 18 days at 5%. Some teachers prefer to use the Six Per Cent Method in finding interest instead of the Cancellation Method used in the preceding explanation. The Six Per Cent Method may be used by teachers who prefer it or whose course of study requires it. This method uses the following data: The interest on $1 for 1 year =$.06 The interest on $1 for 1 month = .005 The interest on $1 for 1 day = .000^ Find the interest on $250 for 3 years, 3 months, 18 days at 6%. Interest on $1 for 3 years = 3X.06 =$.18 Interest on $1 for 3 months = 3X.005 = .015 Interest on $1 for 18 days = 18 X .OOOj = .003 Interest on $1 for the entire time —$.198 Interest on $250 for 3 years, 3 months, 18 days = 250 X$. 198 » $49.50. The interest at any other rate than 6% can. be found by taking -^ of the interest at 6% and multiplying by the given rate. When the times are stated for the beginning and end of the interest-bearing period, the following form is used in determining the time for computing the interest: APPLICATIONS OF PERCENTAGE— INTEREST 87 21. What is the interest on a note for $300 dated April 1, 1906, and paid May 15, 1908, at 6%? Year Month Day 1908— 6 —15 1906— 4 — 1 2— 1 —14 Therefore, the time is 2 years, 1 month and 14 days. Com- pute the interest. 22. Find the interest on $200 from Sept. 26, 1915, to Jan. 24, 1917, at 6%. Year Month Day ^e can not subtract 26 days from 24 1916 — 12 — 64 days, so we reduce 1 month, taken from X9n — I 2^ the months column to days, making 30 days; 1915— 9 — 2 6 add the 30 days to the 24 days, making 1 — 3 — 28 54 days. 26 days from 54 days leaves 28 days. We have already used the 1 month in the months column, so we must take a year from the year column (leaving 1916) and reduce it to 12 months. 12 months— 9 mo. leaves 3 months. 1916—1915 = 1 year. Therefore, the time is 1 year, 3 months, 28 days. Compute the interest. Find the interest on: 23. $750 from April 7, 1915, to July 14, 1917, at 6%. 24. $350.75 frcxn Dec. 18, 1912, to March 16, 1915, at 6%. 25. $2000 from Nov. 1, 1916, to Jan. 1, 1918, at 5%. 26. $150 fix)m July 25, 1910, to March 15, 1912, at 7%. 27. $275 from Oct. 9, 1913, to March 3, 1915, at 6%. 28. $5000 from Aug. 16, 1916, to August 16, 1921, at 5%. 29. $500 from May 22, 1914, to Sept. 22, 1917, at 6%. 88 se\:enth year 80. $850 from Mar. 1, 1915, to Oct. 5, 1916, at 6%. 81. $425 from Feb. 10, 1917, to Mar. 13, 1918, at 6%, 82. $1500 from Jan. 12, 1916, to July 3, 1917, at 5%. 83. $236.25 from Dec. 6, 1916, to Oct. 12, 1917, at 6%. 84. I borrowed $300 on July 18, 1916, at 6%, promising to pay the note on demand. The owner presented the note for pajrment on April 21, 1917. How much interest was there on the not^ at that time? What was the total sum due the lender? Bankers and other firms who have a great deal of interest to compute use tables in order to save time and insure greater accuracy. The following interest table was computed on the basis of 360 days to the year. Some tables are computed on the basis of 365 days to the year if the exact interest is wanted. INTEREST ON $1.00 Montlis Days Time 5% 6% 7% 1 2 3 4 5 6 7 8 9 10 20 $.000139 .000278 .000417 .000556 .000694 .000833 .000972 .001111 .001250 .001389 .002778 $.000167 .000333 .000500 .000667 .000833 .001000 .001167 .001333 .001500 .001667 .003333 . $.000194 .000389 .000583 .000778 .000972 .001167 .001361 .001556 .001750 .001944 .003889 1 2 3 . 4 5 6 .004167 .008333 .012500 .016666 .020833 .025000 .005000 .010000 .015000 .020000 .025000 .030000 .005833 .018667 .017500 .023333 .029167 .035000 1 Year .050000 .060000 .070000 APPLICATIONS OF PERCENTAGE— INTEREST 89 Exercise 6 1. Find the interest on $200 for 2 years, 3 months, 13 days at 6%, using the above table: Interest on $1.00 for 2 years ■»$ . 12 Interest on $1.00 for 3 months » .015 Interest on $1.00 for 10 days « .001667 Interest on $1.00 for 3 days = .0005 Interest on $1.00 for total time =$.137167 Interest on $200 for the given time, 200 X$. 137167 » $27.43+. Using the interest table, find the interest on: 2. $300 for 1 year, 6 months at 6%. 3. $250 for 1 year, 4 months, 20 days at 7%. 4. $500 for 2 years, 7 months, 9 days at 5%. 5. $75 for 1 year, 6 months, 5 days at 7%. 6. $2000 for 3 years, 6 months at 5%. 7. $700 for 8 months, 25 days at 6%. 8. $100 for 2 years, 9 months, 24 dajrs at 7%. 9. $500 for 1 year, 2 months, 23 days at 6%. 10. $375 for 3 years, 6 months at PARTIAL PAYMENTS When a note is given for a long period, the interest is usually to be paid periodically, and not to be deferred until the principal becomes due. A part of the principal may likewise be paid from time to time. Such a payment is called a partial payment. The amount paid should be stated on the back of the note, together with the date on which it is received. The subject of Partial Payments in Arithmetics is one in which there has been much confusion, owing to the diverse 90 SEVENTH YEAR laws of (ii£Ferent states. The tendency is towards unity of practice in partial payments, since nearly all of the states have adopted this rule sustained by the Supreme Court of the United States in cases that have come before it. This is known as the United States Rule, and is in substance as follows: When a partial payment or the sum of two or m^e partial payments is equal to, or more than, the interest due, it is to he subtracted from the amount (principal ^interest du£) at the time; and the remainder is to be considered a new principal, from that time to the next payment. The following form shows the method of recording partial payments on a note:^ ^^^ow Ic^Vi aj thi JQif^tiMi^LQ??^u jfierdate fel__— ^pnmise to pay to order of .^..hft/^ with interest at S2.-W-. — -— .- for value received. l^jOcfu2/y^ f^jkju/ucd/ orut/iw/notb: QuUini^^SO. QofmjJOoO fQmltm^75. ihhrvlDot ^Payments on a note are usually made at interest-bearing dates. If the interest is payable on Jan. 1 and July 1 of each year, it is often specified that partial payments may be made on those dates. APPLICATIONS OF PERCENTAGE 91 Exercise 7 1. Find the amount of the note on p. 90^ due on settlement at maturity. Solution: $400.00 1st principal 24.00 interest from July 1, 1915, to July 1, 1916. 424.00 amount due July 1, 1916. 50.00 payment July 1, 1916. 374.00 new principaL 11.2 2 interest from July 1, 1916, to Jan. 1, 1917. 385.22 amount due Jan. 1, 1917. 75.00 payment Jan. 1, 1917. 310.22 new principal. 18.61 interest from Jan. 1, 1917, to Jan. 1, 1918. 328.83 amount due Jan. 1, 1918. 100.00 payment Jan. 1, 1918. 228.83 new principal. 6.86 interest from Jan. 1, 1918, to July 1, 1918. $235.69 amount due on note at date of maturity. 2. Find the amount due at maturity Jan. 15^ 1918, on a note drawn at Indianapolis, Ind., Jan. 15, 1916, for $1000 with interest at 6%, having the following credits indorsed upon it: July 15, 1916, $80. Jan. 15, 1917, $107. July 15, 1917, $29. 3. What was due at maturity, Aug. 10, 1917, on a note drawn at San Francisco, Cal., Feb. 10, 1915, for $650 with interest at 6%, having the following partial payments indorsed upon it? Aug. 10, 1915, $109.50. Aug. 10, 1916, $219.50. Feb. 10, 1916, $116.50. Feb. 10, 1917, $50.00 4. What amount was due at maturity Jujy 15, 1917, on a note drawn at St. Louis, Mo., July 15, 1915, for $800 with interest at 5%, having these credits indorsed upon it? Jan. 15, 1916, $210. July 15, 1916, $215. Jan. 15, 1917, $50. 92 SEVENTH YEAR COMMISSION If a fruit grower or farmer wishes to sell his produce in a distant city, he can not usually afford to leave his work and go to the city to attempt to find a buyer. It is more profitable for him to have some firm in the city sell the produce for him. Refrigerator cars now make it possible to ship fruits and vegetables thousands of miles to distant cities where higher prices can be secured for them. There are two ways in which the grower can dispose of his products: (1) he can sell directly to some wholesale firm or (2) he can consign it to a commission firm to sell for him at . a certain per cent of the sale. If the grower sells directly to a firm, he usually sends a sight draft attached to a bill of lading, making it necessary for the firm to pay the draft before they can secure the bill of lading and get possession of the goods from the railroad company. This sight draft can be deposited by the grower with the local bank for collection. The local bank then sends this draft to a bank in the city, where the debtor does business, for collection. It is customary for the local bank to allow the grower to check against the amount of the draft, but he must replace the money if the draft is refused by the firm to which he sent the- goods. If a grower asks a commission firm to sell the goods for him, he consigns the shipment to them and they dispose of it to the best advantage, charging a certain commission for their work. After deducting commission, freight, cartage, storage or any other necessary expenses, the commission firm Bends the proceeds to the shipper. APPLICATIONS OF PERCENTAGE— COMMISSIONS 93 Wheat, com and other grains ore bought and sold m large cities in boards of trade where the members, called brokers, are required to pay for the privilege of buying and selling produce. Exercise 8 1. A fruit grower in Michigan consigned to a commission firm in Chicago 240 barrels of apples to be sold to the best advantage. The freight charges were 12f5 per 100 lb. and the apple barrels were considered as weighing 160 lb. each. Find the amoimt of the freight charges. 2. The cartage (or drayage) on these apples amounted to 6^ per barrel. Find the cartage charges. 3. 128 barrels were placed in cold storage at the rate of ISjif for the first month and 12f5 for each month thereafter. 80 barrels were sold out of cold storage during the first month and the remainder during the second month. Find the storage charges.^ 4. The following sales were made: 60 bbl. of Wolf Rivers at an average of $4.25 per bbl.; 35 bbl. of Baldwins at $3.75 per bbl.; 52 bbl. of Northern Spys at $5.00 per bbl.; 93 bbl. of Greenings at $3.50 per bbl. What was the commission on the total sales at 7%? 5. After deducting the commission, storage, cartage and freight, find the proceeds which the commission firm sent to the shipper. 6. A potato grower sold a carload of potatoes consisting of 240 even-weight sacks of 150 lb. each at 80 cents a bushel. What did he receive for the carload? (1 bu. potatoes =60 lb.) 7. The buyer paid freight at the rate of 27 cents per hundred pounds. What was the freight bill? ^Any fraction of a month counts as a whole month in computing storage. 94 SEVENTH YEAR 8. James Condon of New Jersey had 186 bbl. of sweet potatoes which he wished to sell. He wired his broker in Detroit, Mich., to sell them to the best advantage. The broker was offered $3.25 per bbL F. O. B. loading point. This, Condon accepted. How much did Condon receive for the carload of potatoes? 9. How much must he send his broker at 15^ per bbl. brokerage? 10. What were Condon's net proceeds on the sale? 11. A woman canvasser sells an improved kitchen utensil on a commission of 15%. What must be the amount of the sales to pay her $30.00? 12. An administrator for an estate of $750,000 gave a bond for double that amount. . The premium of the bond was $1185. The agent securing the bond received a conmiission of 15% of the premium. What was his commission? 13. A firm bought 42,070 lb. of onions in 111. at 75ji per bu. of 57 lb. and sold them in Michigan at 95|i per bu. of 54 lb. They paid freight at the rate of 7^5 per 100 lb. How much was the firm's actual gain on the onions? 14. If a travelling salesman receives a commission of 10% on his sales, what will be the amount of his commission if his yearly sales amount to $25,000? 15. A real estate agent sells a building for $15,500, receiving a commission of 3%. What does he receive for his services? 16. A collector remits to his customer $114 after deducting a commission of 5%. How much did he collect? 17. A produce broker received $309 to invest in potatoes at 60^ per bushel, on a commission of 3%. How many bushels <ilid he buy?^ ^First find the cost of each bu. of potatoes, including tha nnmraimiion. APPLICATIONS OF PERCENTAGE— TAXES 95 18. A fanner placed 2000 bu. of new com in crib in Novem- ber, 1915, to be sold by a commission firm when the price reached 85^ per bu. This com was sold at that price in June, 1916. The shrinkage on the com was 12%. The commission was 6%. Find the amount of the commission. 19. A real estate agent sold a farm for $20,000, receiving for his services, from the owner,, a commission of 2%. What was the amount of his conmiission? 20. A real estate agent purchased a farm for a customer, and added to the price 5% commission. His bill was what per cent of the price he paid? The bill was for $10,500. What was the price paid? 21. Having deducted $5.00 for expenses, and $45.50 for commission at 5%, a conmiission merchant forwarded to his principal the remainder of the cash received for a consignment of farm products. What amount was remitted to the con- signor? 22. A broker receives $4010 t^o be invested in wheat at $1.00 per bushel, his commission being j% for making the purchase. What will his customer pay for each bushel so purchased? How many bushels can be purchased for the amount stated? TAXES The state, the county, the city and the school district must have funds to pay the expenses of the officers and laborers who render services to those divisions of government. 1. What are some of the services that the officers of the €ity perform for the people in that city? 2. What benefits do the inhabitants of a school district get from the funds spent for school purposes? 8. How do the state and county governments serve the people? 96 SEVENTH YEAR The funds necessary for carrying on the government of the state and various local divisions are usually raised by taxing the people on the amount of property which they own. Property is divided into two classes: (1) real estate, includ- ing lands and buildings; and (2) personal property, consisting of movable possessions such as clothing and jewelry, household furnishings, domestic animals,- and farm products, the merchan- dise and productions of stores and shops, machines and engines, vehicles, mortgages and notes, stocks and bonds, money, etc. Officers, generally called assessors, determine the value of the property. Then the proper officers of each local division of government estimate the amount of money that they will need to carry an the government of their division for the next year. This levy is turned in to some county or state officer who divides the levy by the assessed valuation of the property to find the rate of taxation for each local division. Collectors then collect the proper amount from each person according to the amount of his property. The following table gives an illustration of the manner in which the various rates of taxation are computed: HOW THE TAX RATES ARE COMPUTED Division of Government Levy Assessed Valua- tion of Property* Rate of Taxa- tion = Levy -r- Assessed Val. State $19,994,495.11 198,703.42 1,500.00 4,000.00 14,259.27 $2,499,311,888 42,277,324 1,228,410 295,443 534,055 .0080 .0047 .0012+ .0135-f .0267+ Countv Town Citv School District Tntal Rate of Ti axfttion , . . .0641 + ^Assessed valuation of the property in this state is taken as | of the bual value. Systems of taxation vary in different states. APPLICATIONS OF PERCENTAGE— TAXES 97 Exercise 9 1. What would be a man's taxes who lived in all these divisions if his property was assessed for $15^350? Compute the amount of tax in each local division and then find the total. Why must a ooUector compute these yarioua amounts separately? 2. What is the rate of taxation in your county for county purposes? In your state for state purposes? In your school district for school purposes? Appoint some one in the class to get this information from the collector, the county derk, or consult a tax receipt. 8. If property is taxed at the rate of 15.50 per $1000, what is the per cent of taxation? How many mills is that on the dollar? 4. In a certain village the assessed valuation of the property is, in round numbers, $300,000. The amount of tax needed for canying on the government is $5000. What will be the rate of taxation for village purposes? 5. A school board estimates that the expenses of running their school will be $4500 and make a levy for that amount. If the assessed valuation of the property in the district is $350,000, what will be the rate of the school tax? 6. The assessed valuation of a tract of land adjoining a city is valued at $15,000 and the present rate of taxation is 1.5%. If the land is annexed to the city in which the rate of taxation is 2.5%, what will be the increase in the taxes of the owner of the land? What benefits will he receive for the extra taxes that he pays? 7. If 'the assessed value of the property in a certain county is $18,596,482 and the total taxes levied upon it for state and local piuposes is $650,876.87, what is the total rate of taxation? B. In a certain township (town) a tax of $20,000 is to be 98 SEVENTH YEAR raised. If there are 500 citizens to pay a poll tax of $1 each, how much of the tax must be laid on property? A poU tax is a small tax levied on males without regard to their property. "Poll" means head; that is, the tax is so much a head. Poll taxes are being abolished in many places. Find whether your community still has a poll tax. 9. A man has $1200 loaned out at 6% interest. He is assessed on ^ the amount of his loan and the rate of taxation is 4 J%. How much will be his net returns each year on the loan after he pays his taxes? 10. In a village containing propeity assessed at $200,000, the rate of taxation is 3%. If a poll tax of $2 can be collected from 800 citizens, how much can the assessed rate of taxation be reduced? 11. A village levied $4800 in taxes on property valued at $600,000. Find the rate of taxation. SPECIAL ASSESSMENTS If a city wishes to pave a street, it assesses the cost upon the owners of the adjoining property because the pavement will add to the value of the property. The city usually pays for the pavement of the intersections of the street. Such assess- ments are called special assessments. Drainage ditches are also paid for in special assessments, the amount of the tax depending upon the distance from the ditch. The owners of land adjoining the ditch are benefited most and hence must pay the highest tax. If the object of the special assessment is equally beneficial to all the inhabitants of the city, such as parks and libraries, the special taxes are levied upon all the property in the city. Find an example of a special assessment that has been levied in your community. How was the tax assessed? Make five problems out of the information you secure on this special assessment. APPLICATIONS OF PERCENTAGE— ASSESSMENTS 99 PROBLEMS 1. If the assessment valuation for a certain city is $1,800,000 and there is to be raised for a special purpose $48,000, what will be the rate of taxation required for this purpose? 2. What will this add to the tax of a resident who owns property assessed at 16000? 3. A drainage district was formed for reclaiming some of the low land along the Illinois River. The area drained was 1280 acres. The cost of the work was $25,600. What was the assessment on each acre if the amount was equally distributed? 4. The streets of a city are being paved at a cost of $1.20 per sq. yd. The width of the paving is 30 feet. The cost of the curbing is 60^ per running foot. How much will be the tax on a man with a frontage of 50 feet if he is required to pay for the pavement to the middle of the street? 6. What will be the assessment on the owner of a comer lot in the same city if his lot is 150 ft. long an^d 45 feet wide? The city pays for the intersections of the streets. EXPENSES OF THE NATIONAL GOVERNMENT The principal items in the yearly expenses of the national government in a recent year were as follows: EXPENSES Post Office $311,728,452.70 Army 164,635,576.67 Navy 155,029,425.78 Pensions 159,302,351.20 Miscellaneous 198,538,737.91 Money must be raised by our national government to meet these expenses. The main sources from which the national government derives its income are: 100 SEVENTH YEAR INCOME Post Office $312,057,688.83 Customs Duties 213,185,845.63 Internal Revenue 387,764,776.17 Income Tax. 132,937,252.61 Miscellaneous 51,889,016.28 ' The postal revenues practically balance the postal expenses. The sums above show a profit of $329,236.07 in that depart- ment for the year 1916. CUSTOMS DUTIES « Congress has the authority to fix duties on imports. They pass a law enumerating various schedules or classes of articles and give the duty on each item in a schedule. Such a law is called a tariff. Since tarififs are frequently discussed in political campaigns, you, as future voters, should understand how a duty is levied and its efifect upon prices in this country. Suppose that it costs $1.00 per yard to make a certain grade of cloth in Europe. If the duty on this kind of goods is 35% of the value of the cloth, the duty will amount to 35 cents per yard. Since the importer can not afiford to lose this duty of 35 cents, he must sell his cloth in the United States for at least $1.35 per yard. 1. Suppose on the other hand that it costs $1.35 to manu- facture the same grade of cloth in the United States. Caii our factories compete with the European goods after the importers pay the tax of 35%? 2. Could our factories compete with the European mahu- facturer of that grade of cloth if he only had to pay a duty of 20%? 3. Could the importer compete with our factories if he had to pay a duty of 60% on the cloth? APPLICATIONS OF PERCENTAGE— REVENUE 101 Since a duty of 36% in the above illustration protects our factories against the lower prices of imported goods from Europe, it is said to be a protective duty. The principal discussions in political campaigns have been over raising, lowering or main- taining the tariff duties then in force. In 1916, Congress passed a law creating a tariff commission to consist of representatives from the leading political parties of our country. This commission is to determine accurately the costs of production of various articles in the United States and in foreign countries and to report this information to Con- gress. This should enable Congress to form a much better list of tariff schedules than it has done in the past. Not all imports are taxed. There are some necessities that we want to encourage people to ship to this country and we allow them to come in free. Among the articles on the /r66 list are agricultural implements, bibles, coffee, com, cotton, hides, meats, potatoes, salt, wool, milk and cream. Tariff duties are of two kinds, ad valorem, and specific. Ad yalorem duties are those levied against the valiie of the goods imported. Specific duties are duties based upon the number, weight, etc. For example, if a duty on dress goods is 30% of the value of the goods, such a duty is said to be an od valorem duty. If the duty is 5 cents per pound, the duty is said to be specific. Ad valorem duties are more difficult to levy than specific duties because the goverment must keep experts who can accurately judge the quality of the various kinds of goods. Specific ciuties on the other hand are easily levied because the quantity expressed in yards, pounds, gallons, etc., has merely to be measured. Specific duties, however, have the disadvantage of putting the heaviest burden on the cheaper grades of goods. K the duties are too high, foreign goods will not be imported and there will be a decrease in the amount of revenue obtained from customs duties. 102 SEVENTH YEAR Among the many duties of the Tariff Act of 1913 are the following: Article Schedule Duty Ink Powders A 15% ad valorem. Window Glass B Ic per lb. between 154 and 384 sq. in. Automobiles C Over $2000—45% ad valorem. Less than $2000—30% ad valorem. Mahogany Lumber D 10% ad valorem in rough boards. Horses G 10% ad valorem. Beans G 25c per bu. of 60 lb. Cotton Stockings . . I Value up to 70c per doz., 30% ad valorem. More than $1.20 per doz., 50% ad valorem. Wool Clothing K 35% ad valorem. Silk Clothing L 50% ad valorem. Writing Paper M 25% ad valorem. Firecrackers N 6c per lb. Roman Candles — N 10c per lb. Cut Diamonds .... N 20% ad valorem. Typewriters Free List No duty. Potatoes Free List No duty. Tell which of the above duties are ad valorem and which are specific. Goods are classed under different schedules. For instance. Schedule A includes chemicals, oils, and paints; Schedule G includes agricultural products and provisions, etc. Similar articles are grouped together in the same schedule. The letters of the alphabet A to N are used to designate the different schedules. Exercise 10 Use the preceding table to find the corresponding duties. 1. Find the duty on a French automobile costing $2500. APPLICATIONS OF PERCENTAGE— REVENUE 103 2* Find the duty on an imported automobile costing $1500. 8. I buy a team of work horses in Canada for $300. How much duty must I pay to bring them into this country? 4, A firm in New York buys from a firm in London the following goods: 20 reams of writing paper @ 50^ per ream; 100 lb. of firecrackers; 100 lb. of Roman Candles; 3 typewriters @ $60 each. Find the total amount of the duties on these goods. « 6. If I buy 2000 ft. of mahogany lumber in Central America at $60 per M and import it into this country, how much duty shall I have to pay? 6. A firm imports the following bill of goods: 3 dozen silk handkerchiefs @ $3.95 per dozen; 50 ready-made woUen dresses at $12 each; 6 dozen cotton stockings at $1.80 per dozen. Find the total duties on this bill of goods. 7. A jeweler imported cut diamonds to the value of $50,000. How much import duties did he pay? 8. A firm imported 10 bags of beans weighing 120 lb. each and 20 sacks of potatoes weighing 150 lb. each. Find the amount of his duty. 9. A school supply firm imported ink powder invoiced at $2500 in Liverpool, England. How much duty did they pay on this bill of goods? 10. A glass firm imports window glass in sizes from 154 sq. in. to 384 sq. in. If the glass weighed 1000 lb., how much duty did they pay on the shipment? INTERNAL REVENUE Another important source of revenue for the government is the income from internal duties or excises which are levied on certain kinds of manufactured products in this country, such as distilled liquors, tobacco goods and substitutes for butter. 104 SEVENTH YEAR When extra revenue is needed, special stamp taxes are often levied upon certain drugs, notes, bills of lading, telegrams and certain legal papers. Internal duties as well as import duties are usually added to the cost of the article and the consumer really pays the tax. Since the consumer does not pay these duties directly to the government, excises and import duties are often called indirect taxes. 1. In 1908 the receipts of the national government from internal revenue amounted to $251,711,126.70. The expense of collecting this sum was $4,650,049.89. What per cent of the receipts was paid for the collection of the internal revenue? INCOME TAXES The income tax which the national government collects upon net inarmed over a certain amount is a direct tax.^ Single persons whose net incomes exceed $3000 and married persons whose incomes exceed $4000 are required to make out a schedule for the national government showing the amqunts of their respective incomes. In computing the net income a person is allowed to deduct from the gross income the expenses of conducting the business. Living expenses can not be deducted in computing a person's net income. If a person returns a false amount for his net income, heavy penalties are imposed upon him if he is detected. 1. Why should incomes of less than $3000 (or $4000 for married persons) be exempt (or excused) from the income tax? 2. Why should a married man have a larger sum for exemp- tion than a single man? Since a man with an extremely large income is regarded as ^The sixteenth amendment to the Constitution of the United States adopted in 1913 gave Congress the authority to levy an income tax. APPLICATIONS OF PERCENTAGE— INCOME TAX 105 * better able to pay toward the support of the government than one with a small income, the large incomes are taxed at a higher rate. This extra amount is called a surtax. The following table shows the amounts and rates of the graduated income tax in force Jan. 1, 1917: AMOUNTS AND RATES OF THE INCOME TAX Amount of Net Income Rate of Tax All of Net Income less $3000 or $4000 2% 1% additional 2% 3% 4% 5% 6% 7% 8% 9% 10% 11% 12% 13% $20,000 to $40,000 $40,000 to $60,000 $60,000 to $80,000 $80,000 to $100,000 $100,000 to $150,000 $150,000 to $200,000 $200,000 to $250,000 $250,000 to $300,000 $300,000 to $500,000 $500,000 to $1,000,000 $1,000,000 to $1,500,000 $1,500,000 to $2,000,000 Excess over $2.000.000 Exercise 11 1. A married man has an income of $100,000 per year. Find the amount of his income tax. $100,000 - $4000 = $96,000. 2% of $96,000, the normal tax $1920 1% on income from $20,000 to $40,000 200 2% on income from $40,000 to $60,000 400 3% on income from $60,000 to $80,000 600 4% on income from $80,000 to $96,000 640 Total amount of Income Tax $3760 106 SEVENTH YEAR 2. The net income of a certain married man is $10,000 per year. Find his income tax. 3. The yeariy income of a single woman is reported in her tax schedule as $9327. How much will be her tax? 4. What will be the income tax of an unmarried man who has an income of $22,500? 6. Find the income tax on an income of $8000 if the ex- emption is $4000. 6. The income of a certain wealthy financier is $8,753,200. Find his income tax. (Married man^s exemption.) 7. Find the income tax on a single woman's income amount- ing to $276,450 per year. 8. Find a married man's income tax on a net yearly income of $72,350. 9. A certain wealthy man's net income amounts to $1,150,000 per year. He is married. Find his income tax. 10. Find the income tax for a single person whose net yearly income is scheduled at $23,480. 11. Why should a person with a large income pay a higher rate on the amounts above a certain sum? INSURANCE Insurance is a contract whereby, for a certain payment called a premium, a company guarantees an individual or firm against loss from certain perils. The contract is stated in a document called a policy. Instead of one person carrying all the risk on his life or property, insurance distributes the risk over a large number of persons so that no one person has to bear an extremely heavy loss. The most common forms of insurance are: APPLICATIONS OF PERCENTAGE— INSURANCE 107 Fire Insurance insures against loss from injury to property, or destruction of it, by fire. Life Insurance insures a person against loss through the death of another. Accident Insurance insures a person against disability caused by an accidental injury to him; and in case of his death from the injury received, it insures an indemnity to a specified beneficiary. CasuaUy Insurance, of various kinds, insures against loss resulting from accidental injury to property, such as live stock, plate glass, etc. Fidelity Insurance insures against loss arising from the default or dishonesty of public officers, or of clerks or agents in the employ of the insured. Marine Insurance insures against loss by injury to, or dis- appearance of, ships, cargoes, or freight, by perils of the sea. FIRE INSURANCE In order to prevent insurance from having the nature of a betting or gambling contract, an agent is not supposed to insure property for its full value against loss by fire. The person whose property is insured must bear a portion of the risk himself. • The rate of the premium is generally stated at so much per hundred dollars and varies according to conditions such as the kind of fire department, nearness to other buildings, con- struction of the building, etc. Most firms insure property for three years at two and a half times the yearly rate. Insurance on furniture is strictly construed in accordance with the exact terms of the policy. If the furniture is removed at all without express permission from the building in which it is insured, the insurance fails. 108 SEVENTH YEAR Exercise 12 1. If I deem my house worth $5000, and desire to insure it for one year for three-fifths of its value, what must I pay for the policy when it costs $7.50 for each $1000 of insurance taken? 2. A farmhouse and bam and other buildings pertaining to them, valued at $15,000, are insured for one year for two- thirds of their value, at 75 cents for each hundred dollars of • insurance. What is the cost of the policy? 3. If the furniture in my cottage is worth $1000, and I wish to insure it for 60% of its value, having to pay $1.66f for each hundred dollars of insurance, what will the policy cost, me? 4. A church pays, in all, $180 yearly, for insurance to the amount of $10,000, in each of three separate companies, the rate of insurance being the same in each company. What is the rate of insurance? If my house, insured for $4000, is destroyed and I am unable to prove that it was really worth over $2000, I can recover from the insurance company no more than the latter amount. 6. If when insured against fire for $5000 it was destroyed, and I can prove its value only to the amount of 60% of this sum, what amount of compensation do I receive? To insure a house for three years at a time, one has to pay two and one half times the rate for a single year. 6. My insurance for a three-year period is $31.25. What would have been my insurance for a single year? By insuring a house for five years at a time, one has to pay four times the rate for a single year. 7. If a man pays $200 for the five-year period, what would the insurance cost him for a single year? For a period of three years? For five separate periods of one year each? APPLICATIONS OF PERCENTAGE— INSURANCE 109 8. If I have furniture insured for $1200, temporarily stored in an outbuilding which is not mentioned in my policy, and the outbuilding and furniture are destroyed by fire, what amount can I recover on my loss ot furniture? 9. A rug worth $150 is hung out in the yard to air, uid is ruined by sparks from a passii^ fire engine. If it formed a part of the household furniture that is insured for $1000, can the owner recover its value from the insurance company? 10. What could be recovered if it had been thus destroyed while hui^ on a line on a porch of the residence? 11. A dozen books supposed to be rare and valuable are insured for $1200. They are destroyed by fire, and it is then proved that they were recently manufactured, and of no greater possible value than $3 apiece. What is the limit of indemnity that the company should pay for them? Insurance Applied Mr. Manning owned a suburban lot on which he contracted with a house construction company to build a home at a total cost of $4500. On the completion of the new home, Mr. Manning, rec- ognizing the importance of proper protection to his family, took out an insurance policy on the house. Exercise 13 1. An insurance company insured the house for 80% of its cost. Find the amount of his policy. 110 SEVENTH YEAR 2. Why will an insurance company not insure a house at its full value? 3. The rate of insurance on this house was 72 cents per $100 for a "three-year period." What was the cost of the insurance per year? 4. Mr. Manning made out an inventory of his household goods and estimated them to be worth $950. He decided to take out $800 on his household goods. Why was it a good plan to make out an inventory of the goods before insuring? What should be done with this inventory? 6. The rate of insurance on his household goods was 79 cents per $100 for three years. Find the amount of the premium on the household goods. LIFE INSURANCE There are two principal kinds of life insurance companies: the "oW Ztne" companies and the mutual companies. The old line companies have worked out definite rates for diflferent ages and the premium for each year is definitely stated in the policy. The mutual companies usually levy an assessment at certain intervals, generally each month, to pay the death claims. The '^oZd Zt'ne" companies usually have several kinds of policies such as 15-payment life; 20-payment life; endowment policies; ordinary life policies. In the 15-payment life policy, the person insured makes fifteen yearly payments at the end of which his insurance is paid for the rest of his life. The 20-payinent life, as the title indicates, is paid for at the end of 20 yearly payments. An endowment policy usually requires a larger premium and if the insured person lives to the end of the period named in the policy he can draw out the amount of the policy. In an ordinary life policy a definite yearly payment is required each year until the person dies. All of these forms usually APPLICATIONS OF PERCENTAGE— INSURANCE 111 have a cash surrender value which will be paid the insured person upon the surrender of the policy. Most policies also have a table showing the amount of money which the company will loan on a policy. Since the risk of the death of a person increases with age, the premium increases each year. It is therefore an advantage to take out insurance as early as possible. The age nearest the birthday of the person insured is the age considered. A medical examination is aiso required to protect the company from undesirable risks. Premiums per $1000 Age Ordinary Life • 20-Payment Life 20- Year Endowment 20 $19.21 $29.39 $48.48 21 19.62 29.84 48.63 23 20.51 30.80 48.96 25 21.49 31.83 49.33 27 22.56 32.94 49.73 30 24.38 34.76 50.43 35 28.11 38.34 51.91 40 33.01 42.79 54.06 45 39.55 48.52 57.34 50 48.48 56.17 62.55 Exercise 14 1. At the age of 21, a man insured his life for $2000 on what is called the ordinary life plan, for an annual payment of $39.24. What does he pay in fifteen years? 2. Had he deferred the insurance for five years, it would have cost him $44.10 for each year. How much more would this have been than the amount the insurance actually did cost him for the same period of ten years? 8. A man took out a IS-payment life policy for $1000 at the age of 30 at $40.25 for each annual payment. What was 112 SEVENTH YEAR the total amount of his fifteen payments? How can the com- pany afford to insure him at an amoimt which will yield less than the face of the policy? 4. A man insured his life on the endowment plan for SIOOO at the age of 21, paying $48.63 annually for a 20-year period, and lived beyond the time and received the amount of the policy. What was the total amount of his payments? 5. What did the insurance company receive to pay them for taking the risk of his death during that period? 6. A .man took out a 20-payment life participating policy for $2000 at the age of 24, with a premium stated at $62.16 per year. If his dividends on the policy amounted on an average to $10 per year for 19 years, how much did the insurance cost him? A participating policy pays dividends to the holder after the first year according to the profits of the company. These dividends are usually deducted from the premium, the insured person paying the balance due the company. 7. At the end of the period, the policy had a cash surrender value of $994. If he surrendered his policy at the end of the period, how much will his insurance cost him besides the interest on his payments? ACCIDENT INSURANCE 1. A man has paid $18 for 4 years for an accident insurance policy. Owing to an accident, he is disabled for a period of 6 weeks, during which time he receives $25 a week. What has been the net financial value of the insurance to him? What has been the net loss to the insurance company? 2. A horse insured for $300 is choked to death, being ignor« antly tied with a running noose of rope for a halter about its neck. Is the owner entitled to the insurance? If by a com« promise 40% of the policy is paid, what sum does the owner receive? CHAPTER V BUSINESS FORMS AND ACCOUNTS The Memorandum or Salesman's Slip <Browri ^ Duj^dR /7/6 J9maI2 * 0.6H sold by & Drygood5 £»uf faio, KT purchase Change 2 I I P/u.Ho^ 25 Ha/ruUw\AkjULb I 00 3b 20 15 bH In buying goods at a retail store, a salesman's slip or memorandum of the purchase is usually made by the salesman or clerk. By means of carbon paper placed under the sheet on which the clerk is writing, a duplicate of the slip is made. The firm keeps one copy and gives the other copy to the customer for refer- ence. The form indicated above shows one form of such a memorandum. It shows the items of the purchase, the amount received by the clerk and the change given to the customer. This memorandum should be kept by the purchaser until he is sure that he does not wish to exchange any of the goods. If the purchase is charged, it is so indicated upon a similar memorandum containing the customer's name and address. This memorandum should be kept by the customer to check the account when the monthly statement is rendered. If printed forms of salesman's slips can be secured from local stores, it will save much time in the ruling of these forms by the pupils. 113 114 SEVENTH YEAR Exercise 1 1. I bought the following items at a grocery store; 15 lb. of potatoes for 30 cents; 2 cans of com @ 7 cents per lb. ; and 1 doz. oranges @ 40 cents. Make out the salesman's slip for the customer. 2. How much change should I receive if I tendered the clerk a two-dollar bill? 8. Mrs. Jones bought the following articles at a dry-goods : store; 6 yd. ribbon @ 18^ per yd.; 2 spools of No. 50 white thread @ 5^ per spool; 10 yards of pique (pe ka') @ 30^ per J yd.; 3 yd. of flannel @ 80^ per yd. Make out the clerk's memorandum of the sale. 4. How much change should Mrs. Jones receive from a , ten-dollar bill? 6. I bought the following household supplies at a hardware store: 1 ironing board @ $1.75; 1 pair of waffle irons @ 90^; 2 aluminum kettles @ 65^ each. Make out a salesman's slip for the sale. 6. How much change did I receive from the clerk if I ten- dered him a five-dollar bill to pay for the purchases? Make out salesman's slips for the following orders: 7. Mrs. Stevenson bought ^ doz. plates No. 4 @ $1.25; § doz. plates No. 8 @ $3.00; ^ doz. tea cups and saucers @ $3.00 and ^ doz. sauce dishes at $1.90. 8. Miss Dillon purchased the following articles: 1 whisk broom @ 35 cents; 1 vanity case @ 50 cents; 1 set of cups @ $2.00; and 1 shoe horn @ 50 cents. 9. What are some of the advantages of using the memoran- dum or salesman's slip? 10. Make out a sales slip with prices of articles which you purchased at a store. BUSINESS FORMS AND ACCOUNTS 115 The Invoice or Bill An invoice or bill is a more formal accomit of a transaction than a salesman's memorandum. Invoices are sent to a cus- tomer by a firm with each shipment of goods. The following is a modification of a form used by a large wholesale firm: This sale made subject to conditions on bacK. of invoice OMer ■ 83s;6 j^j^ ^ Company, vuat, Kansas City^ Mo. Soid by AJ«.Grlgg9 QulBCY. 111. Tem\S 2% - 10 days Invoiced J M. 3, ChecKed j.c.t. <Soht to ij^i^jiat J«B. L 11 4 Pet. Hnt HAMI* 4 ** Bacon A/6§ (uBvrpd) 4 ** Cook«d Hau 5 ** Jtaliaa Stylt Haaw 54 15 48 35 ^7 .23 .23 .24 ■ «■ • ••• *The abbreviation 12/1 4# means from 12 to 14 pounds. In the above invoice, the number in the first colmim at the right of the descriptions of the articles shows the number of pounds. The corresponding numbers in the next column give the cost per pound. Multiply the cost per pound by the number of pounds and enter the result in the next column which contains the totals for each article. Exercise 2 1. Extend the invoice shown above, filling in the sums as shown by the dots. 2. Find the net amount of the bill if it is paid within 10 days. (Terms 2% — 10 days, means that 2% discoimt will be allowed if the bill is paid within 10 dayo.) 116 SEVENTH YEAR Extend the following invoices. You may omit the headings but make a drawing for the rest of the invoice form: 8. 2 10# Carton Regular Frankforts 2 Pieces CJooked Pork Loin 10 Pieces Fresh Ox Tails 2 Pieces Bacon 5 to 8# 4. 1 Piece Fresh Beef Round 3 Pieces Fresh Pork Loins 10 Pieces Fresh Spare Ribs 15 Pieces Fresh Pigs Feet 1 Piece Cooked Ham 6. 1 Piece Fresh Beef Ribs 20 Pieces Fresh Spare Rib 1 Piece Fresh Pork Loin 2 Pieces Cooked Hams l-26# Plain Fresh Pork Sausage 6. 1 Fresh Side Beef 8 Fresh Beef Shanks 2 Jelly L. Tongue 2 Boxes Frankforts 2(^ Polish Sausage . Make out bills for the following goods, using fictitious names for the firm and the purchaser: 7. 1 parlor lamp @ $2.95; 3 glass candlesticks @ 29f&; 1 chafing dishy $7.50; 2 brass jardinieres at $1.75; 2 vases at $3.00; 2 cut glass salt cellars at 95ff. 8. 2 granite stew pans @ 39^; 2 muffin pans @ 27i] 1 can opener @ 10^; 2 aluminum measuring cups @ lOfi; 2 pair scissors @ 75ff ; 2 butcher knives @ 50fi; 1 electric iron @ $3.79. 9. 1 pair slippers @ $2.00; 1 pah- rubbers @ $1.25; 2 bottles gilt-edge polish @ 2bi\ 3 pairs shoe strings @ lOfi; 1 pair ladies' shoes $5.50. 20 13* 8 31 10 8 11 25 93 14^ 19 16 10 12^ 15 5 13 29 86 13| 10 12^ 14 15§ 27 28 25 15 179 8 11 7 11 27i 20 12* 20 11 BUSINESS FORMS AND ACCOUNTS 117 The Monthly Statement When salesman's slips oi bills are rendered with orders, the customer is supposed to keep these forms with the various items shown on them in order to check the monthly statement which is sent at the end of each month. The following is one form of a monthly statement that is used: When the customer so desu-es, an itemized statement will be ren- dered, but this makes a great deal of extra work for the firm and is un- necessary if the customer keeps his slips or bills to check the totals listed under the various dates of the monthly statement. Statement '•»»». i. im. In AccomtrWrn tIS.CLAKKE Mfm^mciijWis. Mr*. R»rY«y Buchuian Aug. 1 4 5 14 19 U 30 OroMri** 1 2 3 2 1 3 37 69 46 76 95 30 25 19 42 Exercise 3 1. Make out a monthly statement to Mrs. F. R. Fitzgerald from Adams Bros., Grocers, for the following grocery orders, showing only the totals for each day: Aug. 1 — 2 loaves of bread @ lOff; 2 pounds prunes @ 20^5; 10 pounds sugar @ Ti. Aug. 3 — 1 pound cheese @ 36j!f; § dozen lemons @ 30ji5; 1 peck potatoes Zbi. Aug. 4 — 2 cans com @ 18ff; 1 basket tomatoes @ 25ff. Aug. 9 — Celery lOff; 1 head lettuce lOff; 1 package rolled oats @ lOi. Aug. 12 — 10 bars of soap for 42^5; 1 basket tomatoes 19^; 1 sack flour 95f(. Aug. 17 — 10 pounds sugar @ 7^i; 2 dozen eggs @ 33ff; 2 pounds butter @ 36ff. 118 SEVENTH YEAR Aug. 20 — 1 peck potatoes SQ^; 2 packages crackers @ 10<5; 1 sack salt 10)i(. Aug. 23 — 3 quarts peas for 25f!!; 1 package puffed rice 16^; 10 pounds apples @ 5^, Aug. 30 — 1 jar olives 35^; 2 pounds navy beans @ 12|!f; 5 pounds rice for 39^5. 2. Make out an itemized statement of the same account, showing each of the items and the total for each day. 3, Make out a series of purchases from a dry-goods store during some month and render a monthly statement for them. Receipts When a sum of money is paid on an account, the customer should receive a receipt, showing the date and amount paid as in the following form: GALVESTON, TEXAS, J[jJiU5^9\ 7 ofj^/nj amd/ ^ , ^^ Dollars If the full amount of the account is paid instead of a portion of it, the words "in /uK o/ account to daie^' would be used in place of the expression "on account.'^ If an account is paid by a check, the check stands as a suffi- cient receipt for the payment. For this reason, many persons pay all their accounts by checks. This saves the firm the trouble of making out extra receipts or returning the receipted bill to the customer, because the cancelled checks are returned by the bank with their monthly statement. BUSINESS FORMS AND ACCOUNTS 119 Exercise 4 1. R. A. Milton owes Schneider & Co. S30.25 for hardware supplies. He pays them $25.00 to apply on his account. Write a proper receipt for this payment. 2. J. R. Kennedy pays Dr. L. J. Hammers, $15.75 as payment in full for his professional services. Write a receipt for the settlement of this account. 3. Write a receipt for Hogan Bros, to Mrs. J. C. Veeder for a settlement in full of her account of $11.75. 4. Write a receipt for Adams Bros, to Mrs. F. R. Fitzgerald for a settlement in full of the account shown on page 117. 5. Write a receipt for some actual payment in which you have been the receiver of the money or have paid a sum of money to some other person. 6. I ordered a suit from a tailor. He required a deposit of $10.00 and gave me a receipt for this amount, in part payment for the suit. Write such a receipt for a tailor. 7. Write a receipt to a plumber from his employer for $15.00 in payment for 20 hours' work at 75 cents per hour. The Cash Account Most methodical people, whether engaged in active business or not, keep a cash account of their receipts and expenditures. The cashbook represents the owner's pocketbook or cash drawer. "Cash'' is treated as a real person. It is debited, or charged with all money received; and is credited with all moneys paid out. Two pages are usually used for a cash account, the left hand page being used for the debits and the right hand page being used for the credits. The '^Balance^' or difference between the amounts of the two pages will be the cash on hand. The first entry on each debtor page is the amount of cash on hand. 120 SEVENTH YEAR Debit Side of a Boy's Cash Accoont Nov. 1 Balance on haxsd M 3 Errand M 4 Assisting in Groeary stora N U m n H N M 18 •t N M M 1 I 1 90 25 50 50 50 10 65 Credit Side of the Same Boy's Cash Account NOT, M n N M 6 10 17 21 30 School Supplies Sweater Vast School JSntertainment Book To£a/dnce 2 6 45 50 25 50 95 • 10 65 At the end of each month a cash account is "balanced'' as shown in the above account. This account shows the boy to have a balance on hand of $6.95 on Nov. 30, because it takes that amount to make the credit side of the account "balance'* the debit side. Exercise 6. Prepare a cash account for this boy during December, starting with the cash on hand as shown in the preceding account and entering the following items on the proper side of the account. 1. Dec. 2, Bought a necktie 60^; Dec. 2, Received $1.50 for working in the grocery store; Dec. 5, Received from sale of old books $1.15; Dec. 9, Received from the grocery store $1.50 for services; Dec. 14, Bought Christmas present for mother $2.50; Dec. 15, Received for assistance at opera house $1.25; Dec. 16, Wages from store $1.50; Dec. 19, For Christmas presents bought $3.85; Dec. 23, Wages from store $1.50; Dec. 25, Received as present from mother and father $10.00 in cash; Dec. 30, Wages from store $1.60. BUSINESS FORMS AND ACCOUNTS 121 2. Balance the account on Dec. 31 and enter the proper amount under ''To balance" on the credit side of the account. 8. What would be the first item of this boy's account for January, 1917? The Daybook or Journal When goods are sold on credit, the merchant enters the sales, as they occur, in an account book called the Daybook, or Journal, stating the separate items and the price of each. A single page of such an account book may contain business transactions with various persons. Where memorandum slips are kept, many firms do not keep a day book but keep these slips as a record of the daily transac- tions. These memorandum slips are filed in some systematic way, each customer's slips being kept together. The following illustration shows a typical page of the journal of a men's clothing store: 135. 1916. Nov. 7 William Smith, Dr. To 3 pairs socks @ .25 75 To 1 shirt 1 50 To 1 necktie 50 To 4 collars @ .15 60 To 1 pair suspenders 1 00 Nov. 7 R. P. Jones, Dr. To 3 handkerchiefs @ .20 60 To 2 union suits @ 1.50 3 00 To 2 collar buttons @ .10 20 Nov. 7 John F. Brown, Cr. By cash Nov. 7 L. B. Strayer To 1 hat 4 35 3 80 7 50 4 60 122 SEVENTH YEAR It will be seen that the preposition to is used with debits and by with credits. The abbreviation Dr. is used for debtor and means that Wm. Smith and R. P. Jones are debtors to the firm for the goods which they have purchased. The abbre- viation Cr. is used for creditor and means that John F. Brown is to be given credit on his account for the cash which he has paid. Exercise 6 Prepare a page of a day book containing the following transactions for Nov. 2: 1. Sold J. R. Stock 1 pair of shoes at $5.00; 1 box of Hole- proof hose at $1.50; 2 collars at 15 cents each; and a shirt for $2.00. 2. Received a cash payment from Wm. Smith for $7.50 to apply on his account. 3. Sold Mrs. J. F. Doan 1 pair shoes at $6.00; 1 box of Shinola at 10 cents; and 2 handkerchiefs at 35 cents each. 4. Add other accounts that a general dry-goods and shoe store would have. Fill out the page in this way. Personal Accounts In a book called a ledger a page or portion of a page is devoted to transactions with a single person. These accounts then are called personal accounts and it is from these accounts that the monthly statements are prepared. These accounts are "posted" by a bookkeeper from the memorandum slips or daybook. The account may be itemized or the totals only may be entered for each day^s purchase. A page of a ledger containing a personal account is divided^ into two parts. A person^s indebtedness to the firm is shown on the left or debtor side of the page; and his payments are BUSINESS PX)RMS AND ACCOUNTS 123 shown on the right or creditor side. This account is usually balanced once a month. Here is an account on the page of a ledger • • Dr, lilliam anith Or. 1916 1916 NOT. 1 Balanec tram Oct. 7 SO NOT. 2 Caih 7 50 » 7 lldi«. 4 35 "30 ^afdnce 16 10 * 15 M 3 50 •• 29 M Sdlsnce 8 25 ^•f^r 23 60 23 60 16 10 The above personal account of William Smith shows a balance of $7.50 from his Oct. account still due the firm. He was sent a monthly statement and promptly responds on Nov. 2 with a cash payment. The account shown in the illustration of the daybook on page 121 is shown here entered on the Dr. side of Wm. Smith's account as indicated in the daybook. On Dec. 1, Wm. Smith will be sent a statement of his account, showing a balance due of $16.10. Exercise 7 1. Prepare a similar personal account for December for Wm. Smith using imaginary amounts ajid balancing his account on Dec. 31. 2. Prepare a personal account for R. P. Jones, including as one of the items, the account shown in the daybook on page 121. Use imaginary accounts for the rest of his account. 8. Prepare a personal account for F. W. Trowbridge from the following items found in the daybook: Balance due Nov. 1, as shown in ledger, $8.75; Nov. 3 paid cash, $8.75; Nov. 5 bought a hat at $4.00 and a tie for 76 cents; Nov. 9 bought 1 box of hose at $1.50; Nov. 15 bought a suit for $27.50; Nov. 26 bought a pair of shoes for $6.00; Nov. 29 paid cash, $30 00. 124 SEVENTH YEAR 4. Prepare a personal account of a farmer with a hardware and implement company, inserting items that a farmer buys at such a store. 5. Prepare a personal account of a woman at a druggist's, showing purchases of various medicines, spices, and other supplies which a drug store in your community keeps. The Inventory An inventory consists of a list of articles on hand at the time the inventory is taken together with a statement of the value of the various articles. An inventory is a necessity for a firm in estimating the amount of gain or loss in their business. Inventory of a School Recitation Room Furniture: 1 teacher's desk $15. 00 25 single desks at 3.50 87.50 2 chairs at 2.00 4.00 1 filing cabinet 20.00 1 desk book rack 1 . 25 Supplies: 2 sets practice exercises in arithmetic $19.20 1 ream white practice paper 48 1 hektograph (2 faces) 2 . 50 3 arithmetic texts (Chadsey-Smith) 1 . 35 2 boxes crayon at 20 cents .40 Pictures and Flowers: 2 window boxes of ferns at 5.00 $10. 00 1 picture 10. 00 Total value, BUSINESS FORMS AND ACCOUNTS 125 When there has been a loss of household goods by fire, msurance companies usually demand that an inventory be made of the goods destroyed by fire. It is therefore a good policy to make out an inventory of your household goods at the cost price and keep it in a safe place for reference in case of the destruction of your goods by fire. Exercise 8 1. With the help of the teacher and a supply catalogue, make out an inventory of the supplies and furniture in your school room. This may be presented to the school board for reference in case of fire. 2.. Make an inventory of the furniture and furnishings in your home, estimating the goods at cost and give this to your parents to deposit in the safety deposit box in the bank for reference if it were needed in making out an inventory in case of fire. 3. If your father is on a farm or in a business in the city, assist him in making out an inventory for his supplies that he has on hand. 4. Make an inventory of your own school supplies. The Pay Roll In factories, stores, and offices where the employees are paid by the hour, there must be some system for keeping a record of then- tune. Some firms employ a card system on which each employee has his time checked when he begins and leaves. Others use a system of checks, the worker taking out his check When he begins and returning it when he leaves. Some employers have an electric clock with various numbers, each laborer punching his number on entering and also on leav- ing. The record is made on a revolving sheet of paper on the proper time space. 126 SEVENTH YEAR The following form is a simple arrangement for making out the pay roll: No. N» l!en. Tues. Wed. Thur*. Tri, Snt. Total Tina Rata pap hp. ilpount DM 1. A. Bro«B 8 8 10 49 85# n2.2s 2. R. Jor.«ii 8 8 9 51 25^ 12.75 3. J . Schridt 8 9 9 35^ 4. F. J«in»«n 9 8 9 35^ 5. P. Gregory 8 8 10 40^ «. R. DorB«y 8 9 8 40^ •». S. Stodd»rd 9 9 10 32^ 8. V. Strlpri 9 8 9 36^ 9. N. Costal :e 8 8 8 8 30^ The amount of time is multiplied by the proper rate per hour for each employee and the various sums placed in the last column showing the amount due. From this pay roll the cashier makes out a memorandum showing the number of each kind of bills and each kind of coin in order to put the exact amount in each employee's envelope, to be handed to him at the close of the week. The following form gives one plan for the cashier's memorandum: Cashier's Memorandum No. Wdges *20 ^ ^ *2 ■jfj- 50* 25* 10* 5* 1* 1 U-:iS / / / 2 17.. 7 5 / / / / 3 4 5 6 7 8 9 TOIAL • • ? • • •? a ? • ? ? a BUSINESS FORMS AND ACCOUNTS 127 Ezerdse 9 1. Complete the rest of the pay roll as indicated in the portions already filled out. 2. Fill out the rest of the cashier's memorandum in the manner shown m the first two lines. 8. Fmd the total number of each denomination of bills and coins. 4. What is the total amount of wages due the employees? 5. From the number of bills and coins in each column, see if the cashier's memorandum checks with the total amount in wages. AGENCIES FOR SHIPPING MERCHANDISE When goods are ordered, there are three ways of shipping them to the customer: parcel post, express and freight. The customer should state, when ordering the goods, what method of shipping to use, unless he leaves that to the judgment of the firm. Parcel Post is generally cheaper for small articles. Perish- able goods such as strawberries are generally shipped by express. When the goods are bulky and immediate delivery is not essential, freight is the cheapest means of transporting them. Express and parcel post packages are generally delivered free, but freight is not. We should be informed on the relative cost and convenience of these agencies for shipping goods in order to know how to order supplies of various kinds. Parcel Post Merchandise is shipped by the post office department under a system of parcel post rates. All parcels weighing 4 ounces or less are carried at 1 cent per oimce, regardless of the distance. The rates on parcels heavier than 4 ounces vary according to the weight and the distance of the place to which the goods 128 SEVENTH YEAR are shipped. For convenience in handling the matter of dis- tance, the government has estabhshed a system of zones. Each post office has a book which classes 3ach city in our coimtry in its appropriate zone with regard to that office. The following table gives only a portion of the weights and zones under the parcel post system: HrUl Loeia ZOBM 1*2 Z«M S ZeM4 Zoo* 5 ■or* than 150 ■llM disiaat CitlM 151 to 300 BilM diataai. Cltl»a 301 to 600 BilM dletMrt. CiilM 601 tolOOOaUes dUtwi. Over 4 OS. up to 1 lb. 5# 50 60 70 80 * 1 lb. " * 2 lb. 6^ 60 80 110 140 " 2 lb. * * 3 lb. 6^ 70 100 150 200 " 3 lb. • * 4 lb. 7^ 60 120 190 260 • 4 lb. • "5 lb. 1^ 90 140 230 320 • 10 lb. * "11 lb. 1<¥ 150 260 470 680 " 15 lb. •« "16 lb. 13^ 200 360 670 980 * 19 lb. •• "20 lb. 150 240 440 830 1.22 » 25 lb. •• ••26 lb. 180 300 50 pounds 18 the limit in wei<;ht for parcels in the local lone and zones 1 and 2. 20 pounds is the limit in weight for the other lones. •• 30 lb. •• "31 lb. 200 350 » 40 lb. * "41 lb. 250 450 • 49 lb. " "90 lb. 900 540 ziones o, / and o eluded in this table on lack of space. »re ooii la- I account of Exercise 10 1. A farmer 101 miles from Chicago wishes to ship a package of butter weighing 4^ pounds to a customer in that city. Find the parcel post charges on the shipment. 2. The distance from Pittsburgh to Chicago is 492 miles. How much will it cost to send a 4-pound package from Chicago to Pittsburgh by parcel post? 3. The distance from St. Louis to New Orleans is 748 miles. How much will it cost to ship a 10^-pound package by parcel post from New Orleans to St. Louis? BUSINESS FORMS AND ACCOUNTS 129 4. The distance from Detroit to New York is 595 miles. How much will a parcel post shipment of 15 f pounds cost between those cities? 5. I wish to ship a package of merchandise weighing 4^ pounds to a city in the third zone. How much postage must 1 put on the package? 6. A man in southern Wisconsin advertised a 12-pound case of fancy comb honey for $2.60 per case, charges prepaid. How much more would it cost him to ship to a customer in the third zone than to one in the second zone? 7. A farmer agreed to supply a city customer with 2 pounds of butter per week at 32 cents per pound, the customer paying the parcel post charges. The city was in the first zone. How much will the customer save in a year if he has his butter shipped in 4§-pound packages every two weeks instead of 2 J-pound packages every week? Find the parcel post charges on the following parcel post packages: • Weight Zone Charges 8. 8 ounces Fourth ? 9. 3 pounds Fifth ? 10. 15^ pounds Third ? 11. 50 pounds Second ? 12. 20 pounds Fourth ? 13. lOf pounds Third ? 14. 5 pounds Fifth ? 16. 3^ pounds Fourth ? 16. 2 pounds Fifth ? 17. 11 pounds Third ? 18. 31 pounds Second 19. 40 pounds First ? 20. 19 f pounds Fourth ? 130 SEVENTH YEAR Express Express rates vary with the weight of the shipment and the distance between the shipping points. In computing express rates, the 'rate per hundred pounds is indicated and a scale based upon this rate is indicated. A portion of such a system of rates is shown in the table below. Rat* ptr ICO lb. n.oo «1.25 $1.40 n.so •1.70 n.-'s 12.00 «3.40 C3.85 $4.20 It»t« for 1 lb. as .26 .26 .26 .26 .26 .27 .28 .29 .29 . • 2 « .26 .27 .27 .27 .28 .28 .28 .31 .32 .33 . • 5 • .29 .30 .31 .31 .32 .32 .34 .41 .43 A5 • • 10 * .32 .35 .36 .37 .39 .40 .42 .56 .61 .64 • - 15 * .3« .40 .42 .44 .47 .47 .51 .72 .79 .84 . •• ao " .40 .45 .48 .50 .54 .55 .60 .88 .97 1.04 • - 30 • .47 .55 .59 .62 .68 .70 .77 1.19 1.3? 1.43 . - 40 * .55 .65 .71 .75 .83 .85 .95 1.51 1.69 1.83 • • 45 * .59 .70 .77 .81 .90 .92 1^ 1.67 1.87 2.03 The express rates per 100 pounds from Chicago to the cities mentioned in the following table are: St. Louis $1.40 Minneapolis 2. 00 Fort Worth 3.85 Pittsburgh 1.70 Charleston, S. C 3.40 Denver $4.20 Indianapolis 1 . 00 Columbus, Ohio 1 . 50 Nashville 1.75 Detroit 1.25 Exercise 11 1. Find the cost of an express package weighing 20 pounds from Chicago to Fort Worth, Texas. 2. How much will it cost to ship a box weighing 100 pounds by express from Chicago to Detroit? 8. What will be the express charges on a 1 0-pound package from Chicago to Denver? BUSINESS FORMS AND ACCOUNTS 131 Find the express charges on a 4. 10-poimd package from Chicago to Charleston, S. C. 6. 30 pounds from Chicago to Minneapolis. 6. 15 pounds from Chicago to Pittsburgh. 7. 45 pounds from Chicago to St. Louis. 8. 2 pounds from Chicago to Nashville. 9. 5 poimds from Chicago to Columbus, Ohio. 10* 40 pounds from Chicago to Indianapolis. 11. 30 pounds from Chicago to Fort Worth. 12. 15 pounds from Chicago to Denver. 13. Find the cost of an express package weighing 45 pounds from Chicago to Charleston, S. C. Freight Rates Railroad companies figure freight rates to the large cities and make practically the same rates to the smaller cities in the vicinity of each large city. Merchandise is divided for freight shipments into four classes. Among the various articles listed in each class are: (1) First class — ^Books, clocks, dry goods, fire arms, lamps, rugs, toys, etc. (2) Second class — Bedsteads, cream separators, extension tables, linoleum, refrigerators, wheelbarrows, etc. (3) Third class — Iron kettles, iron safes, stoves and ranges, etc. (4) Fourth class — ^Anvils, poultry food, steel roofing, stock food, plain or barbed wire, etc. The following table shows the rates per 100 pounds on the four classes of freight from Chicago to the cities mentioned: 132 SEVENTH YEAR ciir Pirtt ClM« 8«e«ad ClM» 9liT« ClM* Tmurtk ClMV St. Uuis 1.46 1.37 ♦ .«• I.3S Detroit .39 .34 .23 .17 Nashville .82 .68 .33 .43 ladianapoll* .33 .28 .23 .15 r»rt l»rth 1.67 1.41 1.16 1.06 DraT»r l.fK) 1.45 1.10 .85 'Pittsburg ' .47 .41 .32 .22 Exercise 12 1. How much would a stove weighing 675 pounds cost to ship by freight from Chicago to Indianapolis? Suggestion: Look at the description of the classes of freight to find in which class stoves are listed and then compute by the rate per 100 pounds as shown in the table. 2. A rowboat weighing 150 pounds is shipped from Chicago to St. Louis. If rowboats are classed at a rate 4 times first class, what is the freight on the rowboat? 3. A farmer living near Nashville wishes to order some barbed wire from Chicago. Find the freight which he will have to pay on a shipment of four 80-rod spools weighing 90 pounds each. 4. Find the difference in the charges by freight and express for a box of dry goods weighing 150 pounds from Chicago to Pittsburgh. When would a merchant be likely to order the goods by express rather than by freight? 6. A merchant in Detroit ordered a rug weighing 35 pounds when packed for shipment in Chicago. Find the cost of the freight on this rug. Find the freight rate per 100 pounds on the following articles from Chicago to the city named: 6. Bpoks to Denver. 8. Stock food to St. Louis. 7. Iron safes to Nashville. 9, Refrigerators to Fort Worth. 10. Clocks to Detroit. CHAPTER VI PRACTICAL MEASUREMENTS As a proper preparation for the problems in practical measure- ments a review of the following facts is essential. Refer to the tables in the back of the book to recall facts that you have forgotten. You will need these facts in solving problems in daily Ufe. Exercise 1 1. 1 yard = ? feet. 2. 1 pound = ? ounces. 8. 1 minute =? seconds. 4. 1 foot=? inches. 5. 1 square yard^? sq. ft. 6. 1 dozen =? things. 7. 1 square foot=? sq. in. 8. lton=?lb. 9. 1 long ton = ? lb. 10. 1 gallon =? cu. in. 11. 1 cubic yard = ? cu. ft. 12. 1 week=? days. 18. 1 yard =? inches. 14. 1 quire =? sheets. 15. 1 hour=? minutes. 16. 1 cubic foot=? cu. in. 17. 1 ream =? sheets. 18. 1 quart = ? pints. 19. 1 day = ? hours. 20. : lrod=?feet. 21. : I common year=? days. 22. : I leap year=? days. 28. : I mile =? feet. 24. : I peck=? quarts. 25. : I bushel =? cu. in. 26. 1 gross =? dozen. 27. 1 cord = ? cu. ft. 28. 1 gallon = ? quarts. 29. 1 bushel = ? pecks. 80. 1 niile=?rods. 81. 1 gross =? things. 82. 1 bushel = ? quarts. 38. 1 acre = ? sq. rd. 34. 1 niile = ? yards. 85. 1 cu. foot==? gal. (approx.) 36. 1 square mile = ? acres. 37. 1 square rod = ? sq. yd 88. 1 barrel = ? gallons. 133 134 SEVENTH YEAR Exercise 2. Miscellaneous Problems 1. How many dozen eggs are there in a standard crate containing 360 eggs? 2. How many square feet are there in an acre? 3. How many cubic inches are there in a quart, liquid measure? 4. How many cubic inches are there in a quart, dry measure? 5. How many inches are there in a mile? 6. The capacity of a coal car is 70,000 pounds. How many long tons of coal will it hold? 7. A pile of cord wood is 20 feet long and 6 feet high. If the sticks are 4 feet long, how many cords does the pile contain? 8. If round steak is selling at 24^ a pound, how much should a butcher charge you if the scale reads 1 lb, 12 oz.? 9. A lot is 165 feet long and 65 feet wide. Express the dimensions of the lot in rods. How many feet of fence will it take to enclose the lot? 10. A horse is 16 hands high. (A hand is 4 in.) How high is the horse? (Express height in feet and inches.) Exercise 3 Tell what the following numbers stand for: Example: 1. 36 in. =the number of inches in a yard. 2. 231 sq. in. 7. 27 cu. ft. 12. 24 sheets 17. 1728 cu. in. 3. 160 sq. rd. 8. 144 sq.m. 13. 2000 lb. 18. 7 days 4.5280 ft. 9- 16^ ft. 14. 30|sq.yd. 19. 128 cu. ft. 5. 4 qt. 10. 12 in. 16. 5^ yd. 20. 365 days 6. 2150.42 cu. in. 11. 320 rd. 16. 9 sq. ft. 21. 1760 yd. PRACTICAL MEASUREMENTS— ANGLES 135 The following figures and definitions are very important because they are used in describing the various kinds of figures in measurements, both in this book and in their applications in daily life. A Straight Line •B A straight line is a line which does not change its direction at any point. Two letters, one at each end of the line, are generally used to name a line — as the line A B. Parallel Lines Figure 1 Figure 2 Figure 3 If two straight lines on a flat surface are always the same distance apart and therefore can not meet, no matter how far they are extended, they are said to be parallel. (See Figures 1, 2 and 3.) The rails on a straight stretch of a railroad track are parallel because they are the same distance apart. Give another example of parallel lines. Figure 4 Figure 5 136 SEVENTH YEAR When two lines meet, they form an angle. The size of the angle depends upon the difference in direction of the lines and not upon the length of the lines forming the angle. For example, the angles in Figures 4 and 5 are equal. The point A where the two lines meet is called the vertex of the ajigle. The angle in Figure 4 may be read angle A or angle B A C or angle 1. For shortness Ihe sign < is used for the word angle. Angle A is the same as < A. D 1 C Figure 6 N •B If a straight line is drawn to meet another straight line, so that* the angles thuQ formed (as angles 1 and 2 in Figure 6) are equal, the lines are perpendicular to each other.^ Perpendicular lines form right angles. An angle smaller than a right angle is an a^ute angle. An angle larger than a right angle is an obtuse angle. Angles 1 and 2 in Figure 6 are right angles. Angle 2 in Figure 7 is an acute angle and Angle 1 in Figure 7 is an obtuse angle. iRight angles may be formed by paper folding. Take a sheet of paper and fold an edge over on itself. Then crease with the edges held together. The crease will be perpendicular to the edge of the paper. Show how to fold the paper to make acute and obtuse angles. PRACTICAL MEASUREMENTS— RECTANGLES 137 Rectangles A figure of four sides is a quadrilateral. How many sides has the rectangle AB CD? How are the two pairs of opposite sides drawn? How many angles has a rectangle? What kind of angles are they? A rectangle is a quadrilateral whose opposite sides are parallel and whose angles are right angles. Exercise 4 1. How many small squares are there in one row along the base AB? S. How many rows are there in the width or altitude, B C ? 8. How many small squares are there in the area of the rectangle A B C D? We see, then, that the area of a rectai^le may be found by multiplying 1 square unit of area by the number of units in length by the number of the same kind of units in the width. We can state this more briefly in the : PRINCIPLE: Tbe area of a rectangle is equal to the product of tbe base and altitude. 4. Let A stand for the area, b for the base and a for the altitude. The above principle can be stated in a much shorter form, called a, formula:^ A=bXa. 5. If b and a are f^ven, how do you Snfi the area, A7 6. If the area, A, and the base, b, are f^ven, how do you find the altitude, a? 'Show that the letters are used in a formula t« stand for a word in order that time may be saved when the principle needs to be stated in writing. 138 SEVENTH YEAR 7. If the area, A, and the altitude, a, are given, how do you find the base, b? The perimeter of a rectangle is equal to the sum of its four sides. Exercise 6 1. If the base A B is 15 inches and the altitude B C is 8 inches, what is the perimeter of the rectangle A B C D ? 2. What is the area in square feet of the floor of your recitation room?^ 3. What is the perimeter in feet of this room? 4. How much would it cost to put a baseboard around the sides of the room at 10 cents per running foot? Make allow- ances for the doors. 5. How many board feet of lumber were used in covering this floor if an allowance of j of the area is added to cover loss from cutting and the amount used in tongue and groove work on the boards? 6. What did this lumber cost at $80 per M? 7. In a certain park there is a rectangular wading pool 40 feet long, 28 feet wide and 2 feet deep. How much did it cost to cement the bottom and sides of this pool at 15 cents per square foot? 8. Around the outside of the pool there is a concrete walk 3 feet wide. Find the area of the concrete walk. 9. What is the perimeter of the pool? What is the perimeter of the walk? 10. A rectangular field is 80 rods long and 40 rods wide. How many acres are there in the field? Problems using local data should be prepared by the pupils and presented to the class for solution. PRACTICAL MEASUREMENTS— PROBLEMS 139 11. What must be the dimensions of a rug for a room 18 feet in length and 14 feet in width, if a yard of uncovered floor space is left on each end of the room and 2§ feet is left on each side? 12. How many square feet of floor space will be left uncovered in the room? Show two ways of solving this problem. 13. A rectangular lot contains 9570 square feet. It is 130 feet long. How wide is it? 14. Find the cost of covering the blackboard space in your school room with slate at 15^ a square foot. 15. How much will it cost to cover the floor of a kitchen 9'xl5' with linoleum at 85 j5 per square yard? 16. For a room to be properly lighted, the area of the glass surface should be at least ^ of the area of the floor space. Is your school room properly lighted? 17. A field is 80 rods long. How many rows of com will it take to make an acre if the rows are 3 feet 8 inches apart? 18. A rectangular field contains 60 acres. It is 120 rods long. How wide is it? 19. How long is a tennis court? How wide is it for doubles? How many square feet does it contain? 20. A township is 6 miles long and 6 miles wide. How many acres are there in a township? 21. A mile of a certain city street is to be paved with brick at a cost of $1.20 per square yard. If the pavement is to be 30 feet wide, what will be the cost per mile? 22. The property owners are required to pay for half of the width of the pavement extending in front of their lots.^ How much would the pavement cost in front of a lot 50 feet wide? *The city usually pays for the cost of the pavement at the intersections of the street. 140 SEVENTH YEAR Boy Scouts' Tents Boy Scouts are taught to make tents out of square and rectangular pieces of canvas. The figures below show how to make a tent out of square sheets of canvas. A square 7 feet by 7 feet will provide a shelter for 1 man and a square 9 feet by 9 feet a shelter for two men. The following figures show how to make a tent from a rectangular piece of canvas twice as long as it is wide. See if you can hang and stake such a tent properly. Camping Among the various requirements necessary to obtain a merit badge for Camping, a scout must: 1. Have slept fifty nights in the open or under canvas at different times. 2. Demonstrate how to put up a tent and ditch it. (From the Handbook for Boys — The Boy Scouts of America.) PRACTICAL MEASUREMENTS— BOY SCOUTS 141 Exercise 6 1. How many square feet of canvas are needed in a one-man shelter that is made from a sheet 7'x7'? 2. How many square feet of canvas are there in a two-man shelter? 3. Two Boy Scouts found that they could buy 7'x7' sheets of ducking for $1.75 each or a 9'x9' sheet for $2.50. Which would provide the cheaper shelter for them, the single or the double tents? 4. Four Boy Scouts found that they could buy a canvas 9'xl8' for $4.75. How much would they save by buying this sheet and making a four-man shelter, rather than buying individual sheets costing $1.75 each? Gardening Among the viarious things that a scout may do to obtain a merit badge for gardening is: (a) To operate a garden plot of not less than 20 feet square and show a net profit of not less than $5 on the season's work. Keep an accurate crop report. Exercise 7 1. If the garden plot must be at least 20 feet square, how many square feet does this minimum sized plot contain? 2. Express the area of the minimum plot in square rods. 8. What part of an acre is this minimum plot? 4. A certain boy raised beans on a garden plot 33 feet wide and 132 feet long. His profit was $110.75. Find his profit per square rod. Would he have been able to secure the merit badge for gardening on a minimum sized plot at that rate? 5. What would have been his profit per acre at that rate? 142 SEVENTH YEAR Parallelograms A parallelogram is a quadrilateral with its oppo- site sides parallel. The figure on the left is a parallelogram. A rectangle is a parallelogram with its angles all right angles. A parallelogram with angles not right angles is called a rhomboid. The figure above is likewise a rhomboid. ? $ The line AB is called the ba^e of the parallelo- gram. The line D E, which I is the perpendicular dis- A E B o tance between the base D C and the base A B, is called the aUitvde of the parallelogram. Cut out of a sheet of paper a parallelogram similar to A B C D. Fold over the edge A E on the base A B and crease along the line D E. Cut or tear off the part A E D and fit it in the position B O C. What shape is the figure D E O C? Show that the rectangle D E O C has the same base and altitude as the parallelogram A B C D. Cut out a parallelogram with a base of 6 inches and an altitude of 3 inches. Change into a rectangle with the same base and altitude. What is the area of this rectangle? Since the same amount of paper forms the parallelogram, what is the area of the parallelogram? Then show how we obtain the principle: The area of a parallelogram is equal to the product of its base times its altitude. This principle may also be expressed by the formula: A = b X a. In this formula what is the product and what are the factors? PRACTICAL MEASUREMENTS— PROBLEMS 143 Exercise 8 1. If the base and altitude of a parallelogram are given, how do you find the area, A?^ 2. If the area, A, and the base, b, of a parallelogram are given, how do you find the altitude, a? 3. If the area. A, and the altitude, a, of a parallelogram are given, how do you find the base, b? 4. The base of a parallelogram is 4 feet and the altitude is 3 feet. What is its area? 6. The area of a parallelogram is 24 square feet. The altitude of the parallelogram is 4 feet. Find the base. 6. Find the area of a parallelogram with a base of 7 feet and an altitude of 2 yards. 7. A flower bed is shaped in the form of a parallelogram with each side equal to 6 feet. By measuring I find the per- pendicular distance between the sides to be 3^ feet. What is the area of the flower bed? 8. What is the perimeter of the flower bed described in the preceding problem? 9. How many bricks 8 inches long would it take to build a border one brick thick around this flower bed? 10. The area of a field in the form of a parallelogram is 20 acres. The base is 80 rods. What is the perpendicular distance between the bases (the altitude)? Fill in the missing dimensions: Aba 11. 400 sq. ft. 25 ft. ? 12. ? 5 yd. 12 ft. 13. 36sq. yd. 9 yd. ? ^Such problems as 1 to 3 of this exercise give practice in reviewing the principles relating to product 'and factors. Have pupils state the answers in formulae if possible. 144 SEVENTH YEAR c r Trapezoids \^/ A trapezoid is a quadrilateral Yo with only one pair of opposite A sides parallel. ^ /^\ ThefigureABCDisatrape- ^ ^ ' zoid. 1. By measuring find the middle point O of the line C B. Draw E F parallel to the line A D. By cutting oflf part E B O and placing it in the position O F C, what shaped figure is formed? 2. K A B = 16 inches and D C = 12 inches, what is the length of A E? By using other numbers and remembering that E B is the same length as C F, you can show that the base of the parallelo- gram into which the trapezoid has been changed is ^ the sum of the two bases of the trapezoid. The altitude of the parallelo- gram is the same as the altitude of the trapezoid. With this information show that: PRINCIPLE: The area of a trapezoid is equal to half the sum of the two bases times the altitude. Exercise 9 1. Find the area of a trapezoid whose bases are 12 inches and 18 inches and whose altitude is 11 inches. Solution: § of (12+18) = 16, number of inches in § the simi of the bases. 11X16=166. Therefore: The area of the trapezoid is 165 square inches. 2. Find the area of a trapezoid of which the upper base is 10 feet, and the lower base 18 feet and the altitude 9 feet. 3. A board is 10 inches wide at one end and 14 inches wide at the other end. If it is 10 feet long,, how many square feet are there on the surface of the board? PRACTICAL MEASUREMENTS— TRIANGLES 145 zo leDS. tORI>5. 4. A man once gave me this problem to solve. A railroad cut off a small piece of his land in the form shown at the left. He had threshed oats off of the tract and wished to compute the yield per acre, but he did not know how many acres there were in the piece. Find the number of acres in the field. 5. If the field yielded 210 bushels of oats, what was the average yield per acre? Triangles A triangle is a figure bounded by three straight lines, called its sides. As the name indicates, a ^rt-angle has three angles. Triangles may be grouped according to sides or angles. {Scalene — ^no two sides being equal. Isosceles — having only two sides equal. Equilaleral — shaving all three sides equal. iAcute Angled — Shaving all the angles acute. 2. Angles<06iit5e Angled — having one angle obtuse. [Right Angled — having one angle a right angle. Scalene Isosceles Equilateral Acute Angled Obtuse Angled Right Angled 146 SEVENTH YEAR Areas of Triangles The altitude of any triangle k;"" 7 is the perpendicular from the /jy^Sv / vertex to the base, as the line /!§ \^ / CE. / :< ^s^ / Draw any shaped triangle as L\ :^^ ABC. From C draw a line C D parallel to the base of the triangle, A B. From B draw a line parallel to the side A C. What kind of figure is A B D C? How does its base and altitude compare with the base and altitude of the triangle ABC? Cut out your parallelogram and cut it along the diagonal line B C. How do triangles ABC and B D C compare in size? The triangle A B C is what part of the parallelogram A B D C? The area of the parallelogram = the product of base X altitude. The area of the triangle = ^ the area of the parallelogram. Show that the areas of the other forms of triangles equal \ the area of the parallelograms constructed as shown in the scalene triangle above. PRINCIPLE : The area of any triangle is one-half of the product of the base times the altitude. Draw a triangle on a sheet of paper. Cut it out carefully and number the angles 1, 2 and 3. Cut the triangle into three parts so that you can arrange the angles about a point on one side of a straight line. Show that the sum of the three angles of a triangle is equal to two right angles (or 180°). Draw other shaped triangles to show that this principle holds true for any shaped triangle. PRACTICAL MEASUREMENTS— TRIANGLES 147 Exercise 10 1. The base of a triangle is 16 inches and the altitude is 11 inches. Find the area. Solution: The product of the base times the altitude = 16X11 = 176. ^ of the product 176=88. Therefore: The area of the triangle is 88 square inches. In finding the product, be sure that both base and altitude are expressed in the same linear units. Only the final area, then, will need to be labeled. Find the area of the following triangles: Altitude X Base = Area. 2. 10 ft. 15 ft. ? 3. 8 in. 12 in. ? 4. 20 rd. 35 rd. ? 6. 11 in. 19 in. ? 6. f ft. If ft. ? 7. 6f in. 12 in. ? 8. 1.65 ft. 2.3 ft. ? 9. .3 yd. .5 yd. ? 10. 4 ft. 2^ ft. ? 11. A field in the shape of a right triangle has a base of 20 rods and an altitude of 16 rods. Find its area in square rods. How many acres in this triangular field? 12. A diamond (also called a rhombus) may be divided into 2 equal triangles. If the short diagonal is 6 inches and the long diagonal 8 inches, find the area of the diamond. (Hint — The two diagonals are perpendicular to each other and bisect each other.) 148 SEVENTH YEAR 13. If the bam, of which the end is shown in the illustration, is 36 feet long, find the total number of square feet in the sides and ends of the bam? 14. How much would it cost to paint the above bam at 10^ per square yard? 16. A tract of ground 40 feet square is divided into 4 equal triangles by diagonal lines. What is the area of each triangle? 16. The area of a triangle is 35 square feet and the altitude is 10 feet. What is the length of the base? Solution: Since the area of a triangle is ^ of the product of the base X altitude, the product of the base times the altitude must be 2X35 square feet = 70 square feet. If the product of the baseXaltitude is 70 and the altitude 10, the base must be 70^10 or 7. Therefore: The base of the triangle = 7 feet. Find the missing term in the following problems: Altitude of triangle Base of triangle Area of triangle 17. • 5 ft. ? 25 sq. ft. 18. ? 9 in. 54 sq. in. 19. 7 in. • 28 sq. in. 20. f ft. ? f sq. ft. 21. ? • .32 rd. .384 sq. rd. 22. 5 yd. 7|yd. ? • 23. 20 rd. 15 rd. ? 24. 7 ft. ? • 21 sq. ft. 26. f ft. 1| ft. ? 26. 16 in. ? 96 sq. in. ^ 27. Find illustrations of triangles in your neighborhood and prepare problems for the class to solve. PAPER, PRINTING AND BOOKBINDING 149 APPLIED REVIEW PROBLEMS Print Paper A Modem Paper Mill Next to food, clothing and shelter, paper is probably the moet important necessity in modern civilization. Make a list of the various ways in which paper is used. See which member of the class can make the largest list. Print paper, used in our daily newspapers, is made from wood pulp. The spruce tree furnishes the best wood for making print paper. These trees are sawed into blocks of proper length and ground by stone rollers, on which water is dripping, into a very fine pulp. Chemicals are mixed with some of the wood in order to toughen the fibers so that the paper will not tear easily. The wood pulp is collected on a wire form and run through a series of rollers, being dried during the process. Exercise 1 1. It takes 113.92 cubic feet of timber to make 1 ton of print paper. This is what part of a cord, expressed decimally? 2. A spruce tree 2 feet in diameter will produce approxi- ■ mately 1.8 tons of print paper. How many cubic feet of wood are there in such a tree? 3. How many cords of wood are there in a tree of that size? How much would this wood be worth at $3.50 per cord? 150 SEVENTH GRADE 4. Allowing for waste, and counting 8^ board feet for each cubic foot, what would be the value of the lumber in such a tree at $28.60 per M7 5. Find the value at 3 J cents per pound of the print paper that may be manufactured from a tree of that size. Compare the values of the paper, lumber and wood from such a tree. Print paper is slupped from a certain paper mill in rolls having an average weight of 1700 pounds. The width of the paper in these rolls is 752 inches. 6. A strip of this paper 1 foot in length and the width of the roll weighs 1^^ ounces. What is the length of one of these 1700 pound rolls in feet? 7. How many miles long is one of these rolls? A daily paper, on a certain day, issued an edition of 100,000 32-p^e papers, the size of each page being 18^' X 23^'. Each print paper roll weighed 1650 pounds. The width of the paper was 73 inches and its average weight per foot in length was Ig ounces. 8. What was the length of a roU of this paper in feet? 6. What was the length of a roll in miles? 10. How many sheets were there in each 32-page paper? 11. How many times is the width of a sheet of the paper contained in the width of the roll? PAPER, PRINTING AND BOOKBINDING 151 12. How many inches in length would be used to print one 32-page paper? 13. Each roll will print how many papers? (See Prob. 11.) 14. How many rolls of this paper were required for the edition of 100,000 papers? How many tons would these rolls weigh? 15. How many trees of the size stated in Problem 2 were required to produce the wood pulp used in manufacturing the paper for this edition? Type Look at this page and see how many kinds of type and other characters are used. The type in this line is designated as *'10 point." The type in the lines at the bottom of this page is known as "8 point." The type in the line at top of the illustration is "6 point." Type sizes are classified by "points" and for this purpose the inch is divided into 72 parts or "points." "12 point," which is a standard of measurement (conmionly called pica)j is ^ of an inch high, and "6 point" is ^ of an inch high. In printing; the term "em" applies to the exact square space occupied by a single letter counted as wide as it is high.^ The "em" is the unit of measure of the quantity of type on a page. The number of lines on a page varies with the size of the type and the amount of space separating the Unes. *As a matter of fact, the type letter is so made as to require less space sideways than up and down. On this account, letters and figures are measured by their depth and not their width. Comparison of Type a 6 Point D 8 Point n 10 Point 12 Point 152 SEVENTH YEAR Exercise 2 1. "6 point" type is what part of an inch high? 2. "8 point" type is what part of an inch high? S. "10 point" type is what part of an inch high? 4. "12 point" type is what part of an inch high? 5. Measure very accurately one of the lines on this page. How many picas wide is it? 6. Counting 70 letters to an 8 point line and 38 lines to a page^ how many "ems" would a page contain? (An "em" is equivalent to an average of two characters — ^letters, figures, or punctuation marks.) 7. Counting 58 letters to a line and 33 lines to a page, how many "ems" would a "10 point" page contain? 8. Counting 48 letters to a line and 28 lines to a page, how many "ems" would a "12 point" page contain? Book Making The paper used for school books is necessarily of a much better quality . than the print paper used by newspapers. With wood pulp must be combined a certain percentage of "rags" (cotton or linen) to make this higher grade of paper. Instead of this kmd of paper being shipped in roUs it is marketed flat and sold by the ream, 500 sheets to the ream. By a close inspection of the top of this book, it will be seen that it is bound in sections of 32 pages (16 leaves) each, called forms. Exercise 3 1. Divide the total number of pages in this book, including the 6 introductory pages in the front of the book, by 32 and see how many '^forms^' are required. PAPER, PRINTING AND BOOKBINDING 153 2. Take a sheet of paper 31* by 21* and fold it successively 4 times. Open it up suflSciently to enable you to number the pages in regular order (as they would open if the edges were cut) from 1 to 32. Then spread the sheet out flat and see how the plates are arranged in printing a form. 3. Counting both sides of the sheet, how many printing impressions are required in printing one book of this size? 4. How many sheets of the size stated are used in making one book? 5. How many books will 1 ream of paper make? 6. How many reams of paper are needed for an edition of 25,000 copies of this book? 7. Assuming that each ream of this paper weighs 75 pounds, what weight of paper is required for an edition of 25,000 books? Book Binding A very important step in book making is the binding. This may be of paper, of cloth, of leather, or of some combination of these materials. School books are usually full cloth bound. The printed forms, which are folded by machinery as they come from the press, are ordinarily of 32 pages, although in larger books they may be of 64 pages. Exercise 4 1. If the glueing and re-enforcing of the "back bone" of each book, before the cover is put on, requires an average of ^ minute per book, how many working days of 8 hours would it require for one person to care for that part of an edition of 25,000 books? 2. The cloth required for the outside of this book is cut approximately 8^*^ by 12*. How many yards of binding cloth 36 inches wide are needed for 25,000 copies? 164 SEVENTH YEAR 3. If the "binders' board" which is used inside of the cloth cover is cut 7f 'x5 J*, how many sheets of board, size 22'x28"' would be required for an edition of 25,000 books? Exercise 5 The announced circulation of a metropolitan daily newspaper for a certain date was 681,562 papers of 80 pages each. The following facts were included in this newspaper's statement explaining the issue. This illustrates the extensive use of timber in the production of print paper alone. It required the usable timber from 84 acres to produce the amount of paper needed for this one issue. It required 425 tons of paper for this one issue. It required the labor of 510 men 4 days to make the output. of paper for this one issue. It required a train of 15 cars, each carrying 28 tons, to transport this paper from the mills to the city. It required 60 truckloads, each weighing 7 tons, to deliver this paper from the railroad. It would make a paper path 18 inches wide and 10,843 miles in length if the sheets required for this one issue were spread out end to end. This would be sufficient to stretch from Bering Strait to Cape Horn. It would paper an expanse of 85,- 876,560 square feet if spread out in single sheets over a flat surface. 1. 80 pages means how many single sheets, or leaves? 2. The size of the news- paper here referred to is 18 J inches by 23 ^ inches. What is the length, in inches, of one paper of this issue, the sheets laid end to end? The length in feet? 3. Multiply this num- ber of feet by 681,562 papers, and reduce to miles. 4. How many square inches in one single sheet of this paper? In the 40 sheets (80 pages) of this paper? 6. How many square feet are there in one full paper of this issue? An acre contains how many square feet? 6. Reduce 85,876,560 square feet to acres. How many 160-acre farms would this amount of paper cover? PART II Training for Efficiency. ChecUng Up It ia considered good business practice to check all bills and accounta to be sure that they are accurate. In order to do this checking rapidly and accurately, practice on the different com- putations that are used. Since no business man wishes his work delayed by slow cheeking, it is important that short methods be used whenever it is possible. The following pages not only give examples for rapid work, but also show some of the short methods that are commonly used. In striving for efficiency in rapid computations, use a i>encil just aa little as possible. Pencil and paper are not always at hand and it is therefore necessary to make mental computations to check the work. It is often sufficient to estimate a result roughly and then check more accurately at one's leisure. Practice in this type of checking can be secured by estimating results approximately in order to check solutions of problems. 155 156 EIGHTH YEAR CHAPTER I Exercise 1 Practice on the first ten examples in this exercise until yoH can do all of them correctly in 5 minutes. 1. 2. 3. 4. 5. 2496 8765 2340 5426 1982 1983 4312 5864 3798 4651 7218 9736 3217 4125 3928 4520 1326 8629 7864 5416 6924 5298 . 4837 3907 7718 6. 7, 8. 9. 10. 3178 3927 7856 4455 3792 4056 8220 9742 6872 4891 2792 4065 6319 9987 7726 4695 3918 2390 2436 3555 9781 4639 2945 2856 4930 11. The areas of the six New England States are as follows: Maine, 33,040 square miles; N. H., 9341 ; Vt., 9504; Mass., 8266; R. I., 1248; Conn., 4965. What is the total area of the New England States? 12. The six leading dairy states had the following number of dairy cows in 1910: N. Y., 1,509,594; Wis., 1,473,505; la., 1,406,792; Minn., 1,085,388; 111., 1,050,223; Tex., 1,013,867. Find the total number of dairy cows in these six leading states. IS. The total wheat production in the different continents in 1915 was as follows: North America, 1,351,763,000 bushels; South America, 200,640,000 bushels; Europe, 2,080,819,000 bushels; Asia, 460,245,000 bushels; Africa, 90,859,000 bushels; Australia and New Zealand, 32,480,000 bushels. Find the total production of the world for that year. REVIEW EXERCISES 157 Exercise 2 We should be able to add horizontally (or across a page) as well as vertically (up or down). By adding both ways you get a "cross check" on the correctness of your additions. Work on the following problems until your results "crosscheck." 1. 87+43+26-|r29= 16 23 58 94= 63 05 41 89 = 27 96 38 42 = 81 27 96 54 = 2. 57+36+29+14 76 12 45 38 67 84 15 29 47 36 91 28 56 18 72 39 8. 43+65+81+71 21 58 64 37 83 41 92 65 61 23 59 84 95 64 32 81 4. 32+56+98+41 72 65 41 89 68 24 15 97 41 36 89 27 19 72 43 86 5. 61+57+84+93 68 54 71 29 80 95 43 16 29 85 47 13 37 68 95 82 6. 14+50+97+83 26 81 43 93 80 36 12 75 41 67 83 25 59 88 64 97 7. 73+96+81+24 63 75 98 26 25 76 31 48 58 19 86 57 76 84 39 46 8. 25+83+17+94 52 78 61 27 76 19 94 53 15 64 82 23 82 93 47 90 158 EIGHTH YEAR Exercise 3 Subtract the first 10 examples as a speed test. Keep a record of your time. You should be able to do them in 2 minutes. 1. 2. 3. 4. 5. 2,164 1,907 3,986 2,497 4,000 3,179 2,869 1,964 . 10,100 2,786 6. 10,724 9,847 7. 29,847 18,868 8. 32,809 ' 14,987 9. 40,400 3,976 10. 21,610 19,143 11. The area of Texas is 265,896 square miles. How much larger in area is Texas than Rhode Island, which has an area of 1248 square miles? 12. The population of the United States in 1910, exclusive of the detached possessions, was 92,228,531. Including the detached possessions, it was 101,102,677. What was the population of the detached possessions? 13. If, as computed, the water area of the earth is approxi- mately 144,500,000 square miles, and the total surface of the earth is approximately 196,907,000 square niiles, how much more water surface than land is there? 14. The ancients believed one-seventh of the earth's surface to be water. This would be approximately 20,642,857 square miles. How great was their error as to the amount? 16. The distance from New York to San Francisco by sea, by way of Cape Horn, is reckoned at 13,000 miles. By way of the Panama Canal it is reckoned at 5278 miles. How much shorter is the Panama route? 16. A bushel contains 2150.42 cubic inches and a cubic foot 1728 cubic inches. How much does the bushel exceed the cubic foot in size? REVIEW EXERCISES— SPEED TESTS 150 Exercise 4 Since the subtrahend and the difference together equal the minuendy in subtraction, any one of the three can be easily supplied if the others are given. Supply the subtrahends: 1. 2,837 2. 20,000 8. 240,000 1,956 18,276 20,700 4. 3,500 5. 401,286 6 546,280 3,080 297,497 397,149 7. 5,962 8. 954,362 9. 717,400 3,000 100,000 200,099 10. 75,160 11. 400,000 12. 100,000 42,839 286,934 66,752 18. 19,763 14. 79,080 16. 327,861 11,274 16,111 100,000 SPEED TESTS IN MULTIPLICATION Exercise 6. Time: 3 minutes Multiply: 9389 5 2459 2 6382 7 6195 3 2574 8 3429 9 9837 4 5289 6 4562 5 3768 2 a 6497 7 3869 8 8576 9 6542 4 6347 6 160 EIGHTH YEAR Exercise 6. Time: 6 minutes Multiply: 2459 6382 9837 3429 82 75 46 39 3768 5497 6542 8576 28 57 64 93 SHORT METHODS IN MXJLTIPLICATION 1. 345X10 = 3450 3.45X10 = 34.5 To multiply an integer by 10, add a zero to the number. To multiply a decimal by 10, move the decimal point one place to the right. Read the products without using a pencil: 2. 68 X 10= 6. 120X10= 10. 45.6X10 = 3. 231X10= 7. 5.03X10= 11. 9.74X10 = 4. 4.63X10= 8. 23.4X10= 12. 860 X10 = 5. 938X10= 9. .48X10= IS. 10.35X10 = 14, John has $2.75 and his brother has 10 times as much in the bank. How much has his brother in the bank? 16. The lumber in a book rack costs 15 cents. The lumber in a medicine chest costs 10 times as much. Find the cost of the lumber in the medicine chest. Exercise 7 1. 42 X 100 =4200. .427X100=42.7 To multiply an integer by 100, add two zeros to the number. To multiply a decimal by 100, move the decimal point two places to the right. REVIEW EXERCISES 161 Give products without using a pencil: 2. .625 X100= 7. .7854X100= 12. 83 X100 = S. 68 X100= 8. 471 X100= 13. 62.5 X100 = 4. .5236 X100= 9. 32.5 X100= 14. 45 X100 = 5. 527 X100= 10. 628 X100= 16. .0625X100 = 6. 3.1416X100= 11. 52.3 X100= 16. 42.85X100 = 17. Show a short method of multiplying a number by 200; by 300; by 400; by 500. 18. Show a short method of multiplying a number by 1000; by 2000; by 3000; by 4000. 19. A school bought 100 pamphlets on soil fertility at $.06 each. How much did the 100 cost? 20. A man bought a farm of 157 acres at $100 per acre. How much did the farm cost? Exercise 8 1. 344X 25 = 34,400 =8600. 4 2. 344X125 = 344,000= 43,000. 8 To multiply a number by 25, multiply the number by 100 and divide by 4. • To multiply a number by 125, multiply the number by 1000 and divide by 8. Without pencil: 3. 44X 25= 7. 15X 25 = 11. 64X125 = 4. 24X125= 8. 12 X$ .25= 12. 128 X 25 = 6. 32 X 25= 9. 18 X $1.25= 13. 32X125 = 6. 72X125= 10. 244X 25 = 14. 88X 25 = 162 EIGHTH YEAR 16. My father bought a farm of 80 acres at $125 per acre. How much did the farm cost him? 16. A farmer sold a herd of 12 calves at $25 each. How much did he receive for the herd? 17. Give a short method of multiplying a number by 50. 18. Give a short method of multiplying a number by 75. FRACTIONAL PARTS USED IN SHORT METHODS Exercise 9 33i = 1 of 100. 12| = J of 100. 16f = 1 of 100. 66f = ^ of 200. 1. Show that multiplying a number by 100 and dividing by 8 is the same as multiplying the number by 33^. 2. Show a short method of multiplying a number by 16f . 3. State a short method of multiplying a number by 12 1. 4. State a short method of multiplying a number by 66f . Without pencil give the following products: 5. 45X33| 13. 16X12^ = 6. 36Xl6f 14. 72X33j = 7. 128X12|= 16. 63X66f = 8. 6X66f = 16. 42Xl6f = 9. 32X12^= 17. 40X12 J = 10. 216X33^= 18. 12X66f = 11. 252X66|= 19. 84X16f = 12. 246Xl6f = 20. 96X12| = 21. A merchant bought a bolt of dress goods containing 40 yards at 12^ cents a yard. How much did the bolt cost? 22. A banker bought a tract of timber containing 33^ acres at $60 per acre. How much did he pay for the tract? REVIEW EXERCISES 168 Exercise 10 1. Multiply 45 by 99. 100X45=4500 Subtracting: 1X45= 45 99X45=4455 To multiply a number by 99, multiply the number by 100 and subtract the number from that product. 2. 84X99= 4. 246X99= 6. 420X99 = 8. 37X99= 6. 854X99= 7. 575X99 = 8. By comparison with the above method show how to multiply a number by 9. 9. State a short method for multiplying a number by 999. 10. Show how to multiply a number by 49 by a short method. 11. A ^-barrel sack of flour contains 49 pounds. How many pounds are there in 44 such sacks? 12. Show short methods of multiplying by 19, 29, 39, 69, etc. Exercise 11 1. Multiply 5i by 5|. ^7 In multiplying these two mixed numbers, 5? we have the products 6X5; 6 X^; iX5; and 25 §X|. But (5xi) and (iX5) is the same 2j as 1X5. We then have (5X5) + (1X5) or 2^ 6X5. To this quotient we add the product i of i X|, or i. 30j 5iX5^ = (6X5) + (ixi)=30i. 2. Multiply 8 J X8§. The product=(9X8) + (|x|)=72f 8. 4§X4| = ? 6. 7^X 7^ = ? 4. 6|X6^ = ? 6. 12|X12| = ? 164 EIGHTH YEAR 7. What is the cost of 8§ yards of cloth at 8 J cents per yard? 8. What is the cost of 5 J pounds of apples at 5 J cents per pound? 9. Show that 8^X8f = (9X8) + (Jxf). 10. Show that 9|x9f = (10X9) + (|xf). SPEED TESTS IN DIVISION Exercise 12. Time: 3 minutes 6)1890 9)6273 4)1584 6)5244 3)2919 8)4768 2)1810 7)6475 9)4365 6)5778 7)6118 Exercise 13. Time: 6 minutes 8)3880 '92)29440 39)15093 61)53192 65)46155 83)58764 47)17578 Exercise 14. Time: 8 minutes 67)17152 82)29602 231)106953 347)227979 945)574560 927)377289 SHORT METHODS IN DIVISION Exercise 16 To divide a number by 10, 100, or 1000, move the decimal point to the left one, two, or three places, respectively, prefixing zeros if necessary. 1. 32-^ 10=3.2 2. 32-^100 = .32 8. 32 -r- 1000 = .032 REVIEW EXERCISES 165 4. 67 -^ 10= 5. 3.9-i-100= 6. 62,5^ 10 =» 7. 42.5 -^1000= 8. 4.5 -i- 100= ». 2.37 -i- 10= 10. 3475-5-1000= 11. 675-5-1000 = 1«. 43.5-5- 100 = 18. I bought 2450 board feet of lumber at $80 per thousand. How much did I pay for the lumber? 14. A man shipped 50 sacks of potatoes weighing 4995 pounds. How many hundredweight did he ship? 16. How much was his freight at 20 cents per cwt.? Exercise 16 1. Divide 4225 by 25. 4X4225 = 16,900. 16,900-^100 = 169. To divide a number by 25, multiply the number by 4 and divide the product by 100. 2. 1570-r25= 5. 1225-^25= 8. 475-5-25 = 8. 345-5-25= 6. 1850-^25= 9. 875-5-25= 4. 625-5-25= 7. 2315-5-25= 10. 72-^-25 = 11. A merchant bought some wash ties at 25 cents each. How many would he get for $26.75? 12. Show a short method similar to the above for dividing a number by 125. 13. A farmer paid $20,000 for a farm. If he paid $125 per acre, how many acres did he buy? 14. A real estate dealer sold a tract of 25 acres of rough pasture land for $1125. What was the selling price per acre? 16. My neighbor bought a tract of unimproved land for $6175 at $25 per acre. How many acres did he buy? Pupils should be encouraged to use these short methods in every prob- lem where they apply. 166 EIGHTH YEAR ■ Exercise 17 To divide a number by 33f , multiply the number by 3 and divide by 100. Show that this method is correct by using fractions. 1. Divide 400 by 33^ 3X400=1200. 1200^100 = 12. 4004-33^ = 12. 2. 750-J-33f = 6. 75-^33f = 8. 900^33^= 6. 125-^33^ = 4. 660^33^= 7. 480-^33| = 8. Show a short method of dividing a number by 12^^. 9. Show a short method of dividing a number by 16f . 10. Show a short method of dividing a number by 66f . Exercise 18 One may often save time by dividing a number by two factors of the divisor. 1. Divide 774 by 18. 3)774 6)2^ 774^18=43. 43 Perform the following divisions by using factors of the divisor: 2. 555-^-15= 6. 2720^32= 8. 1176^56 = 3. 1674^27= 6. 28354-45= 9. 2765-4-35 = 4. 688-4-16= 7. 2706-f-33= 10. 1148-^28 = 11. A farmer raised 2860 bushels of corn on 44 acres of ground. Find the yield per acre. 12. A load of shelled corn weighed 1596 pounds. A bushel of shelled com weighs 56 pounds. How many bushels were there in the load? REVIEW EXERCISES 167 REVIEW OF FRACTIONS The diflferent processes in fractions should become just as familiar to us as the four fundamental operations in whole numbers. Practice on the following exercises until you can do each of them in 2 minutes. Exercise 19 f+t = i + i = 1^+1 = f+ii= T^+f = Exercise 20 H-f = 7 3 _ ¥ - I = f-| = 1--^ = Exercise 21 |x| = 4 V ^ - ¥ ^ 4 - fxf = 8 v/ 3 _ r2X 4 - 5 vx 3 _ 6 A 4 — l^Xf =. |xf = 3 y 1 _ 3X2 — AxA= Exercise 22 • l-A= 5 . 3 _ 8 ~ 4 = 2 . 7 _ 3 "^ ^ — 8 "=" 2 = 5 ^ 4 _ 6 • 9 — Exercise 23 f-f= 1 + 1 = 4 . 2 _ 5 ~ 3 — f+t= |x^ = 2 1 _ 3 - 4 - 7 . 5 _ 12 • 8 — Refer to pages 26 to 32 in Part I for explanations of these processes if they are not clear. 168 EIGHTH YEAR MIXED NUMBERS Exercise 24 Add the following: 1. 23f , 45|, 82f , 35f . 7. From 23| subtract ISf . 2. 9j, 13|, 16f , 8|, llj. 8. From 9^ subtract 7|. 3. 7f , 4|, 9|, 12|, 3|. 9. From 32| subtract 19f . 4. 17 J, 25f , 43f , 32f , 57|. 10. From 20f subtract 14f . 5- 6§, 8|, 6|, 9f , 7^. 11. From 5 J subtract 3f . 6. 6|j 2f, 6f, 4|, l|. 12. From 60^ subtract lOf. Exercise 26 Find the following products and quotients: 1. 3|xlf 4.12 Xlf. T.Divide 8|by2j. 2. 8|X3f. 6. 3|x2f. S.Divide 3§by2. 3. lOfxif 6. 22§X2f . 9. Divide 12f by 2f 10. In a track meet the winner of the running broad jump leaped 16 J feet. His nearest competitor jumped 16 J feet. How much farther was the first jump than the second? 11. A square rod is 16j feet by 16^ feet. How many square feet are there in a square rod? 12. Find the cost of 7 J yards of gingham at 12^ cents a yard. 13. In the spring of 1917 a 24^-pound sack of flour sold for 5^ cents a pound. What was the price per sack? 14. How many guest towels f of a yard long can be made from a strip of linen toweling 4§ yards long? 15. Find the cost of if pounds of steak at 28 cents a pound. REVIEW OF DECIMALS 169 MISCELLANEOUS PROBUBMS Exerdse 26 DECIMALS • 1. Add: 8.25; .072; 7.055; .0075; 13.5; .068. 8. Add: .0054; 3.125; 11.2347; 3.1416; .7854; .866. S. 2150.42-1728 = ? 6. 425.68-98.375 = ? 4. 6.5-1.4142 = ? 6. $2-$1.37 = ? 7. Multiply 324.5 by .035. 8. What is the principle of pointing off decimal places in the product? 9. .032X2.8 = ? 12. 4.05 X. 62 = ? 10. 3.1416X25 = ? IS. 63.3X25.7 = ? 11. .0025X.03 = ? 14. .008 X. 0016 = ? 15. Divide 8.575 by 3.43. 16. What is the principle for pointing off decimal places in the quotient? 17. .287 -^ 3.5=? 20. 32.5 -^ 260 = ? 18. .02145-^.007 = ? 21. 82.254-25 = ? 19. 25.5^425 = ? 22. .0025 -h .05 = ? 23. Find the cost of 7725 bricks at $16.25 per thousand} 24. What are the freight charges on a barrel of apples weighing 160 pounds, at $0.22 per hundred pounds? 25. A chicken weighing 4.25 pounds cost $1.02. Find the cost per pound. 26. Find the cost of 225 feet of lumber at $67.50 per 1000 feet. *Use the short method of dividing by 1000 to find the number of thovr sands of brick. 170 EIGHTH YEAR REVIEW OF PERCENTAGE Exercise 27 1. 80% of 520 eggs placed in an incubator hatched. How many of the eggs hatched? How many did not hatch? • 2. The leaves of an alfalfa plant constitute 45% of its weight. How many pounds of leaves are there in a ton of .alfalfa hay? How many pounds of stems in a ton? 3. A girl's spelling paper was marked 96% correct. How many words did she spell correctly out of 50? 4. A hog shrinks about 33^% on being dressed. What is the dressed weight of a 210-pound hog? 6. Which would you rather have— 20% of $864 or 25% of $725? 6. There are 525,000,000 acres of improved land in the United States. About 20% of that amount is planted each year in com. Find the number of acres devoted to raising corn. 7. A farmer took four 100-pound cans of milk to the cream- ery. The milk tested 3.8% of butter fat. How many pounds of butter fat were there in the four cans? 8. 85% of butter is butter fat. How many pounds of butter fat are there in a 5-pound jar of butter? 9. Ice is 91.7% as heavy as water. A cubic foot of water weighs 62 § pounds. How much does a cubic foot of ice weigh? 10. Sandstone is 235% as heavy as water. Find the weight of a cubic foot of sandstone. 11. A manufacturer makes a stove at a cost of $18.00. He sells it to a retail customer at a gain of 20%. The retail dealer pays $1.60 freight and sells it to a farmer at a profit of 25%. Find the price paid by the farmer. REVIEW OF PERCENTAGE 171 Exercise 28 U A pint is what per cent of a quart? 2. A foot is what per cent of a yard? 3. A peck is what per cent of a bushel? 4. A farmer planted 45 acres of com on a farm of 160 acres. What per cent of his farm is in com? 6. A certain prize cow yielded 21,944 pounds of milk in a year. Her milk contained 944 pounds of butter fat. What per cent of butter fat did her milk contain? 6. A farmer tested 180 kernels from one lot of seed com, and 14 kernels failed to grow. What per cent failed to grow? 7. The same farmer tested 160 kernels from another lot of seed com and found 26 kernels that failed to sprout. What per cent of this lot failed to grow? Which lot would be best for planting? 8. There are 135 boys in a school of 250 pupils. What per cent of the pupils are boys? What per cent are girls? 9. Fred played in 10 ball games during the smnmer. He was at the bat 50 times and made 16 base hits. What was his per cent of base hits? Compare his percentage of base hits with your favorite player in the big leagues. 10. A grammar school basket ball team won 9 out of the 12 games that they played. What per cent of games did they win? 11. A girl earned $45.00 during her summer vacation and put $28.80 of that amount in her savings account. What per cent of her earnings did she put in her savings account? 12. A merchant sold eggs which cost him 24 cents a dozen at 27 cents a dozen. What was his per cent of profit? What would have been his per cent of profit at 26 cents per dozen? 172 EIGHTH YEAR 13. An agent bought an automobile for $800 and sold it for $1120. What was his per cent of profit? 14. A cubic foot of wrought iron weighs 489 pounds. A cubic foot of water weighs 62.5 pounds. Water is what per cent as heavy as wrought iron? Exercise 29 1. Sea water contains approximately 3% of salt. How much sea water must be evaporated to obtain 12 pounds of salt? 2. A farmer sold 45 hogs, which were 62^% of his total number of hogs. How many hogs did he have left? 3. Butter fat constitutes 85% of the weight of butter. How many pounds of butter can be made from 6.8 pounds of butter fat which is contained in a can of cream? 4. A horse buyer sold a horse for $161 at a profit of 15%. Find the cost of the horse. 6. A dressed steer weighed 877.5 pounds. This was only 65% of its Uve weight. What was the live weight of the steer? 6. The weight of a cubic foot of water (62.5 pounds) is 5.18% of the weight of a cubic foot of gold. Find the weight of a cubic foot of gold. 7. A merchant sold a suit of clothes for $28 at a gain of 40%. Find how much the merchant paid for the suit. 8. A firm increased the wages of its employees 10%. What was the previous salary of a man who is receiving $132 under the new schedule? 9. The number of girls in a class is 21. If the girls comprise 60% of the membership of the class, find the total number in the class. 10. A basket ball team won 80% of its games during a certain year. If it won 12 games, how many games did it play? REVIEW EXERCISES— INTEREST 173 INTEREST Exercise 30 1. Find the interest dh $750 for 1 year 3 months and 18 days at 6%. 2. Find the interest on $5000 for 10 months and 12 days at 5%. 3. A milliner has a certificate of deposit from a bank for $350. The bank pays her 3% interest on that amount if she leaves it in the bank more than 3 months. What was her interest for 6 months? 4. A merchant borrowed $2500 from a loan company for 3 years at 6%. What was his yearly interest payment? 6. A farmer bought a farm for $12,500. He made a cash payment of $4500. He borrowed $6000 from an insurance company at 5^% and gave the owner his note for the remainder at 6% interest. What was the total of his interest payments per year? 6. A school district issued twenty $1000 (one-thousand- dollar) bonds bearing 5% interest, one of the bonds being paid oflf at the end of each year. What was the interest on these bonds the first year? 7. How much was the interest decreased each year by paying oflf one of the bonds? 8. Find the total interest paid on the twenty bonds before they were all paid off? 9. The interest from a certain note for one year at 6% amounted to $72. Find the face of the note. 10. The interest on a note for $400 for 6 months was $14. Find the rate of the interest. 11. Find the interest on $250 for 3 years 6 months at 6%. 174 EIGHTH YEAR COMMISSION Exercise 31 1. A lawyer charged 5% for collecting debts for a grocer, amounting to $1375. What was his fee? 2. A salesman received a salary of $1200 per year and a commission of 2% on his sales. What was his total income for the year if his sales amounted to $40,000? 3. A eonmiission firm sold a carload of 196 barrels of Black Twig apples at $3.50 per barrel. What was their com- mission at 7% on the sales? 4. A eonmiission firm bought $36,500 worth of cotton for * m a factory. What was the amount of their commission at 2%? Find the total cost of the cotton to the firm. 6. A commission firm sold 300 baskets of Concord grapes at 18 cents each and remitted $50.22 to the owner. Find the rate of their commission. 6. A real estate dealer sold a farm of 160 acres at $125 per acre on a commission of 2%. What was the amount of his commission on the transaction? ?• A collector charged 5% commission for collecting a debt of $1500. Hew much should he remit to the creditor? 8. A real estate dealer sold 5 city lots at $2500 each, charg- ing 3% commission. Find his commission on the 5 lots. 9. What was a broker's commission for selling 1600 bushels of wheat at f j4 per bushel? 10. An agent received $2.50 commission on an article which he sold at $9.60. Find his rate of commission* 11. A real estate agent sold a farm at a commission of 5%. If he received $500 for his commission, what was the selling price of the farm? How much did he remit to the owner? REVIEW EXERCISES— DISCOUNTS 175 DISCOUNTS Exercise 32 1, A certain ice company sells a 1250-pound ice ticket for $4.00. A discount of 25 cents is allowed from this price if it is paid for within 10 days. What is the per cent allowed for prompt payment? 2. My gas bill for the month of January, 1917, was $1.98. A discount of 22 cents is allowed if the bill is paid within 10 days. Find the per cent of discount for prompt payment. 8. A school bought a dozen jack planes listed at $36.00 per dozen. It was allowed the regular discount of 20% and an extra discount of 2% for cash. What as the net cost of the dozen planes? 4. A fmniture store advertised a discount of 20% on all fmniture during the month of July. What was the sale price on a library table formerly listed at $24.00? 6. A retail dealer bought a piano listed at $500 with dis- counts of 20% and 15%. What was the net price of the piano? 6. Which is better for a retail dealer, discounts of 20% and 15% or a single discount of 33f %? 7. A merchant marked dress goods costing $1.20 per yard to sell at a profit of 50%. During a clearance sale he discounted the marked price 25%. Find his sale price per yard on the dress goods. 8. A hardware firm bought a bill of goods amounting to $1345.40. They were allowed a discount of 2% for prompt payment. What was their net bill? 9. A dealer sold straw hats of a certain grade for $3.00 early in the season. Late in the season he sold them at a clearance sale for $1.80. Find the per cent of discount which he gave on this sale. 176 EIGHTH YEAR TAXES Exercise 33 1. The tax rate for a rural school district was $.79 per $100 of valuation. $.79 is what decimal fraction of $100? 2. What was the total amount raised in taxes for this dis- trict if the total valuation of the district was $84,643? 3. In a certain state the assessed valuation of property is taken as ^ of the full value. If I own a house and lot valued at $3600, what will be my assessed valuation on the place? 4. If the total tax rate is $4.35 per $100, what will be the taxes on this house and lot? 6. The state tax on this property amounted to 80 cents per $100. Find the amount of state tax on the house and lot. 6. The school tax on this property was $1.95 per $100. Find the amount of the school tax. 7. The valuation in a certain county was $32,450,000 and the amount levied for taxes in a certain year was $120,000. Find the approximate rate per $100 of taxable property. 8. A single woman schedules her income as follows: Divi- dends from stock, $2500; rent from farm, $1020; rent on city residence, $360; miscellaneous sources, $500. What was her income tax? (See page 105.) 9. A town having property valued at $350,000 made a special assessment of 3 mills on the dollar^ for library purposes. What was the amount raised for library purposes? 10. A county made a special assessment of 2 mills on the dollar for good roads. How much taxes were raised if the valuation of the county was $28,372,480? lA rate of 3 mills on the dollar reduced to a decimal = .003 of the assessed valuation. REVIEW EXERCISES— INSURANCE 177 INSURANCE Exercise 34 1. How much must I pay to insure my household goods val- ued at J500 at a rate of 42 cents per $100? 2. The premium on a house worth $3000, insured at 80% of its value, was $15.60. Find the rate of insurance per $100. 3. A grocer insured his stock of goods valued at $2000 at 80% of their value at a premium of 1% for 3 years. What was the amount of his premium? 4. A school house cost $40,000. It was insured at 80% of its value at a premium of 1 J% for 3 years. Find the amount of the premium. 6. A lawyer took out an ordinary life insurance policy for $5000 at the age of 30. The rate in his company at that age was $19.74 per thousand. What was his annual premium? 6. The agent securing the policy received a commission of 50% of the first premium. What was the agent's commission on the $5000 policy? 7. Why should an inventory of household goods be made out before they are insured? 8. A man carried insurance on his household goods for $1000 at the rate of 40 cents per $100. He paid this rate for 10 years. How much did his insurance cost him? 9. During the tenth year his house was burned and his household goods were a total loss. The inventory of his goods showed that their value was really only $700 and he received that amount in the adjustment with the insurance company. Since he had paid insurance, on $1000, how much insurance did he pay from which he received no returns? 10. If I pay a premium of $37.50 on a house insured at $3000, what is the rate per $100? 178 EIGHTH YEAR APPROXIMATION PROBLEMS Exercise 36 Many problems actually arising in life are not solved at once with exactness, but only approximately. The habit of inspecting a problem and roughly estimating the answer (in advance) is of value in preventing the danger of being satisfied with an absurdly incorrect result. 1. A man owes the following amounts: $173.57, $54.55, $46.10 and $198.28. Does he owe more or less than $500? 2. I can save from my wages $3.50 per day. Working 26 days per month, about how long will it take me to save $1000? 3. A fruit ranch yields 2600 boxes of peaches which sell at 48 cents the box. Will the receipts exceed $1300? 4. 4000 boxes of apples bring $1.14 per box. Will the proceeds exceed or be less than $5000? 6. I have borrowed $1385 for one year at 8%. Shall I pay more or less than $100 interest? 6. A man purchased a house for $6100, and sold it later for $6800. Did he gain more or less than 10%? 7. Give the approximate cost of 16 dozen eggs at 24 cents. 8. Give the interest for one year on $990 at 6%. 9. Give the income from $22,240 at 6%; 7%; 11%. 10. What is 9% of 6,500,000? Is it 58,500 or 585,000? Give the approximate results of the following: 11. 50X49? 1100^50.4? 18,527+1460? 527+110+92? 12. Is 6,521,865 divided by 276 about 2000 or 20,000? 13. What is the distance covered by an automobile in 21 hours when averaging 18 f miles per hour? 14. The assessed valuation of a school district is $21,945,865. The expenses of conducting the schools are $112,000. What is the approximate rate of taxation for school purposes? CHAPTER II BA»ES AND BANKING interior of a Metropolitan Bank A bank receives money on deposit. A bank also cashes checks, lends and transmits money, and discounts promissory notes. Nalional banka are authorized by the national government and are inspected by national officers to see that the business is conducted in compliance with the provisions of the National Banking Act. State banks are organized under state laws and are inspected by state officers. Trust companies, organized under state laws, not only do a banking business, but also settle estates, take care of the property of minors, and perform other services in the nature of trust. 179 180 EIGHTH YEAR In some states certain individuals or partnerships call their offices "private bankSj'^ although they possess no bank charters and are not subject to any official inspection. In order to organize a National bank, shares of $100 each are sold to a group of stockholders. National banks must have a capital of at least one hundred thousand dollars, ^'except that banks with a capital of not less than fifty thousand dollars may, with the approval of the Secretary of the Treasury, be organized in any place the population of which does not exceed six thousand inhabitants." National banks are required to keep on deposit with the government, United States bonds equal to one-fourth of their capital stock, as security for their circulating notes which they may issue to that amount. If a National bank fails, the government pays the bank notes that the bank has in circulation from the sale of the government bonds deposited to secure them. The bank notes, then, are accepted by people as readily as the government paper money or "greenbacks." Notice different bills to see if you can find: (1) silver certifi- cates; (2) gold certificates; (3) government notes or "green- backs;" (4) national bank notes. Hundreds of years ago men who made a business of borrowing and lending money had benches in the market places of the principal cities and drove bargains with borrowers and lenders. The Italian word **banca'' meant bench and from it we derive our word hank. When one of the old- time bankers failed, his bench was broken. "BanJcrupt" meaning broken bendi, came to mean a debtor who could not pay. For the protection of their depositors, National banks are required to keep on reserve at least 12% of their deposits. Experience has shown that this is sufficient to meet the daily withdrawals by depositors. Part of this reserve may be de- posited in certain city reserve banks. BANKS AND BANKING— FEDERAL RESERVE 181 Federal Reserve Banks In order to furnish an elastic currency, to afiford means of rediscounting commercial paper, and to establish a more eflfective supervision of banking in the United States, the government of the United States established in 1914 a system of Federal Reserve banks.^ Federal Reserve Banks are to be found only in the twelve specified Federal Reserve cities, viz.: New York, Chicago, Philadelphia, Boston, St. Louis, Cleveland, San Francisco, Minneapolis, Kansas City, Atlanta, Richmond and Dallas. No Federal Reserve bank is permitted to begin business with a capital of less than $4,000,000. ^ny one may own shares in a Federal Reserve bank, but only a member bank of its district is permitted to own at any one time more than $25,000 of the capital stock of one of these banks. Exercise 1 1. If a capitalist owns the maximum amount permitted in a Federal Reserve bank in each of the cities named, what is the par value of his investment? 2. What was the minimum capital required for the be- ginning of business by eight Federal Reserve banks? 8. The shares of stock of a Federal Reserve bank are of the par value of $100 each. How many shares are required to be taken, to amount to the minimum sum required for beginnmg the busmess of the bank? 4. Three State banks and two business houses each purchase the maximum peirmitted amount of stock in a Federal Reserve bank. What is the amount of their stock in it? *A Federal Reserve bank is essentially "a banker's bank." It sus- tains with its members much the same relation that ordinary banks sustain with their depositors. 182 EIGHTH YEAR 6. If a certain Federal Reserve bank has a capital of $20,000,000 and yields a dividend of 6% annually on the capital stocky what will be the amount of the dividends dis- tributed in one year? Checking Accounts FARMERS' NATIONAL BANK DEPOSITED TO THE CREDIT OF / tcAf. sormiXfu y" Co< Fort Dkarborn. i. . UMXaM/<gtoi7 (CHKCKS ARK RKCKIVEO FOR COLLECTION) QjouJ,(o All kinds of banks receive money on deposit for safe keeping. Some banks make a small charge for their care of money deposited in small amounts, and some pay a low rate of interest for large deposits left with them on check- ing account. Gen- erally, however, the depositor neither receives interest upon, nor pays for the care of, money deposited on check- ing account. With the money to be deposited, at any time, the depositor hands to the receiving teller of the bank a deposit slip filled out with his name, the date and the items of amount deposited and the nature of the deposit, whether it consists of bills, coin or checks on banks. What are the three headings on the deposit slip shown above under which the various amounts are listed? DRAFTS ... G8 20 CHECKS .... H3 GS CURRENCY . . . , Q> HO ■ TOTAL 118 .25 BANKS AND BANKING— CHECKS 183 1. Make a deposit slip similar to the form given and fill out the deposit slip for John Smith for the following items: a draft for $50.00; three checks for $7.50, $3.75 and $14.25; and the following amount of money: 2 ten-dollar bills; 7 five- dollar bills; 13 one-dollar bills; 11 half-dollars; 17 quarters; 22 dimes; 31 nickels; 48 pennies. 2. Write a deposit slip for Richard Roe on a deposit slip secured from one of the local banks. Turn in a list of the kinds of money, etc., as shown in Problem 1. (It will be more con- venient for the teacher to secure the blank forms from a bank for class use.) Check Books Check books with blanks which can be easily and rapidly filled out are supplied by the banks. They contain stubs from which the checks may be torn oflf, and which are prepared to retain a memorandum of each check drawn, so that when all the blank checks have been used, the stubs will show a record of all the moneys withdrawn from the bank by means of them. •hli ^ . flot^tA^ ^ ^ovSaM ^I •^ iL iio.3^s: 'W.i ^.'7l wu 4 / 'Tn^Y^s, wlz-%^ Mt '^j^Mve^ntu^ cfjutty y ^mo ^ e. f./focMjU When the depositor wishes to withdraw from the bank a,ny of the money deposited to his credit, he fills out a check, which is an order for the amount to be withdrawn. The check may be made payable to himself or to some other person to whom he wishes to make a payment. 184 EIGHTH YEAR The person who presents the check to the paying teller, to be "cashed," must indorse it. This is done by writing his name on the back of the check, as shown below :^ If the depositor makes a check payable to himself and indorses it, any one may present it for payment. If he makes it payable to some particular person, that person (called the payee) must indorse it, whether he transfers it to any one else or pre- sents it for payment at the bank. Checks should be presented promptly for payment. When checks are received by a bank for deposit, they are credited as cash, for they are immediately collected from the banks on which they are drawn. 8. If you receive a check made payable to yourself and you lose it before you have indorsed it, can the finder cash it at the bank without forging your name? 4. If you receive a check made payable to yourself and you indorse it and then lose it, can the finder cash it at the bank? 6. If you receive a check made payable to "bearer," can any one cash it at the bank without your indorsement of it? Is it best to make checks in this way? 6. If in sending a check you indorse it with an order to pay a certain person (giving his name), can any other person who finds it cash it? *An indorsement should be on the back of the left end of the check at least one inch from the end. BANKS AND BANKING— CHECKS 185 A check so indorsed is said to be ^'indorsed in full." An Indorsement in Full 7- If you receive a check made payable to yourself, and if^ instead of presenting it personally at the bank, you send it to another person with the mere indorsement of your name (which is called an indorsement in blank), and it is lost in transit, can any finder of it cash it? 8. Write a check for a fictitious amount to be paid to John Doe,^ and sign the name Richard Roe. 9. Write a check for a fictitious amount to be paid to Richard Roe, and sign the name John Doe. 10. Indorse in blank the check written in Problem 8 above. 11. Indorse in full the check in Problem 9, using any other fictitious name. 12. On a check made by John Doe to himself, write an indorsement in full, authorizing payment to Richard Roe. The use of checks renders it easy to pay bills by mail, and in various ways it lessens the risk of loss in the transmission of money. At stated periods, usually at. the close of each month, the paid checks are returned by banks to the persons who issued them; and they thus serve as receipts, since they show that the moneys have been paid. *"John Doe" and "Richard Roe" have been for centuries legal desig- nations for supposititious or unknown personages. 186 EIGHTH YEAR Savings Accounts State banks usually have savings departments in which they pay a small rate of interest (usually 3% or 4%) on savings deposits. One dollar is usually required for opening a savings account. When the interest is due, it is added to the depositor's account and draws interest the same as the original deposits. The following quotation from a savings account book shows their method of computing interest: "Interest will be allowed from the first day of the month following the deposit, except that deposits made up to the 5th of any month shall be considered as being made upon the first day of the month, and will draw interest accordingly. Interest will be computed on the first da3rs of Janu- ary and July of each year on all sums then on deposit, at the rate of three per cent per annum on all savings deposits which have remained on deposit for one month or more, but interest will not be allowed upon fractional parts of a dollar, nor for fractional parts of a month, nor on any sum with- drawn between interest days, for any of the periods which may have elapsed since the preceding interest day. All withdrawals between interest days will be deducted from the first deposit." — ^Woodlawn Trust and Savings Bank. Form of a Savings Accoimt Date Teller Withdrawals Deposits Balance 7/ 2/16 W $100 $100 8/15/16 W 50 150 10/ 1/16 W 30 180 10/30/16 W $20 160 11/26/16 W 10 170 Exercise 3 1. Compute the interest on the above savings account for the interest-paying date Jan. 1, 1917> according to the rules given in the quotation from the Woodlawn Trust and Savings Bank. BANKS AND BANKING— INTEREST 187 2. If there were no deposits or withdrawals between Jan. 1, 1917, and July 1, 1917, what would be the balance on the latter date? Compound Interest If, when due, the simple interest is added to the principal to form a new principal for the next interest period and this process is repeated during all the interest periods of the loan, the difference between the final amount and the original prin- cipal is called compound inter^t. From the preceding exercise it is seen that savings banks make use of compound interest. The calculation of compound interest for any considerable length of time involves so many steps that it is generally avoided by the use of a Compound Interest Table. The following table shows the amount of one dollar for twenty annual interest periods: Tabub bkowino amount or $1.00 at compound xntsbbbt, bxtindbd to nvB DBCXMAL8 FOB BACH OT TWBNTT PBBIOD8 VBOM 1 TO 7 PBB CBNT. 1 2 3 4 5 6 7 Tbab PbbCbmt PbbCbnt PbbCbnt PbbCbnt PbbCbnt PbbCbnt Pbb Cbnt 1 1.01000^ 1.020109 1.03030 ^1.02000 1.03000 1.04000 1.06000 1.06000 1.07000 2 1.04040 1.06090 1.08160 1.10250 1.12360 1.14490 8 1.06121 1.09273 1.12486 1.16763 1.19102 1.22604 4 1.04060 1.08243 1.12551 1.16986 1.21561 1.26248 1.31080 6 1.05101 1.10408 1.15927 1.21665 1.27628 1.33823 1.40255 6 1.06162 1.12616 1.19405 1.26532 1.34010 1.41852 1.60073 7 1.07213 1.14869 1.22987 1.31593 1.40710 1.50363 1.60578 8 1.08286 1.17166 1.26677 1.36857 1.47746 1.59385 1.71819 1.00368 1.19509 1.30477 1.42331 1.55133 1.68948 1.83846 10 1.10462 1.21899 1.34392 1.48024 1.62889 1.79085 1.96715 11 1.11567 1.24337 1.38423 1.63945 1.71034 1.89830 2.10485 12 1.12682 1.26824 1.42576 1.60103 1.79686 2.01220 2.26219 13 1.13809 1.29361 1.46853 1.66507 1.88565 2.13293 2.40985 14 1.14947 1.31948 1.51259 1.73168 1,97993 2.26090 2.57853 15 1.16097 1.34587 1.55797 1.80094 2.07898 2.39666 2.75903 16 1.17258 1.87279 1.60471 1.87298 2.18287 2.64035 2.05316 17 1.18430 1.40024 1.65285 1.94790 2.29202 2.69277 8 ! 37993 18 1.19615 1.42825 1.70243 2.02682 2.40662 2.86434 19 1.20811 1.45681 1.76361 2.10685 2.62696 3.02660 S. 61663 20 1.22019 1.48595 1.80611 2.19112 2.65330 3.20714 3.86968 188 EIGHTH YEAR The preceding table is made out for annual payments. For semi- annual periods take half the rate for double the number of years. For example: to find the compound amount on $1 at 6% for 10 years compounded semi-annually find the amount in the table for 3% for 20 years. The compound interest is the difference between the com- pound amount and the original principal. Exercise 4 1. Find by the table the compound amount of $1000 at 6% for ten years, payable annually. 2. Find the compound interest of the same. 8. How much greater is this than the simple interest would be? 4. Find by the table the compoimd amount of $1000 at 6% for ten years, payable semi-annually? 5. How much greater is this than the compoimd amoimt of the same principal at the same rate per cent, the interest being paid annually? 6. What is the nearest full year at which the original principal will double itself at compound interest at 6%, payable annually? 7. What is the nearest full year at which the original principal will treble itself at compound interest at 6%, payable annually? Bank Discount PromissoryNotes, which may be transferred from one person to another by being properly endorsed, are called Negotiable Notes. In lending money on notes or discoimting notes payable to another party, banks require the interest to be paid in advance. That is, they deduct it from the face of the note and the borrower receives the remainder. 6% is the rate usually used in bank discount. BANKS AND BANKING— DISCOUNTS 189 The money which a borrower actually receives is called the proceeds of the note. The interest deducted in advance is called bank discount. The note given to the bank to secure the loan does not promise to pay interest, since this is paid at. the time when the note is received. Only the face of such a note is to be paid. ^smoq iM^^^^^fh^ ... afterdate C/ _ promise to pay to the - . QdOdi . /j9P. . ^.OUl^^d^.. for value received, lh^,S^. Exercise 6 1. What is the hartk discount on the above note? 2. What are the proceeds of the above note? 8. Find the bank discoimt on a note for $450 for 60 days at 6%. Find the proceeds. 4. What is the bank discount on $180 for 30 days at 6%? 6. If you give a bank your note for $2360 for 90 dajrs at 6% discoimt, what will be the proceeds? 6. If I wish to borrow $250 from a bank for 1 year at 6%, for what amoimt must the note be drawn? Explanation: 6% of $1 = $.06. $1.00 - $.06 = $.94, proceeds of $1. The note then must be drawn for as many dollars as $.94 is contained times in $250. Find the amount 190 EIGHTH YEAR 7. In order that the proceeds of a note discounted at a bank for 60 days at 6% may be S160, what must be the face of the note? 8. In order that the proceeds of a note discoimted at a bank for 30 days at 6% may be $850, what must be the face of the note? 9. John Doe has a note from Richard Roe for $300 for 1 year at 6% interest.^ How much would he receive for it at a bank if the discount was 6%? 10. In order to secure the sum of $248 as proceeds of a note at bank; discount of 6%, for what sum must a 60-day note be written? Exchange One of the most important functions of a bank is the pa3nnent of debts without the actual transfer of money through the interchange of checks and drafts. To collect a debt from a debtor in another town or city, the creditor may "draw" on him for the amount due. This is done by sending to a bank in the debtor's home town or city an order to pay the amount. This order is called a draft. Generally the draft is sent to a bank with which the debtor does business. The draft may be made payable to the creditor himself, and sent to the bank for collection, or it may be made payable to the bank itself. The order is addressed directly to the debtor drawn upon, the address being written generally in the lower left comer of the paper. If the debtor is ordered to pay the draft "at sight," the paper is called a sight draft. . If the order calls for payment at a stated later time, it is called a time draft. . ^In discounting a note bearing interest, the amount of the note at maturity is cUscoimted. BANKS AND BANKING— DRAFTS 191 Sight Draft ^t50.00 j4i sight pay to the order of ^A^f^. ,P/]^M^yi(!(}^k^ for value received ^nd charge the same to the account of .^.^lS?!^i?^-/Kfc. .&Q£m,£)QO., ,.Cfuf^gJi^ Time Draft .^di^Ma^frrw, sight, pay to the order of ^ddsmeiT-Ss^^^m:... ^MJO'<MM/ncl/ucOamd)^^tlk'£}xla^i4^ %o)i fir vaiut rtceived and charge to wY« » a^B •• «S •^■MWWBBW ^«i «««•••■ If a draft is a time draft, the bank receiving it immediately presents it to the party addressed and if it is satisfactory that party writes his acceptance and the date across the face as shown in the above illustration. A check drawn by one bank upon another is called a "bank draft." It is used largely to avoid the needless transmission of actual money from one city to another. The cashier signs for the bank making the draft and the name of his institution appears at the top of the paper, as on a letterhead, while the name of the bank drawn upon appears below. 192 EIGHTH YEAR A Bank Draft ItPMOO %ru^^ Pay to the order of .^Smmi^OU £){t^,SJio^^ in current fu fids. !^^.^^^i^!^^ .Jy^fi:^^ ...^J^iJ^m^JtQ^t/rUj.JMi ^oA^UJf/U The banks in large cities have a cUaring hxmse where each bank presents checks and drafts which they have cashed for the other banks in the city and only the balances due are paid in actual currency. Clearing houses in central banking cities provide for the exchange of checks and drafts of banks in di£ferent cities. Balances are paid in clearing house certificates or in actual currency. Where the obligations of the business houses (including banks) of one city to those of another city are pretty evenly balanced by obligations of the latter to the former, there will be no occasion for the transmission of cash from one city to the other for the settlement of the obligations; the obligations of the business houses of the one city will largely cancel those of the other, and this is effected by the use of drafts. If the business houses of St. Louis owe to those of New York a large surplus over the indebtedness of New York to St. Louis, there must be a shipment of money to settle the balance. Be- cause of the desire to avoid the actual shipment of money, bank drafts on New York will be sold in St. Louis at a slight premium;^ while drafts on St. Louis will be sold in New York at a slight discoimt. ^A premium is an extra amount over the face value. The premiimi or discoimt is calculated on the face of the draft. BANKS AND BANKING— DRAFTS 193 According to the condition of the money market, drafts may be "at par*' or they may "appreciate" or "decline." Exercise 6 1. Write a sight draft, using fictitious names. 2. Write a time draft, using fictitious firms' names. 8. Find the cost of a sight draft for $500 where there is in the money market a premium of f %. 4. Where exchange is at a discount of f %, what will be the cost of a sight draft for $500? 6. What is the cost of a sight draft for $1200 where exchange is at a premium of f %? 6. What will be the cost of a sight draft for $625 where exchange is at a discoimt of ^%? Time Drafts In the case of time drafts, the element of time has to be taken into account. The bank discount for the time specified is deducted from the face of the draft, and the premium, or discount, is then calculated on the face of the draft and added to or subtracted from the remainder. Exercise 7 1. A sixty-day time draft for $300 must be bought where exchange is at premium of ^%. What is the bank discount? 2. What can be obtained for a draft for $400 payable in 90 days from sight, and discounted at the time of its acceptance? What was its cost at a discount of f %? 8. What must I pay for a 60-day sight draft for $600, the premium being i%, discount 6%? 4. What will be the cost of a draft for $1000 payable 60 day^ after sight, at a premium of j%, discount 6%? 194 EIGHTH YEAR STOCKS AND BONDS Stocks To a very great extent the business of the country is now conducted by corporate companies, called corporations. A corporation is regarded in law as an artificial person created by law for specified purposes and having specified powers. The capital stock of a corporation is divided into shares generally having a face or par value of $100 each and are usually spoken of as stocks. A corporation with a capital stock of $50,000 has 500 shares of $100 each which have been sold to different individuals. All who own any of the stock of a corporation are members of it and have votes in it in proportion to the number of shares of stock which they possess. If the corporation is large and its members widely scattered, the members elect a Board of Directors to manage the affairs of the corporation. The advantages of corporations are: (1) They enable a large amoimt of money to be collected from small investors who would not be able to invest this money profitably in small ' amounts. (2) The stockholders of a corporation are subject to a limited liability (usually the money invested in the stock) in the case of failure in the business of the corporation. In a partnership or an unincorporated company each person must stand responsible for the debts of the firm and even his private property can be taken to pay the debts of the firm. The certifixxAes of stock issued to the members of a corporation state the numbers of shares held, the face value of each and how the stock may be transferred. The following reproduction illustrates the form of a stock certificate: STOCKS AND BOND&-STOCKS Stock oerlificateB vary somewhat in statement, but the Comnton Stock Certificates are usually in the general form here illustrated. Exercise 8 1. What is the par value of each share of stock? S. How many shares of stock are there in this company? 8. In what state was this company incorporated? i. How may the stocks in this company be transferred? A dividend is a sum received for each share when all or a portion of the profits of a corporation are distributed to the shareholders. 8. If the dividends of the Regal Hat Company were $5000, how much of a dividend would be paid on each of the 500 shares? 196 EIGHTH YEAR 6. The dividend of $10 on each share would be what per cent of the par value of each share? 7. Will investors be anxious to buy stock that is paying 10% dividends when money usually only yields 6% interest? In order to secure stock which pays a high dividend, investors will pay more than the par value of the stock. They may pay $150 for a share of stock whose par value is only $100. Such stock would be quoted as worth 150 in the newspaper report of the stock exchange. The following were among the items in the report of a daily paper on the New York Stock Exchange for Nov. 11, 1916: Sales High Low Close Net Change 1. Am. B. Sugar 2900 102j 101 J lOlf - ^ 2. Am. Exp 200 139i 136 139| 3i 3. Am. Wool 1000 53 52f 53 -f 4. do.ipf 100 98 98 98 5. Beth. Steel 200 670 665 665 '-10 6. do. pf 600 152 149 152 We see from the above sales that stocks in items 1, 2, 5 and 6 are selling above par. Hence those companies must be paying good dividends to the investors. Items 3 and 4 show those stocks were sold below par. What are the net changes in each kind of stock since the preceding day? 8. Bring to the class for study extracts of the stock quo- tations in the daily paper showing a table similar to the above table. Large corporations sometimes issue stock of two kinds or classes, common and preferred stock. The preferred stock guarantees that all dividends up to a certain per cent of the par value must first be divided among the holders of the pre- ferred stock. If there are any profits left, they are distributed among the holders of the common stock. *The expression do. in the above table means the same as the preceding item and thus is a short way of expressing Am. Wool again. STOCKS AND BONDS— STOCKS 197 The stock quotations given in the preceding table show that the preferred stock in Item 4 is more valuable than the common stock in Item 3. That corporation then is not doing a profitable enough business to enable sufficient dividends to be paid regularly to the common stock holders. In Item 6 of the table, the common stock is selling at $670 per share. This extremely high price was caused by unusually large profits coming from the manufacture of munitions for i^e in the European War. The excess profits were divided as shown above among the common stock holders, thus making their stock much more valuable than the preferred stock in that company. The amount a broker receives for buying and selling stock is called brokerage. . In buying and selling stocks the brokerage is generally \% of the par value of the stocks. When stocks are bought, the brokerage is added to the market price to find the total cost. When stocks are sold, the brokerage is taken from the selling price to find the proceeds due the owner of the stock. If the class can secure data from some local corporation, a study of the organization of this local company will prove a valuable exercise. .Exercise 9 1. If a gas and electric company, incorporated, pays quarterly dividends, two of them being 3% and two of them 2%, what income is derived annually from 10 shares, of $100 each? 2. What will be the cost of 100 shares of stock of a certain railway (par value $100) if you buy them at 125% and pay \% brokerage? Solution: 125%+|% = 125|%. 125|%X$100 = $125.125, cost of 1 share. 100 X $125. 125 =$12,512.50, cost of 100 shares. 198 EIGHTH YEAR 8. A broker sells 200 shares ot American Express stock at 139 J%, brokerage J%. Find the amount of the proceeds which he sends the previous owner of the stocks. Solution: 139j%-i% = 139|%, proceeds from 1 share. 139i%X $100 =$139,125, proceeds from 1 share. 200X139.126 =$27,826.00, proceeds from 200 shares. 4. A broker sells 500 shares of American Wool preferred at 98, brokerage f %. What is the amount of the proceeds which he sends his principal? 6. If money is worth 5%, what must be the dividends from one share of the Bethlehem Common Steel in order for it to sell for 670? What per cent of the par value is this? Solution: 5% X $670 = $33.50, amount of dividends on one share. $33.50 =X%X $100. X% = ^i^= .335 or 33.5%, per cent of par value. 6. If money is worth 5%, what will be the market quotation for stocks of good security pajdng an annual dividend of $9.00 per share? $9.00 is 5% of what value? 7. If the common stock of a great steel manufacturing corporation is sold at 72% (par value $100 per share), what will be the cost of 300 shares, including brokerage at f %? 8. If the preferred stock (par value $100 per share) of a certain coal mining corporation sells at 115%, what will be the cost of 10 shares of it, including the brokerage of J%? 9. What profit is made by purchasing 100 shares ($100 each) of stock of a certain railway at 97% and selling them at 107%, paying f % brokerage for each transaction? 10. How much stock of a certain street car company, incor- porated, must be purchased to insure an income of $600 from it if the stock pays semi-annual dividends of 4%? STOCKS AND BONDS— BONDS While corporate companies usually provide the necessary capital for the conduct of their business, through the sale of stock certificaies, they may also provide for additional capital by the sale of bonds, which are generally secured by the tangible property of the corporation, and the bonds become the first lien on the business. In case of default in the payment when due, either of the accrued interest or of the principal, the holders of the bonds are in most instances legally empowered to sell the property of the corporation issuing the bonds, and to re-imburse them- selves from the proceeds. Bonds bear a fixed rate of interest, while the stock proceeds are governed by the earning power of the business. Bonds issued by the Federal government, by a state or by a county must be previously authorized by legislation, or by a direct vote of the people, who become the guarantors. On page 206 is ^ven an illustration of a typical city bond. In addition to the ugnatiu^ of the proper executive officers, all stocks and bonds must have affixed to them the seal of the government, the state, the county or the business corporation issuii^ them. (rest Seal FacrimUe ol the Seal used 3tat<^s. re- by a buaiaess corporatiOD, >i o( the reduced to about Hot Ota EIGHTH YEAR STOCKS AND BONDS— BONDS 201 Detachable interest coupons, or small dated certificates, are generally issued with and as a part of each bond. These are to be separated from the bonds and presented for payment on the dates named upon them.* Bonds, like stock oertificatea, necessarily vary more or lees in st&tement. The illustration on the preceding page showe the general form of a corporation bona, and the illustrations on this page tne general form of the detachable coupons. These coupons are usually transferable, beit^ deemed equivalent to cash, and are collectible by any person holding them. Bonds without coupons are called regist^ed bonds, and their transfer from one holder to another must be recorded upon the books of the corporation issuing them. What are the advantages of registered bonds in case of theft? Exercise 10 1. A village issues corporation bonds to the amount of $40,000 to build a school house. The bonds bear 5^% interest. What is the amount of interest paid to the bondholders in one year? S. If a man receives £480 for the coupons of his bonds, bearii^ 6%, what amount of the bonds does he hold? The coupons attached to a bond are numbered from right to left, or from the bottom up. In this way they may be detached in the order of number and dat«. For the bond here illustrated thirty-nine coupons are required — one for each semi-annual interest payment from January, 1915, to January, 1934 — covering a period of 20 years. 202 EIGHTH YEAR 8. In order to secure an income of $1200 annually, how many bonds of the denomination of $100, bearing 6% interest, must I buy? 4. A bank buys 50 U. S. bonds of the denomination of $1000, pajdng for them a premium of 3 J% and a brokerage fee of f %. What do the bonds cost the bank? 5. How much must be paid for the Gas and Electric Com- pany bonds of a certain city, at a premium of 3%, the brokerage being M%? 6. If I paid $3200 for bonds of the face value of $4000 and receive 6% interest on the face of the bonds, what do I receive in a year, and what per cent do I receive on my invest- ment? 7. Which is the better investment, a 6% bond bought at $92 for $100 face value, or a 6% bond bought at par? Suggestion: $6 is what per cent of $92? 8. What must be paid for 6% bonds in order to receive an income of 6% on my investment? Suggestion: $5 is 6% of what amount? 9. An American business corporation operating a rubber plantation in Mexico issues bonds for $60,000, payable in 15 years. If they are sold at $93 for $100 of par value, what is realized from them when 80% of the issue is "taken," or sold? 10. Find out what bonds have been issued in your commu- nity. For what amounts were they issued? What rates of interest do they bear? 11. If a conmiercial corporation issues bonds to the amount of $60,000 to run eight years at 7%, and after paying interest for five years fails, and after a year of delay pays only 78% of the face of the bonds, what does the holder of each $100 bond receive in all? INVESTMENTS 203 12. What would he have received on a 6% bond for the full period? 18. To secure an income of 8%, how much below par must I buy bonds bearing 6%? The organization of an imaginary corporation or a study of some local corporation by the class would prove an excellent means of understanding stocks and bonds. If the time permits, the class should undertake such a problem. INVESTMENTS The supply or amount of money on hand, together with the demand for loans, determines, to a large extent, the rate of interest which must be paid to secure a loan. If the supply of ready money is large and the demand for loans is weak, the rate of interest will be low. On the other hand, if the supply of ready money is small and there is a large demand for loans, the rate of interest will be high. The risk involved in a loan is also an important factor in determining diflferences in the rates of loans. If the risk of loss is great, a high rate must be paid to secure a loan. If there is very slight chance of any loss, the rate of interest is low. Many new enterprises are started in the United States every year. Some of these enterprises are successful and yield large dividends. On the other hand, a large per cent of these enter- prises fail and the investors suffer either a partial or a total loss. One should never take only the agent's word as to the safety of an investment, but should consult some reliable disinterested party who is well posted in the field of investments, such as a reliable banker or broker. The policy of "Safety First'' is a very good one to follow in the field of investments. 204 EIGHTH YEAR Exercise 11 1. U. S. Government bonds usually sell at or above par value v/hen the rate of interest is as low as 2%. Government bonds are non-taxable. What other reason is there for the rate of interest on government bonds being so low? 2. Municipal bonds usually bear from 4% to 5% interest. Why is the rate higher on these bonds than on U. S. Government bonds? Are these bonds taxable? 3. What is the usual rate that is paid on certificates of deposit or safety deposits in a bank? 4. Why are careful investments in real estate considered good investments? What are some disadvantages of such investments? 5. A certain company advertised that they would give 2 shares of common stock free with each share of preferred stock purchased before a certain date and claimed that both kinds of stock should soon be worth more than par. Would you invest in this stock? Why? 6. Another company advertises a certain sugar stock that will pay 10% on the investment. How would the risk on this investment compare with a good municipal bond yielding 5% interest? 7. The following advertisement appeared in a daily paper: "Absolutely safe, exceptionally profitable, long-time invest- ment;^ as good security as municipal bonds, with five times the returns." As an investor, how would that advertisement appeal to you? • 8. An agent for a certain mining company was selling stock at about f of the par value. He stated to a prospective buyer that he would guarantee that the value of the stock would ^Teachers should show that the investment could not yield five times the returns if the security was as good as municipal bonds. INVESTMENTS 205 double in less than 6 months. Would you have bought this stock on the strength of the agent's statement? 9. An insurance company loaned a farmer $3000, taking a first mortgage^ on his farm valued at $5800. Was this a safe investment for the insurance company? 10. If you had $20,000 to invest, would you invest it in one place or divide it among several forms of investment? Discuss the advantages and disadvantages of both of these methods. Exercise 12 1. A girl deposited $75 in a State bank, deceiving a certifi- cate of deposit, bearing 3% interest. How much interest should she receive at the end of 6 months? 2. How much interest would she have received in a Postal Savings bank for 6 months at 2%? Was her risk of losing her money any greater in the State bank than it would have been in the postal savings bank? 8. If I buy a'^municipal bond bearing 4^% interest for $106.50, including brokerage, what is the rate of income on my investment? Suggestion: $4.50 is what % of $106.50? 4. What is the rate of income on stock costing $138.50, including brokerage, if the yearly dividend amounts to $6.50 per share? 5. In deciding which is the better investment, a municipal bond bearing 4^% interest, quoted at 106f , or a stock quoted at 138| and known at that time to be yielding yearly dividends of $6.50 per share, what other factors must be considered besides the present rate of income? *A mortgage is a contract by which the owner of the property agrees to let the party loaning the money sell his property to secure payment for a loan if he fails to meet the terms stated in the contract. 206 EIGHTH YEAR 6. A man wishes to buy a city residence. It rents for $60 per month, and he estimates that his expenses for this property would amount to $240 a year. How much can he ofifer for the property if he wishes to secure an income of 6% on his invest- ment? 7. A carpenter in a certain village bought a house for $1875. After spending $400 on improvements, he sold the property for $2850. Find his per cent of gain on the money invested. 8. An 80-acre farm sold for $4000 in 1900. In 1903 the same farm was sold for $4800. In 1915 it was sold for $9000. Find the per cent of increase in its value between 1900 and 1903 ; between 1903 and 1916. What other returns were secured by the owners beside the increase in the value of the land? 9. Mr. Bentley inherited $5000 from his father. He has an opportunity to loan it to a farmer at 5% on a first mortgage on a farm valued at $12,000 or invest it in a pecan grove which an agent assures him will yield 10%. His banker tells him the latter investment is very risky. Which shoyld he take? 10. An agent of a mining company canvassed the citizens of a small village to sell mining stock. He told them that the company wanted to keep the stock from getting into the hands of rich capitalists. Would this statement have induced you to buy or deterred you from investing in the stock? 11. A company invests $12,000 in "stump lands,'' from which the pine timber has been removed, and $3000 in machinery to uproot and pulverize the stumps, for the extraction of turpentine. The annual profit is 15% on the investment, for four years, at the end of which time the land has doubled in value, and the machinery is sold for half the cost price. What is the real per cent of annual profit? 12. Does it pay to invest money in an education? See if you can get figures to prove your answer to that question? CHAPTER III REMITTING MONEY On account of the heavy expense of shipping actual money, much of the business of the country is carried on by means of commercial forms of various kinds. Postal Money Order One of the most common forms for sending small amounts of money is the postal money order. The government charges a small fee for these orders, varying with the amount of the order. snoo, Ut Angdet, CaL 193989 United stales Postal Mone y Order A^C-jT^ — "^ ■wnkMMA nemn. nu, mv of piiiBiuwSg JiL4^)^^||^[2XU TAC-SDIZLI. or NO VAUUT . I' ^ " Coupon lofPiTtatOffl*"^ •Jr ' MtnHMnoinnMUM MOMS THAU LAIWI IMOieATlDOfI OP TMi owom 2 THHOII AMY ALTBlfr ■wrrt The following Not exceeding Exceeding % 2 Exceeding 5 Exceeding 10 Exceeding 20 Exceeding 30 Exceeding 40 Exceeding 50 Exceeding 60 Exceeding 75 table shows the fees for the various amounts: $2.50 3^ .50 and not exceeding % 5.00 ^i .00 and not exceeding 10.00 8|i .00 and not exceeding 20.00 \^i .00 and not exceeding 30.00 \2i .00 and not exceeding 40.00 15|i5 .00 and not exceeding 50.00 \%i .00 and not exceeding 60.00 20^ ,00 and not exceeding 75.00 25^ .00 and not exceeding 100.00 30|4 207 208 EIGHTH YEAR Actual money may be sent by registered mail for a charge of 10 cents in addition to the regular postage. An indemnity not to exceed $25.00 will be paid by the government if a first- class package or letter is lost. Exercise 1 1. How much will money orders for the following sums cost: $2.50; $15.00; $30.00; $52.14; $7.26; $76.00? 2. Which will be cheaper, to send $25 in a letter by regis- tered mail or to buy a postal money order for $25? (The postage on the letter is extra in both cases.) 3. Which is cheaper, sending $10 by registered mail or sending a postal money order for $10? 4. What is the fee on a postal money order for $5.00; for $50.00; for $100.00? Express Money Orders Express companies issue express money orders which are similar in form to the postal money order and for which the same fees are charged. The table on page 213 may also be used in computing charges on express money orders. FMPRrSS MOUC DHUI *^'".S2Si:ifSS?r*i« - 15- 0000000 • AM PLC- INOTOOOO^ ftKCMHBnwiMta LJY ^ r^^ - ^^^ !^ ls ^ ^fff^^^fT^;:rT^r^^^rJ^ ! ^ ^^ I SJtJt tmmtmmam m mm An Express Money Order REMITTING MONEY— DRAFTS 209 Exercise 2 1, Who purchased the express money order here shown? 2. To whom is this order made payable? S. How could Mr. Brooks transfer this order to some other person for collection? *■ How much will an express money order for $18.75 cost? 8, How much will an express money order for $50 cost? Bank Drafts A bank draft is really a check by one bank on another bank. For regular patrons of the bank who have checking accounts, most banks write drafts for small amounts without extra charge as a matter of accommodation. For large amounts drafts are sold at a premium or a discount, depending on the state oi the balance between the banks of the two cities involved. A Bank Draft Exercise 3 1. Where was the above draft purchased? 2. To whom was it made payable? 8. How can it be transferred to some other person? 210 EIGHTH YEAR 4. On what bank is the draft drawn? 5. A fanner wishes to pay off the mortgage on his farm that is held by a certain insurance company. He finds that tjbe rate for a draft on the city where the insurance company is located is 20 cents per $100. Find the cost of the draft for $3000. 6. How much would an express money order for the same amount have cost him? Checks Business firms and most individuals have checking accounts in some bank. Instead of buying drafts, most firms send checks to settle their accounts. A check is returned by the local bank to the firm who issues it when the account is bal- anced. The check thus serves as a receipt for the transaction. ORpEROl PA/TOTHFr^^ 5^ >f .^, ^^ ^^JJ^'JJP. ^'j ^^.^f ^^ '^^A/^.^y^.^^^y^/^s^:^ ^^ /^ -^ •^■*-*^ '^^^jy?tZ&ty AdjC^tjC^'oa^*^*^ A Business Firings Check Exercise 4 1. What firm issued the above check? In what bank do they carry their banking account? 2. To whom is this check made payable? 8. When the check is returned to the First National Bank of Boston for collection, how will they enter it on their accounts? REMITTING MONEY— CHECKS 211 "^'FiRSTllSmo: "j/g/T ,A f /4/^ OF €HI€A002-i PAY TO THE ORDER OF J 973647 A Personal Check 4. Who issued the above personal check? To whom is it made payable? Show how this check would have to be indorsed when it is cashed. (See page 190.) 5. If a certain man has a balance of $125.82 in the bank on Jan. 1, 1917, and issues three checks as follows: for rent, $35.00; for light bill, $1.58; for gas bill, $2.56; how much will he have to his credit in the bank? 6. Mr. Hill issues Mr. Johnson a check for $25.00 to pay for services rendered. Mr. Johnson loses the check and promptly notifies Mr. Hill of his loss. How can Mr. Hill arrange to pay Mr. Johnson without danger of having to pay twice should the check be found at a later date? 7. Why do banks refuse to cash checks for strangers? 8. Discuss the advantages and disadvantages of remitting money by means of checks. Foreign Remittances Remittances to foreign countries may be made by inter- national money orders, by foreign express orders or by foreign drafts called hiU% of exchange. 212 EIGHTH YEAR Emergency Remittances When an agent wishes money immediately in order to close an important transaction, he often finds it an advantage to have his firm telegraph him the money. In the telegram in the illus- THE WESTERN UNION TELEQRAPH compaiiy' tration Richard Doe of Wash- ^«« 1 — ^*^ ^ ington is sending his brother tC^^^^sZiL^A^Mp^ •^^^. ^^ "^ ^®^ Orleans a Tragwrf ^o, ^ . Certain sum of money by tele- ^ o^ OL .di^ ^ y7' ^ ^^ graph. In order to prevent ^/a,..^^^y^ — f jy^ ^ ^^ji^f^ ^,>^, Others from leammg about the ^^f a^ /tM-^^uj- ^^4oA^in, < ^,fe amount of money involved in nL-w« .va^y Mpfit — the transaction, the message is ,__ ^^ expressed in terms of a code. The word ring in the tel^ram refers to the amount of money and can be understood only by a person familiar with that particular code. Note the writing in the last line. It was made by the sending agent with his left hand while he was transmitting the message with his right hand, showing a high degree of efficiency in operation. Upon the receipt of this message, the agent in New Orleans sends to John Doe the following notice: "We have received a telegraphic order to pay you a sum of money upon satisf actoxy evidence of identity. The amount will be paid at our office if called for within 72 hours; other- wise under our arrangement with the remitter the order will be canceled and the amount thereof refimded." When money is remitted by telegraph, there is a transfer charge on the money in addition to the regular charge for the telegram which is computed on the basis of a 15-word message. Exercise 6 1. In remitting $25 (or less) by telegraph between certain cities, the charge for that amount is 60 cents. The telegraph charges between these cities is 36 cents for a 15-word message. Find the transfer charge for that amount. REMITTING MONEY— BY CABLE 213 2. What would be the cost of remittmg $25 by an express money order? How much cheaper is the express money order than the remittance by. telegraph given in Problem 1? When is money usually remitted by telegraph? 8. The cost of a 15-word message between two cities is 35 cents. What will be the total charges for remitting $100 by telegraph if the transfer charges for the money are 85 cents per $100? 4. The charges for remitting $200 by telegraph between those cities are $1.45. How much is charged for the extra $100? At the same rate per $100 beyond the first $100, what will be the charges on remitting $1000 between those cities? Remitting by Cable If an emergency arises for a quick transmission of money to a firm or person in a foreign country, money can be remitted by cable in the same manner that it is telegraphed in this country. The amount of the money is then expressed in the money values of the foreign country to which it is sent. The following illustration shows a form for such a cablegram: In the cablegram shown in the illustration ^'Bruzzolo, Lon- don" stands for the registered address of the London telegraph office that pays the money. "Rabbit" is a guard word neces- sary in sending such messages. *'Jewel" is the code word for "pay to." "John Doe, 76 Downing Street, London" is the payee. "Bracket" is a code word which stands for the amount to be paid John Doe. ^'-^<e>rvCibf£tL ... <( Darby" means "from." "Richard Roe" is the name of the sender of the money and "Jentant" is the code word standing for the signature of the transfer agent at New York. 214 EIGHTH YEAR Exercise 6 The charges on sending money by cablegram are $4.65 for the cable charges (15 words) and 1% premium on the amount of money sent. 1. Find the total amount that must be paid the agent in New York to remit $100 to a party in London. 2. What will be the transfer charges on remitting $500 by cable? Find the total amount which must be paid the transfer agent in this country. 3. If the word "Bracket" stands for $250, how much did Richard Roe have to pay the transfer agent in New York? 4. Find the total transfer charges by cable on $300, on $1000, on $5000. Remitting Money by Wireless To facilitate business, leading banks and express companies, in normal times, keep large amounts of money on deposit at the principal conmiercial centers in the European countries. During the period of the European War communication with certain countries in Europe was maintained mostly by radio means, and the transmission of money by "wireless" reached large pro- MONIY REMITTED BY WIRELESS —TO— knaif lid Anlrli-llnpiy 4MI Fort iMftrtMra National Bank portions at rates indicated in the following problem: Exercise 7 1. A firm in Chicago remitted $1000 by a wireless radiogram to a firm in Berlin on Jan. 28, 1917. The charges were quoted by the bank at $4.00 per order of 6 words, plus the usual postal charges of 15 cents per order, excess words to be paid at the rate of 57 cents per word. If the radiogram contained 9 words, what were the charges on the radiogram? FOREIGN MONEY AND TRAVEL Foreign Money and Travel Our trade and travel among foreign nations are so exten- sive that some knowl- edge of the money systeans of those nar lions is a dedrable acquisition fw any my or girL The f oUowing table l^vee the essential Facta in the mon^ systems of some of the leading foreign countries: Courtny White Stu lins Countey Monty Unit Equivalent in Lower Value of Unit inU.S. Money Great Britain £ (pound) 20 shillings $4.8665 mark 100 pfenn^e 100 centimes .238 France .193 Auatoia-Hungaiy.. krone 100 heUer .203 Itafer lira 100 centesimi .193 Spain 100 centimoa .193 drachma 100 leptBs 100 gulden 100 ore .193 HollMid guilder krone .402 Den.,Nor.aiid8we. .268 Russia ruble 100 kopeks .518 Japan 100 aen .498 Portugal milreis 1000 reis 1.08 Brazil milreie 1000 reia .646 All of these systems are centesimal except those of Great Britain, Portugal and Brazil. Money in the centesimal systems is treated as oiu* dollars and cent«, the decimal point wparating ttte larger unit from the smaller denonmiations. 216 EIGHTH YEAR Exercise 8 1. How many shillings are there in 3 pounds 4 shillings? 2. What is the value in U. S. money of £20? 3. What is the value in English money of $486.65? 4. What is the value in U. S. money of a shilling? 6. 12 pence = 1 shilling. What is the value in U. S. money of an English penny? «. Reduce to U. S. money 2 francs, 46 centimes. Solution: 1 franc = $.193. 2 francs, 46 centimes = 2.46 X $.193 = $.47285 or 47 cents in U. S. money. 7. What is the simi of 4 francs 5 centimes; 6 francs 15 centimes; 26 francs 10 centimes; and 15 francs 76 centimes? What is the value of this sum in U. S. money? 8. What is the siun of 20 marks 15 pfennig; 42 marks 26 pfennig; 68 marks 40 pfennig; and 12 marks 20 pfennig? Express the value of this simi in U. S. money. 9. Add 14 pesetas 10 centimos; 16 pesetas 18 centimos; 25 pesetas 14 centimos; and 26 pesetas 58 centimos. Find the value of this sum in our money. 10. Add 60 yen, 30 sen; 46 yen, 15 sen; 26 yen, 45 sen; and 14 yen, 20 sen. What is their exact equivalent in our money? Exercise 9 Many travelers in foreign countries use rough estimates where small sums are spent for personal expenses. A franc or lira or drachma or peseta is called 20 cents; a ruble or a i^en a "half-dollar," and a vmrk or a krone a "quarter," etc. In the following problems the money unit of the country visited and its centesimal parts are left to be stated by the pupil: FOREIGN MONEY AND TRAVEL 217 1. If, when visiting Marseilles, your expense for a luncheon and for table service is 2.05, for carriage hire 10.15, and for a souvenir 1.20, how will you compute the total? What will be its approximate equivalent in American money? What its exact equivalent? 2. If in Rome the charge for your hotel room is 6.10, for meals and table service 9.10, for street car and carriage expense 20.15, for a guide 10.20, and for souvenirs 14.50, what will be the total? What will be its approximate equivalent in American money? 3. If in Copenhagen you pay 1.90 for a luncheon, and 7.50 for a drive about the city, what will be the cost of both, and what its approximate equivalent in American money? 4. If a friend writes you from Lisbon that he paid 3000 reis for an automobile ride, what do you understand to be the cost of the ride in American money? 6. If at Paris he buys a souvenir for 2 francs 50 centimes* at Rome another for 4 lira 10 centesimi, and at Barcelona another for 3 pesetas 50 centimos, what is the approximate sum of the purchases in U. S. money? 6. If a friend in Rio de Janeiro writes to you that he has invested 5000 milreis in mate, or Paraguayan tea, what do you understand to be, in U. S. money, the amount of his investment? 7. If in Moscow an American tourist pays for a week's board and lodgings 16.20, for souvenirs 4.20, and for carriage and guides 60.00; what is the approximate expenditure for these, stated in U. S. money? What is the exact amount? 8. If in Rotterdam one of your traveling friends states that he paid 1.50 to a hack driver and 3.10 for souvenirs, together with 1.10 each for breakfast, lunch and dinner, what was the amount of these expenses, roughly stated in U. S. money? What was the exact amount? EIGHTH YEAR Travelers* Checks Exercise 10 Touiist companies, express companies, and sometimes banks, issue travelers' checks, in convenient amounts of $200, $100, and sometimes $20 and $10, or other sums, for travelers to carry with them on tours to foreign lands. These are bound together in the form of a folded check book, and are detachable one at a time. The purchaser of a book of such checks must sign each one of them in the office at which he procures it, and f^terwarda, when he cashes it, at one of the fore^ agencies of the company or bank issuing it, or at one of their agencies in his own country. 1. If I buy travelers' checks to the amount of $480.00, and pay J% of the aggregate face of them for the accom- modation, what do the checks cost me? How much do I receive for them in London? 2. If, instead of cashii^ all the checks in London, I cash those for half the amount in Paris, what do I receive for them? If in Rome what? If in Madrid what? 8. If I cash all the checks in Berlin and Munich, what do I receive for them? 4. If I cash half the amount of the checks in Moscow and half of them in Amsterdam, what do I receive for them? CHAPTER IV PRACTICAL MEASUREMENTS Exercise 1. Review of Quadrilaterals 1. State the principle for finding the area of a rectangle. 2. What is the area of a rectangle 16 inches long and 8f inches wide? (See page 137.) 3. Find the number of square yards in the area of a baseball diamond which is 90 feet square. 4. How many square inches are there in a sheet of paper 8§ inches by 11 inches? How many square feet of space would a ream of 600 sheets of this paper cover if the sheets were placed edge to edge? 6. How many square feet are there in a rectangular garden 15 yards long and 30 feet wide? How many square yards? 6. A certain farm is 1^ miles long and f of a mile wide. How many square rods does it contain? How many acres? 7. A field 60 rods long and 40 rods wide yielded 360 bushels of wheat. What was the yield per acre? 8. There are usually 40 apple trees planted on an acre of ground. How many square feet of space does that allow for each tree? 9. A ball club bought a field for a ball park. It was 400 feet long and 395 feet wide. How much did it cost at $310 an acre? 10. School architects usually allow 16 square feet of space as the proper amount for each pupil. How many pupils can be properly seated in a school room 24' x 28'? 219 220 EIGHTH YEAR 11. How many pupils are there in your school room? Find the number of square feet of floor space for each pupil, using the total area of the room for the computation. 12. The area of a rectangle is 96 square inches and the base is 16 inches. Find the altitude. 13. The area of a rectangle is -3^ of a square foot. The width is f of a foot. What is the length? 14. Find the area of a parallelogram with a base of 18 inches and an altitude of 12 inches. (See page 142.) 16. The length of a parallelogram is f of a foot and the alti- tude is f of a foot. What is its area? 16. Find the area of a trapezoid with its parallel sides equal to 8 inches and 15 inches and its altitude equal to 12 inches. (See page 144.) 17. Two converging roads form a field in the shape of a trapezoid. The two parallel sides are 60 rods and 100 rods and the altitude is 64 rods. How many acres are there in this field? 18. How much is this tract of land worth at $175 an acre? Exercise 2. Review of Triangles 1. State the principle for finding the area of any triangle. 2. What is the area of a triangle whose base is 8 inches and whose altitude is 7 inches? (See page 146.) 3. The area of a triangle is 54 square inches and the altitude is 9 inches. Find the base. 4. The area of a triangle is ^ of a square foot and the base is f of a foot. Find the altitude. 6. A triangular flower bed has a base of 3 yards and an altitude of 4 yards. Find its area in square yards. PRACTICAL MEASUREMENTS— SQUARES 221 Squares and Square Roots A square is a rectangle with all of its sides equal. What kind of angles has a square? If a side of a square is 4, the base and altitude are each-4, and the area of the square is 4X4, or 16. ^ Square 16 is called the square of 4. This may be written 4^ = 16. The small figure 2 at the upper right hand side of the four is called an exponent. An exponent shows how many times the number is taken as a factor. For example, 5* means that 5 is taken twice as a factor, or 5X5. Exercise 3 1. Make a table showing the squares of all numbers from 1 to 25 as follows: 1P=? 12«=? 132=? 142=? 152=? 2. Learn this table so that you can give any square quickly. 3. What are the squares of 30, 40, 50, 60, 70, 80? Since 16 is the square of 4, 4 may be called the square root of 16. The two equal factors of 16 are 4 and 4. One of the equal factors of a number is called the root of the number. In order to find the square root of a number, we must find a factor which, when multiplied by itself, will give the number. Square root is very important in solving problems in right triangles. 4. What are the square roots of 4, 9, 25, 36, 49, 64, 81, 100, 144, 225, 625? 1*= 1 6*=? 2«= 4 7*=? 3"= 9 8*=? 4* =16 9*=? 6*=25 10*=? 16«=? 21*=? ir=? 22*=? 18*=? 23*=? 19*=? 24* = ? 20*=? 25*=? 222 EIGHTH YEAR 6. Find the square root of 1296. The number 1296 is larger than any of the squares that we have learned, so it is more difl&cult to see the square root of this number than those in Problem 4. Try different numbers until you find one which multiplied by itself will give 1296. There is a much more convenient method of finding the square root of a number than trying various numbers until we find the correct one. The following form shows the method of extracting the square root of a number: Extracting the Square Root of a Number 1. Begin at the decimal point and point 1296 36 ^ff ^^® number into periods of two figures 9 each (12'960. 66 396 2. Find the largest square (9) in the left- 396 hand period (12). Put its square root (3) as the first figure of the square root and subtract the square (9) from the first period (12). 3. To the remainder (3) bring down the next period (96). 4. Take two times the number in the root (3) and use this product (6) as a partial divisor into the first figure or two figures of the remainder (396). Place the figure thus obtained (6) as the next figure of the square root. Also add this figure (6) to the partial divisor, making the complete divisor (66). 5. Multiply this complete divisor by the last figure of the root (6). 6. If there are other periods proceed, as in steps 3, 4 and 5. There is no remainder in this problem. The square root, then, of 1296 is 36. By reference to the following diagram on cross section paper the reasons for the various steps in the preceding problem can be understood: PRACTICAL MEASUREMENTS— SQUARE ROOT 223 When the number 1296 is separated into two periods, the period 12 really stands for 1200 and contMos the square of the tenS' figures in the root. The largest square of tens contained in 1200 is 900 or the square of 3 tens (or 30). Note in the diagrajo at the right the large square of the three tens (or 30) which contuns 900 of the small squaxea. In order to find the units figure, the 900 must be taken from the 1200, leaving 300 of the small squares. To these must be added the ne3rt period, 96, making the total remainder, 396. This means that 396 small squares compose the two rectangles and the small square at the top and right-hand side of the figure. Since the two rectangles have the same length as the large square, each rectat^le is 3 tens or 30 units long. There are two of the rectangles and so both of them are 2X3 tens or 6 tens or 60 imits long. Using 60 as a partial divisor Into the 396, we can find the altitude of the rectai^es, which we find to be approximately 6 units. Adding the length of the small square (approximately 6) to the length of the two rectangles, we have a rectangle which is approximately 66 units loi^ and 6 units wide: 224 EIGHTH YEAR When the base 66 of this long rectangle is multiplied by the altitude 6; we find that the two rectangles and the small square which formed this long rectangle were composed of 396 small squares, which made up the remainder after the large square had been subtracted from the figure. The square root then consists of 3 tens and 6 units, or 36. Exercise 4 Find the square roots of the following numbers: 1. 256 8. 3969 16. 3249 2. 1156 9. 5041 16. 116964 3. 1764 10. 11025 17. 173889 4. 4489 11. 18225 18. 822639 6. 3364 12. 1225 19. 123904 6. 5184 13. 6889 20.' 229441 7. 7056 14. 9604 21. 42436 Find the square roots of the following numbers: 1. 3 '3.00'00'00ll.732+ 1 27' 200 189 343 1100 1029 34€ >2 7100 6924 If the square root does not come out as an integer, add ciphers in periods of two each and proceed as in other problems. For practical pur- poses it is not necessary to carry the result beyond 3 decimal places. 2. 15. 4. 34. 6. 50. 8. 5. 10. 83. 3. 13. 6. 12. 7. 18. 9. 16. 11. 45. Compare your results in these problems with the values found in the following table: PRACTICAL MEASXJREMENTS— SQUARE ROOT 225 SQUAKB ROOTS OF NUMBERS From 1 to 100, Carried to Three Places of Decimals Number Square Root Number Square Root Number Square Root 1 1 34 5.831 67 8.185 2 1,414 35 5.916 68 8.246 3 1.732 36 6 69 8.307 4 2 37 6.083 70 8.367 5 2.236 38 6.164 71 8.426 6 2.449 39 6.245 72 8.485 7 2.646 40 6.325 73 8.544 8 2.828 41 6.403 74 8.602 9 3 42 6.481 75 8.660 10 3.162 43 6.557 76 ' 8.718 11 3.317 44 6.633 77 8.775 12 3.464 45 6.708 78 8.832 13 3.606 46 6.782 79 8.888 14 3.742 47 6.856 80 8.944 15 3.873 48 6.928 81 9 16 4 49 7 82 9.055 17 4.123 50 7.071 83 9.110 18 4.243 51 7.141 84 9.165 19 4.359 52 7.211 85 9.220 20 4.472 53 7.280 86 9.274 21 4.583 54 7.348 87 9.327 22 4.690 55 7.416 88 9.381 23 4.796 56 7.483 89 9.434 24 4.899 57 7.550 90 9.487 25 5 58 7.616 91 9.539 26 5.099 59 7.681 92 9.592 27 5.196 60 7.746 93 9.644 28 5.291 61 7.810 94 9.695 29 5.385 62 7.874 95 9.747 30 5.477 63 7.937 96 9.798 ' 31 5.568 64 8 97 9.849 32 5.657 65 8.062 98 9.899 33 5.745 66 8.124 99 100 9.950 10 You will find it an advantage to use the preceding table to find the square roots of all numbers between 1 and 100. Engineers and advanced eUidents of mathematics and science use books with similar tables. 226 EIGHTH YEAR Exercise 6 1. The area of a square is 64 square inches. What is the length of one side? 2. The area of a square is 40 square inches. What is the length of one side? 3. A square field contains 40 acres. What is the length of one side in rods? 4. What is the length of one side of a square whose area is 81 square yards? 6. What is the length of one side of a square whose area b 64 square yards? 6. By the use .of the table find the square roots of the following numbers: 17, 56, 97, 62, 43, 35, 2, 5, 77, 32. Right Triangles A right triangle has one right angle. The other two angles of a right triangle are always acute. In the right triangle A B C, A C and A B are called the legs and B C is called the B hypotenuse. Suppose the side A C is 3 inches long and A B is 4 inches long, as shown in the figure below: Exercise 6 1. How many square inches are there in the square constructed on the leg that is 4 inches long? 2. How many square inches are there in the square constructed on the leg that is 3 inches long? vV ■/y V / PRACTICAL MEASUREMENTS— RIGHT TRIANGLE 227 3. How many square inches are there in the square on the hypotenuse, which is shown to be 5 inches long? 4. How does the square on the hypotenuse compare in size with the number of square inches in the sum of the two squares on the legs? This relation may then be stated in the following principle: PRINCIPLE: In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.^ Exercise 7 1. The two legs of a right triangle are 15 feet and 20 feet. Find the hypotenuse. Solution: 152=225; 202=400. The sum of the squares on the two legs = 225+400 = 625, which is equal to the square on the hypotenuse. The hypotenuse then must be the square root of 625 which is 25. Therefore: The hypotenuse is 25 feet long. 2. The hypotenuse of a right triangle is 20 inches and one of the legs is 12 inches. Find the length of the other leg. Solution: Since the square on the hypotenuse (400) is equal to the sum of the squares on the two legs, the square on either leg must be equal to the difference between the square on the hypotenuse and the square on the other leg (144). The square of the unknown leg =400— 144 = 256. The leg is the square root of 256 = 16. Therefore : The leg is 16 inches long. 8. A right triangle has two legs equal to 6 feet and 8 feet. What is the length of the hypotenuse? ^This principle was first stated by Pythagoras, a Greek mathematician, over 2000 years ago. 228 EIGHTH YEAR These dimensions are very frequently used in constructing a right angle with cords. By making the two sides 6 feet and 8 feet and then using a 10-foot cord to regulate the spread of the two sides an accurate right angle can be formed. Find the missing leg or the hypotenuse in the following problems: (Carry to three decimal places if the result does not come out even.) Leg Hypotenuse 12 in. ? ? 17 in. 32 ft. ? 24 in. 30 in. 11 in. ? ? 18 rd. 36 in. ? 11. What is the length of the diagonal of a square that is 8 inches on each side? 12. A baseball diamond is 90 feet square. How far is it from first base to third base? 13. A congressional township is 6 miles square. How long would a road be if it ran on the diagonal line of the square? How much shorter is this road than one which goes along the two sides of the square to the opposite comer? 14. Draw a square 4 inches on each side. Divide it into two equal squares. Suggestion: Draw the two diagonals as shown in the illustration. Cut along the dotted diagonals, thus dividing the square into 4 parts. See if you can arrange these parts so that they will make two smaller squares. 15. How long is the side of one of the small squares? PRACTICAL MEASUREMENTS— PROBLEMS 229 16. Two boys were making a model of an automobile in a wood shop. They were making out a bill for lumber which they wished to order. The sides of the hood were 12 inches apart, and they wished to make the ridge 4 inches above the tops of the sides. Their problem was to find how wide to order the slanting boards for the top of the hood. How wide should they be in order to leave no waste? 17. A girl wished to put up a window shelf for flowers. The distance of the edge of the board from the wall is 10 inches and the bottom of the board is 16 inches above the baseboard. She wanted to cut her props so that they would reach from the outer edge of the board to the top of the base- board. How long must she cut her props on the outside edge so that her shelf will make a right angle with the wall? 18. A ladder 27 feet long leans against a house from which its base is separated by a distance of 18 feet. How high from the ground is the top of the ladder? 19. A man has a piece of land in the shape of a right triangle. He measures the two legs and finds them to measure 21 rods and 28 rods, respectively. Show how he can compute the amount of fence which he will need to enclose the field, without actually measuring the other side. 20. In building a chicken house of the dimensions shown in the diagram, a man wished to cover the top with ship-lap boards which were to extend 6 inches over the edges at each end. How long must he order his boards for this roof? 230 EIGHTH YEAR 21. At one comer of a level rectangular field 8 rods long and 6 rods wide is a tower 165 feet high. How long a wire will be required to reach from the top of the tower to the ground at the comer diagonally opposite? Note that you must use two right triangles to solve this problem. 22. In the figure representing the end of a bam you find the dimensions given. How long must the builder order his rafters for this bam if he wishes them to project 1 foot at the eaves? 23. A man setting a telephone pole which projects 25 feet above the ground wishes to brace it with a wire attached 6 feet from the top of the pole to a stake 30 feet from the base of the pole. How long must he cut his wire if he allows 3 feet additional for fastening the brace at both ends? 24. Construct very accurately a right triangle. Then draw accurate squares on each of the three sides as shown in the illustration. Extend the sides of the large square as shown in the diagram and draw a line perpendicu- lar to the dotted line, as shown in the square on the long leg. Number the parts of the small squares and cut them out. If you arrange them properly, they will cover the square on the hypotenuse. See if you can arrange them in the right order, showing that the sum of the squares on the legs is equal to the square on the hypotenuse. This is a practical way of proving the principle on page 233. % % 1\ \ •"5 PRACTICAL MEASUREMENTS— PROBLEMS 231 The pitch or slant of the roof of a house is found by dividing the height above the eaves by the width of the house. In the illustration the pitch is 12-5-24, or ^. 26. How high would the ridge of the house be above the eaves to give a pitch of f ? 26. Find the length of a rafter for a house with a width of 24 feet and a pitch of f , allowing 1 foot for a projection at the eaves. 27. The pitch of a house 30 feet wide is J. Find the length of a rafter for this roof, allowing 1 foot for a pro- jection at the eaves. A carpenter can very readily determine the length of a rafter by using a ruler and the steel square. Along one arm of the square he lays off a number of inches equal to the number of feet in f of the width of the house. Along the other arm he lays off the height of the ridge above the eaves, using inches to represent feet. A ruler joining these points as shown in the illustration will show the number of feet in the rafter. -29 ■n -V -3» ■» -» -17 » -B -M -B -9 -» -r 6 hs 4 3 -8 -1 ? ^^??T??y 28. Find by this method the length of a rafter for a house 24 feet wide and a pitch of §. Equilateral Triangles The altitude of an equilateral triangle is a perpendicular drawn from the vertex (C) to the base (A B). The altitude divides the equilateral triangle into two equal right triangles. Measure A D and D B to show that they are equal. 232 EIGHTH YEAR Exercise 8 1. An equilateral triangle has each of its sides equal to 12 inches. What is its perimeter? 2. What is the altitude of an equilateral triangle with each side equal to 10 inches? Solution : Since A B = 10 inches and A D = D B , then D B = 5 inches. In the right triangle D B C, B C = 10 inches and D B=5 inches. 102-52= 100-26=75. The square on C D must be 75. C D then is the square root of 75, or 8.66+ . Therefore: The altitude of an equilateral triangle with a side of 10 inches is 8.66+ inches. 3. Find the altitudes of the following equilateral triangles and fill out the table as indicated: pROButn Length or siot or EQUILATERAL TRIANGLEr LENGTH or Altitudi:, ALTITUDE, -7- SlDt . I 10 8.66+ .866 4- 2 12 « ? 3 8 ? • 4 16 *? P 5 6 '? • 4. What do you find the quotient of the altitude divided by the side of each equilateral triangle to be? Since we have found that the altitude of any equilateral triangle is .866 of the side, we may now use this fact and save ourselves a great deal of computation. 6. Find the altitude of an equilateral triangle whose side is 25 inches. Solution: .866X25 inches=21.65 inches. 6. Find the area of an equilateral triangle whose side is 8 inches; one whose side is 5 inches. PRACTICAL MEASUREMENTS— CIRCLES 233 Circles A circle is a figure bounded by a curved line every point of which is at a given distance from a point within, called the center. The bounding line is called the cir- cumference of the circle. A straight line drawn through the center of the circle and terriiinating at both ends in the circumference is called a diameter of the circle. The distance from the center to the circumference is called the radius of the circle. The diameter is how many times as long as the radius? Class Experiment The problem is: To find the ratio^ of the circumference of any circle to its diameter. The ratio of the circumference to the diameter (C-r-D) is known as jd and is designated by the Greek letter tt. Each pupil in the class should measure very carefully the circumference of some circular object. This may be done with a tape line or by measuring with a string and then measuring the length of the string with a ruler. Then measure the diameter of the same object. Next divide the circumference by the diameter and carry out the quotient 4 decimal places. Enter the results found by each member of the class in a table similar to the form given below, reduced to decimals: PUPlL C IRCUMFERENCi: DiAMETCR ir=c-^D. RlCMARD T^Ot 4.125 in. 1.3125 in. 3.1428+ • ^The ratio of one number to another is the number of times the first contains the second. For example, the ratio of 8 to 4 is the niunber of times 8 contains 4, or 2. 234 EIGHTH YEAR Find the average value of tt for all the pupils in the class and compare the value which you have found with the accurate value 7r= 3.1416. Since ir is the quotient of the circumference divided by the diameter, the circumference is equal to the diameter multiplied by TT, or C = 7rXD. Since the diameter is twice the radius, C =ir X2 r, or 2irr. In formulas the sign X is frequently omitted, but the expres- sion 27rr is understood to mean 2X7rXr. It is much shorter to write it 27rr. Exercise 9 1. Find the circumference of a circle whose diameter is 8 inches. Solution: C = 7rD=3.1416X8 inches =25.1328 inches. 2. Find the circumference of circles with the following diameters: 12 inches, 10 feet, 15 inches, 5 yards. 3. The radius of a circle is 9 inches. Find the circumference. 4. The circumference of a circle is 50.2656 inches. Since ir is already known, find the diameter of this circle. 5. A circular flower bed is 8 feet in diameter. How many bricks must I buy in order to put a border of bricks around the bed 1 brick thick? (A brick is Sinches long.) 6. A farmer builds a circular bam having a diameter of 40 feet. What is the length of the circumference of the barn? 7. The Equator of the earth is approximately 25,000 miles. What is the equatorial diameter of the earth? 8. How much fringe is needed to trim the edge of a circular lamp shade 14 inches in diameter? PRACTICAL MEASUREMENTS— SHOP PROBLEMS 235 9. How long a piece of tatting would it take to edge the cuflfs of a girl's sleeves if the cuflfs are 2f inches in diameter? 10. A farmer's roller is 32 inches in diameter. How many revolutions will the roller make in roUii^ a com row a quarter of a mile long? 11. A bicycle has wheels 28 inches in diameter, outside measurement. How many revolutions will each wheel make in going a mile? 12. A circular wading pool 40 feet in diameter has a concrete side walk 3 feet wide extending around the border. How much longer is the outside circumference of this walk than the inside circumference? Exercise 10 C^ZD^ 1. The trough of a pen tray is 2 inches wide. How wide apart must I set the points of my compass in order to draw the semi-circle at each end? 2. If the board is 2f inches wide and the end of the trough is to be ^ inch from the end, locate the point for the center of the semi-circle at each end. 8* A boy in the forge shop wishes to make a ring 8 inches in diameter out of f -inch stock. Allowing 3 times the diameter of the rod for extra in welding, how loyig must he cut the piece of stock to make this ring? 4* How long must a rod be cut out of f -inch stock to make a ring 18 inches, inside diameter? Make allowance for welding. 6. A grindstone 36 inches in diameter makes 40 revolutions per minute. What is the cutting speed in feet per minute of this stone? (Find the number of feet of the circumference that will pass under the edge of a tool in 1 minute.) 236 EIGHTH YEAR 6. Another gnndstone in the shop is only 24 inches in diameter. How many revolutions per minute must it make to have the same cutting speed as the grindstone described in Problem 5? 7. A pulley on a countershaft in a shop ia 14 inches in diameter. How many inches of belt will pass over this puUey in one revolution? 8. The pulley on a wood lathe is 6 inches in diameter. How many inches of belt will pass over this pulley in one revolution? «. How many revolutions will the lathe pulley make for one revolution of the pulley on the countershaft? 10. If the speed of the countershaft is 720 revolutions per minute, what is the speed of the lathe? It. If you have a shop in your school, visit it and make other problems similar to the ones given above Area of Circles When a circle is cut into pieces as shown in this illustration, the pieces are al- most triangular in shape, the bases being slightly curved. If we arrat^e these triangles in a row with half of the triangles pointii^ up and halt of them filling in the spaces between as shown in the diagram on the next page, we should have approximately a paratleli^ram: The circle divided ioto triangles PRACTICAL MEASUREMENTS— CIRCLES 237 The base of this parallelogram is what part of the circumference of the circle? The altitude of the parallelogram is the same as the radius of the circle. Since the base of the parallelogram = ^ of the circumference of the circle (which = 27rr), the base of the parallelogram = 7rr. The area of the parallelogram = base X altitude or irrXr=7rr*. But the area of the circle is the same as the area of the parallelogram. Therefore the area of a circle = 7rr2. PRINCIPLE: The area of a circle is equal to the square of the radius multiplied by TT. Exercise 11 1. Find the area of a circle 8 inches in diameter. Solution: Radius of circle 8 inches in diameter =4 inches. Area of circle=OT2 = 3.1416Xl6=50.2656. Therefore the area of the circle =50.2656 square inches.. 2. What is the area of a circle with a radius of 8 inches? 8. Find the area of a circle 3 feet in diameter? 4. Find the area of the 8-inch circle in the diagram at the left. Find the area of the 12-inch circle. Find the area of the ring. 6. A cow is tethered to a stake in a grass field by a rope 100 feet long attached to one of its fore feet. What is the area in- cluded within the sweep of the rope around the stake? 6. If the rope be attached to one of the hind feet of the cow, giving the animal a reach of five feet more from the stake, how much additional area will she have to graze over? 238 EIGHTH YEAR 7. A circular lake three miles in diameter is drained until it is only two miles in diameter. What area has been reclaimed by the receding of the water? Draw diagram. 8. By irrigation from a central artesian well, with radiating ditches extending half a mile in each direction, a circular area of arid land has been reclaimed. How many acres does it contain? Draw diagram. 9* If the radiating ditches be extended to twice their length, what will be the gain in irrigated area? Draw diagram. 10. Bottles two inches in diameter are packed in a box one foot square, inside measure. How much of the area of the bottom of the box is covered by the bottles? Would this be the same if there were but one bottle, and if it were one foot in diameter? Draw diagram. 11. A certain revolving searchlight illuminates the land to a distance of five miles. What area is included in the circle of its illumination? 12. A farmer builds a circular bam having a diameter of 40 feet. Its circular wall will have 3.1416 times the length of the diameter. What will be the length of it? Suppose this length of wall were used to enclose a square. What would be the length of one of the sides? What would then be the area of the bam? 13. What is the area of the circular bam? What is the gain in area from having the bam circular in form? 14. A concrete side walk 3 feet wide surrounds a circular fountain 15 feet in diameter. How many square feet are there in the surface of the walk? 15. How many 3-inch circles for jelly glass Uds can be cut from a rectangular piece of tin 24 inches wide and 36 inches long? How many square inches are left in the waste pieces? Have pupils bring to class other practical problems on circles. PRACTICAL MEASUREMENTS— CIRCLES 239 16. Tbe square in the figure at the r^ht is said to be ciVcum- scribed about the circle. The circle is said to be inscribed in the square. If the side of the square ia 12 inches, what ia the area of the square? What is the area of the inscribed circle? 17. Divide the area of the inscribed circle by the area of the square. If your work is accurate, the result should be .7854. That is, the area of a circle is .7854 of a square with a side equal to the diameter. 18. From this fact we get the rule: To find the area of a circle multiply the square of the diameter by .7854. 19. liind the areas of circles 6 inches, 8 inches and 12 inches in diameter by this rule. Exerdse 12. Review of Circles 1. How many square feet are there in the area of a circular flower bed 7 feet in diameter? 3. Two girls made a set of doihes consisting of a center- piece IS inches in diameter and 6 small doilies 5 inches in diameter. How many inches of crochet edging did they have to make to trim all the doilies in that manner? S. How many square iaches of muslin were wasted in the squares from which the doilies were cut? 4. Find the area of a circle 3 inches in diameter. Find the area of a circle 6 inches in diameter. The area of the second circle is how many times the area of the first circle? 5. In a 4-inch steam pipe the iron is j of an inch thick. Find the area of the opening in the pipe. 6. Find the area of a cu-cular flower bed 8 feet in diameter. Find its circumference. 240 EIGHTH YEAR 7. The cold air inlet for a furnace should have the same area as the sum of the areas of the hot air pipes. If there are six 6-inch hot air pipes leading from the furnace, what should be the area of the cold air inlet? 8. If the cold air inlet is rectangular in shape and has a length of 15 inches, what should be its width to furnish sufficient air for the six furnace pipes? 9. A circular asbestos pad is 7 J inches in diameter. How many of these pads can be made from a piece of asbestos padding 30 inches square? Draw a diagram to show the arrangement of the circles. 10. How many square inches of waste material would be left in cutting out these circular pads from the 30-inch square? Hexagons A regular hexagon is a six-sided figure with equal sides and equal angles. A regular hexagon may be inscribed in a circle by taking the compass spread to the length of the radius used in drawing the circle and marking off six arcs intersecting the circumference as shown in the figure at the left. Then join the six points of division as indicated to form the regular hexagon. Exercise 13 1. Construct a regular hexagon with a ruler and compass as directed above. 2. Divide the regular hexagon into six triangles as shown in the figure at the left. How do these six triangles compare in size? Why? PRACTICAL MEASUREMENTS— SOLIDS 241 8. Find the area of an equilateral triangle with a side equal to 6 inches. (See page 238.) 4. Since the six equilateral triangles of the hexagon are all equal, show how to find the area of a regular hexagon. 6. Find the area of a regular hexagon with each side equal to 6 inches. 6. What is the perimeter of the regular hexagon described in the preceding exercise? 7. Find the area of a hexagon with a perimeter of 48 inches. Find the area of a square with the same perimeter. Also find the area of a circle with a circumference of 48 inches. Which figure contains the greatest area for the given perimeter? 8. Why do bees have hexagonalnshaped cells? Consider both area and convenience of arrangement. Measurements of Solids We have been studying triangles, rectangles, trapezoids, hexagons, circles, etc. All of these figures have two dimensions, length and breadth. The term polygon is a general term, meaning many-sided, which applies to all of these figures. A figure which has three dimensions, length, breadth and thickness, is called a solid. The term solid does not mean that the figure be composed of some compact material, for it may apply equally well to an empty bin, box or jar. There are certain solid figures with which we ought to be familiar because we see them about us in daily life. A prism is a soHd having two bases which are equal and parallel and whose lateral (or side) faces are parallelograms. The most common prisms are triangular and quadrangular. 242 EIGHTH YEAR Triangular Prism Quadrangular Prism Triangular glass prisms are used for bending rays of light. They are used in some forms of opera glasses. The luxfer prisms are used in upper parts of thrwinSows of large rooms to bend and throw the light farther across the room. You wiU find how a prism bends a ray of Hght in your science work. The most common forms of quadrangular prisms are rec- tangular solids such as bins, rooms (rectangular in shape), boxes, freight cars, bricks, etc. Exercise 14. Area of Surface of a Prism In finding the area of the surface of a prism, we are using no new principles. We simply find the areas of the two bases and the areas of the lateral surfaces and add these to get the total surface of the prism. 1. Find the total surface of a room 15 feet long, 12 feet wide and 10 feet high. 2. What is the area of the surface of a triangular glass prism 3 inches long and whose bases are equilateral triangles with each side equal to 1 inch? 3. What is the area of the surface of a brick 8 in. x 4 in. x 2 in.? 4. What is the area of the surface of a rectangular block of wood whose length is 4 feet and whose bases are 6 inches square? 6. Find the number of square inches of cardboard in a box 6 in. X 3^ in. X if in. without a top. PRACTICAL MEASUREMENTS— PRISMS 243 Volumes of Prisms If you made a quadrangular or rectangular prism out of inch cubes as shown in the figure which is 3 ini:»hes long, 3 inches wide and 3 inches high; how many cubes would it take to make one row along the bottom? How many such rows are there in one layer? How many layers are there in the prism? How many cubes are there in the volume of the prism? How many inch cubes are there in the volume of the prism? The volume of a prism is generally expressed in cubic units, though it may be expressed in gallons, barrels, bushels, and various other measures which are made up of a certain number of cubic units. A short way of thinking the above process is: PRINCIPLE: The volume of a prism is the product of the area of the base and the altitude. The above prism is a cube, which has 6 equal square faces. The volume of the cube is equal to (3 X 3) X 3, or3*. The expres- sion 3^ is read 3 cubed and means that the volume of a cube is equal to the cube of its edge. Exercise 16 1. What is the volume of a rectangular prism 12 inches long, 8 inches wide and 6 inches high? 2. How many cubic feet are there in a box 4 feet long, 3 feet wide and 2§ feet high? 3. How many cubic inches are there in a brick? (A brick is 8^ inches long, 4 inches wide and 2^ inches thick.) 4. How many cubic inches are there in a cubic foot? How many bricks would make a cubic foot if there was no mortar between them? 22 bricks are figured as making a cubic foot of wall. How many bricks are saved by the space occupied by the mortar? 244 EIGHTH YEAR 6. An excavation for a house is 40 feet long, 32 feet wide and 4 feet deep. How many loads of .earth were removed? (1 cubic yard = 1 load.) 6. A bin is 20 feet long, 8 feet wide and 6 feet deep. How many bushels of wheat will it hold? (1 bushel = how many cubic inches?) 7. What is the volume in cubic feet of a rectangular horse trough 6 feet long, 3 feet wide and 2^ feet deep? 8. How many gallons will the tank in Problem 7 hold? (1 cubic foot = how many gallons?) 9. The swimming tank in a certain club house is 40 feet long, 20 feet wide and has a uniform depth of 5 feet. How many gallons of water are there in this tank? 10. A freight car is 30 feet long, 8^ feet wide and 4 feet deep. How many tons of anthracite coal will it hold if 1 ton of anthra- cite coal occupies 34 cubic feet of space? 11.* A rectangular block of ice is 30 inches long, 24 inches wide and 9 inches thick. How much will it weigh if a cubic foot of ice weighs 57.5 pounds? 12. An excavation for a house contains 6000 cubic feet. If it is 40 feet long and 30 feet wide, how deep is it? 13. A bin 22^ feet long and 6 feet wide must be how deep to contain 576 bushels, estimating the bushel at 1 j cubic feet? 14. A wagon box is found to have the following inside measurements: 36 inches wide, 26 inches high and 10 feet 4 inches long. How many bushels of com on the cob will it hold if 4000 cubic inches of corn on the cob = 1 bushel? 16. A rectangular com crib 20 feet long and 12 feet wide is filled with ear com to a depth of 10 feet. How many bushels of com does the crib hold? PRACTICAL MEASUREMENTS— FARM PROBLEMS 245 Exercise 16 Problems Prepared by a Fanner 1. I sold my neighbor a crib of com 20 feet long, 9 feet 4 inches wide and 10 feet 2 inches high. How many bushels of com were in this crib, counting 4000 cubic inches to the bushel? 2. A neighbor asked me to help him measure three cribs of com which he had sold. We found the cribs to measure as follows: Crib 1 — 9 ft. 3 in. long, 9 ft. 1 in. wide, 8 ft. 5 in. high. Crib 2—9 ft. 3 in. long, 8 ft. 11 in. wide, 8 ft, 4 in. high. Crib 3 — 9 ft. 4 in. long, 8 ft. 11 in. wide, 8 ft. 4 in. high. How many bushels were there in the three cribs? (4000 cubic inches = 1 bushel.) 8. How many bushels of com are there in a frame crib 20 feet long, 10 feet wide and 9 feet high if there are 20 studding 2''x4''x9 feet long to be deducted from the contents on account of bemg on the inside of the crib? 4. I sold 20 wagon loads of com to be measured in wagons, counting 4000 Cubic inches per bushel. How many bushels were there in the 20 loads if the wagon box was 10 feet 6 inches long, 3 feet 1 inch wide and 2 feet 1 inch high? 6. How many tons of hay are there in a mow 36 feet long, 14 feet wide and 17 feet high, allowing 512 cubic feet per ton? 6. I sold a stack of hay which was 24 feet long, 14 feet wide and had an average height of 15 feet. How much did I receive for the hay at $10 per ton? (Allow 512 cubic feet per ton.) 7. How many tons of hay are there in a mow 32 feet 6 inches long, 12 feet 8 inches wide and 14 feet high? 246 EIGHTH YEAR Cylinder A cylinder is a solid bounded by a uniformly curved surface and two parallel circular bases. The cylinder, on account of the small amount of material in its walls, is one of the most common of the solid forms in practical use. Cisterns, stove pipes, water pipes, hot water tanks, boilers and ^ ^ silos are usually cylindrical in shape. PRINCIPLE: The Yoltune of a cylinder is equal to the area of the circular base multiplied by the altitude (or height). Exercise 17 1. Find the volume of a cylinder whose base is 6 inches in diameter and whose altitude is 20 inches. 2. A cistern is 6 feet in diameter and 8 feet deep. How many gallons of water will it hold? (1 cubic foot = 7.5 gallons.) 3. A barber once gave me this problem. "I have a hot-water tank 14 inches in diameter and 60 inches high. How many gallons of water does it hold?" What answer should I have given him? 4. A fanner has a silo 12 feet in diameter and 35 feet high. How many tons of silage will it hold, counting 34 pounds to the cubic foot? 5. A cylindrical boiler is 3 feet in diameter and 12 feet long. If it is half full of water, how much water does it contain? 6. A bushel measure contains 2150.42 cubic inches. If it is 12 inches in diameter, how high is it? 7. A cylindrical bucket 8 inches in diameter and 15 inches high will hold how many gallons? 8. Bring to class for solution any problems you can find on the volumes of cylinders, such as gasoline tanks, cisterns, . standpipes, stock watering tanks, etc. PRACTICAL MEASUBEMENTS— THE SILO 247 The silo is one of the chief factora in successful dairy- ing and cattle ris- ing. It is usually filled with com, the stalks and ears be- ing chopped up while still green. To secure the for the beat preser- vation of sil^e, the silo should be of a height equal to at least twice its diameter. The greater the height of the silo, the greater will be the weight of the ;^lage and the more it will be compressed. The cylindrical form allows the greatest area in proportion to the wall space and also offers less friction in the settling of the silage. Exercise 18 1. If the silo in the above illustration is 14 feet in diameter Eind filled to s depth of 28 feet, what is the total weight of the silage, the average weight being 38 pounds per cubic foot? 2. How many days will this silage last a herd of 20 cows, allowing each cow 35 pounds each day? S. How long will a silo 15 feet in diameter and filled to a depth of 32 feet feed a herd of 30 cattle, allowing 1 cubic foot of silage for each head? 4. In order to prevent silage from spoiling, a layer 1 ^ inches deep must be fed each day. If my silo is 12 feet in diameter and filled to such a depth that it weighs 36 pounds per cubic ■ 248 EIGHTH YEAR foot, how many cows should I keep to feed a layer of that depth, allowing each cow 38 pounds each day? The weight of silage varies from about 32 pounds per cubic foot for 18 feet in depth to about 43 pounds per cubic foot for a depth of 36 feet. B. A certwi silo is 14 feet in diameter and is filled with sil^e to a depth of 25 feet. U the silage weighs 36^ pounds per cubic foot, what is the amount of it in tons? 6. How long will this silage last a herd of 24 cows, allowing each cow 40 pounds each day? 7. I wish to build a silo large enough to supply a herd of 20 cows for 190 days. Plan the dimensions for a cylindrical silo, allowing about 1 cubic foot per day for each cow. (See Problem 4 for minimum depth that must be fed each day to keep the silage from spoiling.) nUUGATION Elephant Butte Dam, New Mesico The Elephant Butte Dam, built across the Rio Grande ' River in New Mexico by the United States Reclamation Service IRRIGATION 249 is 1250 feet long and 200 feet high. It is 18 feet wide at the top and 215 feet wide at the bottom. 610,000 cubic yards of masonry were used in the construction of this immense dam. Water for irrigation is measured by the acre^foot, which is the amount of water necessary to cover an acre to a depth of one foot. Exercise 19 !• An acre-foot is equal to how many cubic feet of water? 2. The storage capacity of the Elephant Butte Reservoir is 2,642,292 acre-feet. This is equal to how many cubic feet of water? 3. What is the storage capacity in gallons of this reservoir? 4. The state of Connecticut has an area of 4965 square miles. How deep would the water stored in the Elephant Butte Reservoir cover an area equal to the state of Connecticut? 5. The water surface of this reservoir is 42,000 acres. Find the average depth of water in the reservoir. 6. The Roosevelt Dam in the Salt River Valley of Arizona stores up 1,284,200 acre-feet. The surface of this reservoir is 16,329 acres. What is the average depth of the reservoir? 7. It is estimated that 27,000 horse power of electric energy can be developed from the water in the Roosevelt Reservoir. If this energy is worth $50 per horse power per year, how much revenue would this yield per year if it were all used? 8. A weir (a device for measuring the amount of water) shows that a certain box in an irrigation canal is delivering water at the rate of 2 cubic feet per second. How long will it take to irrigate 40 acres of land, supplying ^ of an acre-foot per acre? 260 EIGHTH YEAR 9. Land was offered in the Salt River Valley, Arizona, at $30 per acre before the Roosevelt Dam was built. Unimproved land sold at about $100 per acre after the irrigation system was completed. The area of the completed system is 250,000 acres. Find the increase in the value of the land as a result of the building of this dam. 10. A farmer raised 8 tons of alfalfa hay per acre on irrigated land worth $200 per acre. He sold this hay at $10 per ton. If his expenses were $25 per acre, what were his profits on a field of 20 acres of alfalfa? What per cent was this on the value of the land? 11. A truck farmer planted a 10-acre irrigated tract in pota- toes on Feb. 10. He harvested this crop on May 10, making a profit of $100 per acre. On July 25 he planted com and in the autumn of that year sold the roasting ears so as to yield a profit of $60 an acre. What was the. total profit on the 10- acre tract for that year? 12. Find other examples of irrigation projects and make problems similar to the ones in this exercise. GOOD ROADS The Lincoln Highway When the Lincoln Highway is finished from New York to San Francisco, it will be a magnificent and useful memorial to the great president for whom it was named. This road is planned to be concrete throughout its entire length of over 3000 miles. GOOD ROADS Exercise 20 1. In 1916 the distance on the Lincoln Highway from New York to San Francisco was 3331 miles. How many days will it take a touring party to make the journey if th^ drive 8 hours per day at an average speed of 15 miles per hour? 3. The distance from Boston to New York by road is 234 miles. How far is it from Boston to San Fraacisco by way <A the Lincoln Highway? 8. Of the distance from New York to western Indiana, 659 of the 802 miles of the Lincohi Highway are hard roads. How much will it cost to complete the rest of this section of the road at $12,000 a mile? i. U the average cost for concrete roads b S13,000 per mile, what will be the total cost of the Llncohi Highway from New York to San Francisco when completed? B. Mention other important state and national highways with which you are familiar. Exercise 21. The Construction of Good Roods 1. The maximum grade of ascent or descent for im- poHant roads has been fixed, generally, at 5%, or 5 feet of rise or fall hi 100 feet of length. For a rise of 528 feet, what would be the length of road, at this maximum grade? s. Gutter grades, at the Sides of roadways, should have a minimum fall of 6 inches in 100 feet to the culverts. If the culverts are 600 feet apart, how much will the gutters 8k)pe to meet them at this minimum fall? 252 EIGHTH YEAR 3. For a road 15 feet or less in width, the middle line, or crown, should be 5 j inches higher than the sides. For a greater width of road, the crown should be raised ^ inch for each foot of distance from the boundary. What should be the height of the crown of a road 18 feet wide? — ^24 feet wide? 4. A road commission found that 26,509 square yards of concrete roads cost $23,154. If the roads averaged 15 feet wide, find the average cost per mile of the concrete roads in that locality. 5. The same commission found that 13,699 square yards of brick-paved roads cost $20,294. Find the cost of brick pave- ment per mile for an 18-foot surface. 6. 651,123 square yards of macadam roads were found to cost $401,470. Find the cost per mile of a 15-foot macadam road. 7. A tar binder is often placed on macadam roads to hold the fine particles of crushed stone together. About 2 gallons are required for each square yard. If the binder costs 8 cents per gallon, what will be the cost of the binder for a mile of macadam road 15 feet wide? 8. The earth work on a certain road averaged about 5§60 cubic yards per mile. Find the cost of this earthwork at 28.5 cents per cubic yard. 9. In building a burnt-clay road in the South for 300 feet as a test, the following expenses yrere incurred: 30 J cords of wood at $1.30 per cord; 20 loads of bark, chips, etc. at 30 cents per load; Expenses for labor and teams^ — $38.30. What was the cost of the 300-foot road? What would a mile of this road cost at the same rate? 10. If a ton of broken rock for a macadam road will cover 3.13 square yards of surface, how many tons of this material GOOD ROADS 253 will be required for a macadam road a mile long and 15 feet wide covering it to the same depth? 11. A county road commission decides to build 4 miles of macadam roads each year at an estimated average cost of $7600 per mile. The state pays ^ of this expense. If the assessed valuation of the county is $3,800,000, what will be the tax rate for hard roads in this county? r—T'CT- — — r- ^'-O- ^ — 7^^— ^T Cross Section of a Concrete Road Concrete for road purposes should consist of a mixture of 1 part of cement to 2 parts of sand to 3§ parts of gravel or crushed stone. 12. The cross section of the concrete road shown in the diagram shows the concrete to be 6 inches thick. How many cubic yards of concrete are there in a mile of this road? 13. The crown of this road shows a fall of 3 inches in half the width of the road. Find the fall per foot. 14. Under each edge of the concrete a longitudinal drain ditch is dug and filled with loose stone. How many cubic yards of stone will it take to fill a mile of these ditches if they are S'^xlO''? 15. How much stone will it take to fill 120 lateral drains for each side of the road per mile, the drains being 8'^xl0''xl0'? 16. How much would the stone cost for both longitudinal and lateral drains at $1.00 per cubic yard? 17. How much would it cost to haul this stone at 50 cents per cubic yard? 18. How much would the concrete cost for a mile of this road at $6.00 per cubic yard? EIGHTH YEAR Mr. Davis lives 2 miles from a hard road on which there is no grade exceeding 5%. A certdn city, where he markets his produce, is located on the hard road 6 miles from the point where his branch road meets the hard road. Mr. Davis sold his crop of 1260 bushels of wheat to a firm in the city. 19. The road leading from his farm to the good road was so rough and hilly that he could only haul 18 two-bushel sacks of wheat to a load. How many such loads would he have had to haul to market the wheat in this manner? 20. If he had hauled two loads per day, what would have been the cost of hauling in this way, counting Mr. Davis and his team as worth $4.00 per day? Find the cost per bushel. 31. On the good road a team could haul 35 sacks of 2 bushels each at a load. Had the good road extended to his farm, what would have been the cost of marketing the wheat at $4.00 per day for 2 loads? Find the cost per bushel. 32. Comj)are the cost per bushel for hauling on a good road with the cost per bushel on the unimproved road. 38. Mr. Davis decided to hire an extra team to haul sacks from his farm to be transfered to his w^on at the hard road. He then hauled the large loads from that point to the city. By this system they marketed the wheat in 6 days. At $4.00 per day, for each team, find the coat of marketing the wheat in this way. 24. How much was saved over the method described in Problem 19? CHAPTER V GRAPHS Graphs are used so extensively to illustrate statistics that a knowledge of how to make them and how to read and interpret them should be obtained by every one. The Pictorial Graph The pictorifil graph uses pictures of the things to be compared, showing dif- ferences in the numbers of the tliii^ by the relative sizes of the pictures. In the pictorial graph in the „ ^__ _ _ , ^ . „. .. '^ o- r Courtesw Office of EipeniriBiitatftUom, illustration a comparison is u. s. Depdrtment of Agncuitu™ made of the eggs laid by a hen the first year (Fig. 1), the sec- ond year (Fig. 2) and the third year (Fig. 3) . Which year was the most productive? How many ^gs did the ben lay each year? The exact number of eggs can not be told by such a graph. Such a graph merely enables us to get a general impression of the numbers compared. Pictorial graphs are much improved when the num- bers represented by the pi(v tures are also shown in the graph. The graph at the left shows an improved ~Coart«y InWrn.tion.1 Harve.Wr Co. tyP^ of pictorial graph. 255 256 EIGHTH YEAR The Line Graph A line graph is a much more accurate way of representing certain kinds of statistics. Line graphs are also much more easily made than pictorial graphs. Suppose that the wholesale prices of eggs for a certain year are to be represented by a line graph. The prices averaged as follows for the different months: Jan. 30i; Feb. 2Qi; Mar. 24f{; Apr. 18f{; May 17f{; June 17ff; July 17ft; Aug. 17^; Sept. 19ff; Oct. 22j4; Nov. 25j4; and Dec. 29ff. On the cross section paper let the vertical lines represent the different months and the horizontal lines represent the prices from to 36, increasing 4 cents from one horizontal line to another. On the January vertical line a dot is placed half-way between the 28|!t line and the 32^ Une, thus representing 30ff for January. On the February line a dot is placed one-fourth of the distance from the 28ff line to the 32f!f Une, representing 29^ for February. After the dots for all the months have been located in this manner, a broken line is drawn to connect them. This graph represents very clearly the fall and rise in the prices of eggs during that year. 1 lit in t 1 » 3 " « I ■ < ui o a •1 1 M \ ■■ ^ J \ 4 / V y iT \ .^ ^ ^ ' Exercise 1 1. From this graph give the wholesale prices of eggs for the following months: March, April, July, September, October, November and December. 2. During what four months did the average price of eggs remain the same? GRAPHS 257 3. How did the decline in price from February to April compare with the rise in price from August to December? 4. The production of coal in long tons for the United States for the years 1905 to 1914 was as follows: Year Anthracite Bituminoua 1905 69,405,958 281,230,252 1906 63,898,803 306,084,481 1907 76,487,860 352,408,054 1908 74,384,297 296,903,826 190» 72,443,624 338,987,997 1910 75,514,296 372,339,703 Iftll 80,859,489 362,195,125 1912 75,398,369 401,803,934 1913 81,780,067 427,190,573 1914 81,090,631 377,414,259 Suppose that we represent the years on the vertical lines. The next step is to determine how many tons are to be represented by the distance from one horizontal line to another. Suppose that we decide on a graph 19 squares high. The smallest num- ber of tons is 63,698,803 and the largest number is 427,190,573, the difference between these numbers being 363,491,770. Dividing the difference by 19, we find that the most convenient number to represent the distance from one horizontal line to another is 20,000,000. The numbers in the table can be plotted only approximately. 69,405,958, the first number of tons of anthracite coal, may be represented by a dot slightly less than half-way from the 60,000,000 line to the 80,000,000 line. Draw the graphs for both anthracite and bituminous, repre- senting the anthracite by a solid line and the bituminous by a dotted line. Compare your graph with the one in the book. In which one of these kinds of coal did the production increase more rapidly during this period? 258 EIGHTH YEAR 6. A pupil made the following grades on his practice exer- cises for two weeks: Feb. 1, 80; Feb. 2, 87; Feb. 6, 100; Feb. 6, 83; Feb. 7, 78; Feb. 8, 93; Feb. 9, 100; Feb. 12, 93; Feb. 13, 97; Feb. 14> 100. Draw a line graph to show his record. 6. The immigration into the United States each year since 1907 is shown in the table at the J5^;;;;;;;;;;^^782SJ left. Draw a line graph to show 1909. ,,,..,... 751786 *^® increases and decreases for the 1910 1,041,570 various years. In what year during 1911 878,587 this period was immigration largest? ^^^2 838,172 What year shows the least number 1913 1,197,892 .. _._ x o rr i ,. -g- . 1 218 480 unmigrants? How do you account 1915 .......... 326 Voo ^^^ ^^® rapid drop for the years 1916 298^826 1915 and 1916? 7. The cost per pupil for education in the United States for the years 1901 to 1914 is 1901 $21.23 1908 $30.55 , • xu x ui n/r i 1902 21.53 1909 31.65 shown m the table Make 1903 22.75 1910 33.33 ^ lin^ graph to show the 1904 24.14 1911 34.71 costs for the various years. 1905 25.40 1912 36.30 What does the graph show 1906 26.27 1913 38.31 ^bout the cost per pupil for ^^ 28.25 1914 39.04 ^i^i, p^^od? "^ ^ ^ 8. Keep a record of the tt^mperature at 9:00 o'clock at the school house for a month and plot the graph for the temperature record for that month. The Bar Graph The bar graph is one of the easiest to construct and interpret. For comparative purposes it is superior to other forms of graphs because the size of a number is shown by the length of the bar. Thus only one dimension has to be considered, while in pictorial graphs two or three dimensions must be considered. The illustration at the right shows a typical bar graph. The lei^hs of the bars are drawn to represent the numbers written at the right of each. In this graph the longest bar is one inch and represents 5.4 tons. The bar representing brome grass (1.3 tons) must then be drawn approximately ^ inch long, and the bars representil^ the yields of Couiuay IntenuxJaiutl HurvesUr Ca clover and timothy must be drawn to the same scale. Exercise 2 1. Draw a bar graph showing the comparative values of the products of the leading industries in the United Statea for a recent year as shown in the followiI^; table: Industry Value of Product 1. SUughterii^ and packing $1,370,568,000 2. Foundriea and machine ehopa 1,228,475,000 8. Lumber and timber 1,166,120,000 4. Iron and flteel 985,723,000 5. Flour and grist mills 883,684,000 6. Printing and publishing 737,876,000 7. Cotton goods 628,392,000 8. Men'a clothing 668,077,000 Suggestion: A suitable scale for determining the length of the bars in the above problem is 1 inch =$300,000,000. a. In 1900, 40.5% of the inhabitants of the United States were Uving in cities of 2500 or more inhabitants. In 1910, 46.3% of the people were living in cities of this size. Show the comparison between these two years by a bar graph. 280 EIGHTH YEAR S. Draw a bar graph representing the production for crude petroleum in the United States as shown in the table: 1904 4,916,663,682 1910 8,801,364,016 1905 5,658,138,360 1911 9,258,874,422 1906 5,312,745,312 1912 9,328,756,156 1907 6,976,004,070 1913 10,434,740,660 1908 7,498,148,910 1914 11,162,026,470 1909 7,649,639,508 1915 .16,806,372,368 The Distribution Graph Another form of graph used extensively by the United States government in its reports is the distribution graph. The distribution graph in. the illustration shows the distribution of poultry in the United States. Each dot in this graph repre- sents 1,000,000 fowls. The first Step in the con- struction of such a graph is to determine the number for each dot. Then determine the number of dots for each state and arrange them in some syste- matic order. From the distribution graph for poultry, name the chief poultry-producing states in our country. Exercise 3 1. Find the population for each county in your state and make a distribution graph showing the distribution of popula- tion in your state. 2. On a map of the United States draw a distribution graph showing the distribution of horses in the United States according to the census of 1910, which was as follows: GRAPHS 261 California 445,349 Kentucky 425,884 Tenneaaee 333,025 Virginia 318,831 Montana 304,21 Colorado 284,647 Washington... 2eg,S01 Oregon 261,627 Arkansas 245,861 Miasistiippi . . . West Virginia. 176,530 Louisiana 175,814 New Mexico . . 175,057 N.Carolina... 162,783 Wyoming 150,98 so that you will get at least one dot tor Rhode Island. Make your number per dot as large as passible, however, so that there will not be so many dots for the states containing large numbers. Iowa .1,449,652 lUinoia .1,402,649 Texas .1.125,834 Kansas .1,099,738 Missouri . . . .1,035,884 Nebraska.. . 971,279 Ohio . 888,027 Indiana, . . . . 785,954 Minnesota. . . 738,578 Oklahoma. . . 708,848 S. Dakota. . , 645,639 N. Dakota. . 625,984 V'isconsin. . . 608,657 Michigan. . . 602,410 New York. ,. 587,393 Plan your numbers Maryland 150,159 Alabama 132,611 soTpa 118,583 Utah 111,135 107,210 Arizona 93,803 New Jersey. .. 88,239 Vermont 80,556 South Carolina 79,105 Nevada 65,717 Massachusetts. 64,109 Connecticut... 46,248 46,154 Florida 45,029 Delaware 31,943 Rhode Island. 9,527 The Circle Graph The circle graph at the right rep- resents the approximate per cents of the different food substances in peanuts. The circumference of a circle is divided into 360 equal parts called degrees. The angle showing the pro- portion of fat cuts off 29.1% of 360 degrees (360°) or 104.76°. 1. Find the nmnber of degrees in the angles for each of the other food substances in the peanut. 2. In alfalfa 65% of the food value is in the leaves and 35% in the stem. Draw a circle graph to show the relative proportions of each. Use a protractor to lay out the angles. CHAPTER VI PRACTICAL MEASURING INSTRUMENTS The Thermometer i The Fahrenheit thermometer is the standard measm« of temperature m the United States. A thermometer consists of a small glass tube ending in either a spherical or a cylindrical bulb. At the temperature of your room, the bulb and part of the tube is filled with a liquid (usually mercury). Hold the bulb of a thermometer at your mouth and slowly blow on it. What happens to the mercury? The heat from your mouth has caused the mercury to expand. Hold the bulb for a few moments in some cold water. What change has taken place in the column of mercury in the tube? The thermometer can thus be used to measure the temperature of the air and certain liquids. There are two important points on a Fahrenheit thermometer: the freezing point of water, which A Standard jg marked 32° above zero, and the boiling point "^ of water, which is marked 212° above zero. Most scientists use the Centigrade thermometer, which has the freezing point marked 0° and the boiling point marked 100°. Exercise 1 1. Find from a physics book or the encyclopedia how a thermometer is made. Explain to the class how the freezing and boilii^ points are found. PRACTICAL MEASURING INSTRUMENTS 263 2. How many d^rees are there between the freezing and boiling points'on a Fahrenheit thermometer? In order that temperatm'es above and below zero may be distinguished, the signs + and — are usually used; +20° meaning 20° above zero and —20° meaning 20° below zero. 8. What is the difference in degrees between a temperature of +20° and a temperature of -20°? 4. At a certain city the temperature on a certain day at noon was 25°. At midnight of the following day the tempera- ture was —4°. How many degrees had the temperaturefallen? Give the changes in the temperature indicated by the follow- mg readings: 5. +50° to +32^ 9. - 5° to +10^ 18. +4(f to +101° 6. +15° to- 2r 10. +32°to+98§° 14. - r to- 16^ 7. +77° to +92^ 11. + 2° to +36° 16. -16° to+ 15^ 8. +60° to +43° 12. -20° to +32° 16. +98§°to+10l|° At government observatories, the temperature is taken each hour. The f ollowii^ extract from a daily paper shows a portion of the weather record in a certain city on Feb. 9, 1917: 12 midnight 4 7 a. m — 1 1 a. m 3 8 a. m — 2 2 a. m 2 9 a. m 3 a. m 1 10 a. m 2 4 a. m 11 a. m 4 5 a. m — 1 12 noon 4 6 a. m — 1 17. What was the maximum, or highest, temperature during the time indicated? 18. What was the minimum, or lowest, temperature? 19. What was the range or change in temperature during the 12 hours indicated? >o :o 264 EIGHTH YEAR SO. Keep a d^y record of the outade temperature at the school house. Leave this for the pupils of next year's class. They vill be able to make some interesting comparisons with the record that they are keeping. The Barometer A barometer is an instrument to measure the pressure of the air. A simple barometer may be made by inverting a tube, filled with mercury, in a dish of mercury. If the tube is longer than 30 inches, the mercury will drop from the end of the tube, leaving a vacuum above it. The pressure of the. air on the surface of the mercury in the dish will support a column of mercury 30 inches high at sea level. If one goes up in a balloon or climbs a mountain, the column of mercury in the tube will gradually fall because the higher above sea level one rises the less air there is to press down. The barometer is a very important instrument in predicting weather conditions. When the barometer is very law, stormy weather usually A Standard resulte, and when the barometer is extremely high, Barometer fair weather usually results. Exercise 2 1. Suppose the barometer tube has an area of 1 square inch at the base, and the air supports a column of mercury 30 inches high. How much is the pressure of the air per square inch, if mercury weighs .49 pound per cubic inch? Solution: A column of mercury 1 square inch at the base and 30 inches high contains 30 cubic inchee. 30X.49 pounds = 14.7 pounds. Since the column of mercury weighs 14.7 pounds, the air pressure must be 14.7 pounds on each square inch of surface. PRACTICAL MEASURING INSTRUMENTS 265 2. Find the number of square inches on the top of your desk. How much pressure does the air exert on the top of this desk? 8. The area of an average person's body is 30 square feet. Find the total pressure, which the air is exerting on our bodies. Our bodies are built to withstand this enormous pressure. If we go up a high mountain, the outside pressure becomes so much less that the pressure of the blood is apt to break the blood vessels, and bleeding at the nose and ears often results. The Hygrometer It is important not only to know whether the air is light or heavy as shown by the barometer, but also to know how much moisture it contains. The instrument for measuring the amount of moisture in the air is called a hygrometer. One of the common forms of hygrometers is the wet and dry bulb type. One of the thermometers is an ordinary thermometer; the other thermom- eter has its bulb covered with a wick which is dipping in a can of water. Evaporation of any liquid has a cooling effect. Drop some gasoline on the back of your hand and see how cool it feels when it is evaporating into the air. If there is a very little moisture in the air, the water will evaporate rapidly from the wick and cool it. The tyei ther^ mometer will then read lower than the dry thermometer. If there is a great deal of moisture in the air, the evaporation will not be so rapid and the difference in the readings of the two thermometers will not be so great. By the use of tables pre- pared for this hygrometer, the amount of moisture in the an- can be found. The amoimt of moisture in the air is expressed in terms of its reiative humidity. If we say that the relative humidity of the EIGHTH YEAR air is 65%, that means that the air now contains 65% as much moisture as it is capable of holding. The relative humidity of a livii^ room should be between 50% and 65%. If the air gets too dry, moisture will evaporate too rapidly from the body and chill the skin. The pores of the skin will then be closed, preventing the elimioatioa of certain waste products through the glands of the skin. If the air of a room is too dry, an open vessel containing water should be placed on the stove or radiator to supply the necessary moisture. WEATHER REPORTS WEATHER FORECAST For City and vicioity— Partly oloudy WedDBi- day and Thunday, probably loo.l Ibun- dcnhciwars. coatinued warm WedaMday; not ■a warm Thundsy; Wodnesday. beoomiiif variable 'Hiursday. For Central territm^- Partly oloudy Wed- ueadav and TburHJay, probably local thua- I TEMPER ATI! RB ■SI itZ- ■ti iV.m'.'. A Daily PapH'a Weather Rmid. One of the most beneficial depart- ments of our govern- ment is the weather bureau. By means of observations taken in various cities scat- tered all over the country, weather fore- casts can be made which save farmers and shippers thou- sands of dollars. The weather record of the preceding day is shown at the left as it appeared on a certain day in a large daily paper. We have now studied some of the instruments which are used in makii^ these observations. PRACTICAL MEASURING INSTRUMENTS 267 By reference to the above record answer the following ques- tions: 1. What was the mean temperature for the day? 2. Was this temperature wanner or cooler than is usually observed on this particular day of the year? 8. What was the difference between the maximum and the minimum temperature for the day? 4. Has the weather during this year since Jan. 1 been warmer or cooler than the average year's temperature? 6. Did any rain fall during the day? Has as much rain fallen during this year since Jan. 1 as is usually observed? (The amount of rainfall is measured each day by the amount of water falling in an open vessel with perpendicular sides.) 6. From what direction was the wind blowing? What was its velocity? (The velocity of the wind is measiu^ by an instrument called an anemjofmeUr^ which may be described as a cupnshaped windmill so arranged that it shows the velocity of the wind by the rapidity with which the wind makes it revolve.) ?• What was the relative humidity of the air at 7 a. m.? At 7 p. m.? Explain what is meant by relative humidity f 8. What was the change in the pressure of the air, as measured by the barometer, between 7 a. m. and 7 p. m.? 9. From the preceding observations and other similar ones made in other cities scattered over the country, the weather forecaster makes predictions on what the weather will be. What was hip forecast? 10. Bring in other daily records clipped from your daily papers an^ compare the records and forecasts with this one. 268 EIGHTH YEAR Uses of Weafher Reports By taking observations over this country and Canada, forecasters are able to warn farmers and shippers of storms and cold waves. Rain storms usually sweep over the country from the southwest to the northeast, taking several days to travel across the country. Farmers can thus be warned of an approaching storm and make their plans accordingly. Shippers pack perishable produce in cars to withstand certain temperatures. If a cold wave is approaching, they must pack their cars to withstand the lower temperature. In the summer, more ice must be put in the refrigerator cars if a hot wave is approaching. The government issues bulletins to shippers telling them what temperatures they may expect. Exercise 4 1. A farmer had, in process of curing, five acres of new mown hay. Counting on fair weather and failing to profit by his daily paper's "Weather Forecast," he had his crop damaged to the extent of 35% during an unexpected rainstorm. How much did he lose, on 11 tons of hay, counting the full market value at $11.40 per ton? 2. In a certain fruit belt the temperature dropped unex- pectedly, over night, from 51 degrees to 30 degrees above zero. The peach crop that year in a certain locality yielded 3768 baskets. In the season following, under normal conditions, the yield was 7348 baskets. What was this increased product worth at 55^ per basket? 3. In some localities the temperature of the air is kept higher by building fires all over an orchard. If the fruit growers in the locality described in the preceding problem had heeded the warning issued by the government and built suitable fires, how much loss might they have prevented? , PRACTICAL MEASURING INSTRUMENTS 269 4. A farmer observed that the weather report said: "Con- tinued dry weather may be expected." He draped an old mower wheel between the rows of his com, thus forming a mulch and conserving the moisture in the ground by preventing its evaporation. His jrield was 40 bushels per acre. Another farmer who paid no attention to the reports of the weather bureau and knew nothing of dry farming methods plowed his com deep and his ground dried out so that his yield was only 25 bushels per acre. If both farmers had equally good land and prospects for com, how much did the first farmer make per acre by dragging his corn, if it sold for 75f5 per bushel? 6. The precipitation ih a certain township in one season was 26.8 inches. The wheat yield that year in the township aggregated 137,540 bushels. In the succeeding year the pre- cipitation during the same period was 19.7 inches, and the wheat yield aggregated 68,430 bushels. What was the differ- ence in the value of the crops at 95f5 per bushel? 6. A gallon contains 231 cubic inches. An acre of ground contains 43,560 square feet. What would be the weight, in tons, of a rainfall of one inch in depth over a quarter-section of land, estimating the weight of each gallon of water at 8§ pounds? 7. A fruit grower in Georgia shipped a carload of peaches which were damaged by a hot wave striking the country while the car was on the way. Having insufficient ice to withstand the hot wave, the peaches were damaged 2b^ per bushel. If the car contained 420 bushels of peaches, what was the shipper's loss due to the change of weather? He might have prevented this loss if he had heeded the government's warning. 8. Tell of any instances in which you have heard of farmers or fruit growers profiting by the weather reports m the news- papers. 9. Bring to class newspapers containing weather reports. 270 EIGHTH YEAR THE ELECTRIC METER If we bum coal under a boiler, we generate steam. This steam may be used to run a steam engine which in turn may run a dynamo which generates an electrical current. This electric current supplies the power for electric lights, electric motors and runs our street cars and interurban lines. Steam engines and gas engines are generally rated by the horse power in this country. We say the engine in an automo- bile is 40 horse power or 60 horse power. ■ Electric energy is measured in terms of kilowaUs. A kilowatt is equal to 1 J horse power. Thus an engine rated at 40 horse power would be rated at 30 kilowatts. Electric light companies generally measure the current you use in terms of kilowatt-hours. A kilowatt-hour is equal to the use of 1 kilowatt of energy for 1 hour. For clearness we may say that a kilowatt-hour is equal to the energy which a good horse would supply in working steadily for 1^ hours. Electric meters are instruments used to measure the amount of electrical energy which we use. How to Read an Electric Meter Beginning at the left indicator on the dial we see that the reading is some- where between 2000 and 3000 because over this dial we see that these figures are read in thousands. Going to the right we see hundreds, tens, ones, and tenths dials. We can easily read such a dial because it is just like writing numbers with figures in thousands, hun- dreds, tens, units and tenths. As we read the dial we take the figure that the dial is at or has just passed. The reading is 2438 kilowatt-hours. Amjk 5 y Inte^rdtin^ Watt-Meter V^sX Type K. PRACTICAL MEASURING INSTRUMENTS 271 1000 s 1005 lOS 1 s Kilowatt - Hours The dial at the right is the same as the preceding dial except that the tenths indi- cator is absent. Some meters have differ- ent dials on them. If the dial on your meter at school or at home is different, work out the method of reading it and then check your result by the reading on the light bill. If you can not read it, have the officer of the company, who calls each month to get the reading, explain how it is read. Exercise 6 1. What is the reading on the dial with 4 indicators on it? 2. The reading of the meter of Problem 1, for the previous month, was 1782. How many kilowatts has the family used during the past month? 8. If the local rate is 12^fi per kilowatt, what was the light bill for last month? 4. Many light companies have a sliding scale for the use of electrical energy. The following shows a bill of a company which generates its energy by water power. Note the low rates for energy from water power. Meter Readings Dec. 13. . . . 2416 Nov. 13. . . . 2368 Total consumption in k.w.hrs. 48 First 9 k.w. hrs. ® 10c= $0.90 Second 9 k.w. hrs. @ 6c = .64 30 k. w. hrs. excess over 18 @ 3c= .90 Gross Bill $2.34 18 Date: Dec. 22, 1916. Discount on first 18 hrs. if paid on or before Jan. 1, @ Ic per k. w. Net BiU $2.16 6. The reading on Jan. 13 of the meter described in Problem 4 was 2458. (Problem 4 gives the reading for Dec. 13.) Figure out the bill for this month according to the plan shown in Problem 4. 272 EIGHTH YEAR 6. A company in a small village charges 15^ per kilowatt hour for their electrical energy. How^ much will a family pay which uses 16 kilowatts during a certain month? 7. Draw a diagram, similar to the one shown in the book, of the dial of some electric meter which is convenient for you to read. What is the reading of the meter shown by your diagram? 8. Determine the system of computing charges for your community. Get some actual readings from bills in your community and make a problem. Present it to the class for solution. 9. Electric cars are run by storage batteries. They can be charged by running an electric current through them. After they are disconnected from the charging current they will give back the energy stored up on their plates. Find the cost of charging a storage battery. How many miles will this battery run the car in which it is used? Find the cost per mile for the current necessary to run this electric car. 10. Find the number of miles a gallon of gasoline will run an automobile of about the same weight. Find the cost per mile of the gasoline. Compare this cost per mile with that of the electric car. THE GAS METER Uluminating gas is made from soft coal by driving off the volatile gases by means of fires under closed retorts. This gas is then run through several processes to take out the impurities which are driven off with the gas. The purified illuminating gas is then pumped into large tanks where it is kept under a pressiu*e which forces it through the pipes to the con- sumers. The consumption of illuminating gas is measured in terms of cubic feet. The gas meter records the number of thousand cubic feet used. The indicators on the dial at the left are PRACTICAL MEASURING INSTRUMENTS 273 labeled 100 thousand, 10 thousand and 1 thousand. They really read in 10 thousands, thousands and hundreds. Hence the cor- rect reading is only one- tenth the reading as indi- cated on the dial. The reading on the dial at the right as above corrected is 87,300. Exercise 6 1. The reading on my gas meter on Oct. 27 was 83,800. On Nov. 27 it was 85,600. What was my gas bill for the month, gas selling at 00^ per 1000 cubic feet? Solution: Nov. 27 85600 Oct. 27 83800 1800 number of cubic feet consumed. 1800 cubic feet at 90f( per thousand = 1.8X90^ =$1.62 (gross bill.) 2. If I am allowed a discount on this bill of 10|i5 per 1000 cubic feet if I pay it within 10 days, what is my net bill? 8. Problem 1 gives the reading for Nov. 27. If my reading for Dec. 27 is 87,400, what is my gas bill for the month of Dec? (Find both gross and net bill, using the same rates as given in Problems 1 and 2.) 4. If I use 2400 cubic feet of gas during the month of July, what is my gas bill at 90^ per thousand cubic feet and 10^ per thousand cubic feet discount if paid within 10 days? 5. If you live in a city where gas is used, find the cost per thousand cubic feet. Is there a discount for prompt payment? 274 EIGHTH YEAR 6. Get an old gas bill and make a problem similar to the ones given above and present it to the class for solution. Check their solution by the amount as stated on the bill. THE STEAM GAUGE The steam gauge is an instrument to measure the pressure of the steam in a boiler. These gauges can also be used to indicate the pressure of compressed air in tanks. They are usually graduated to read pressure in so many pounds to the 'square inch. The gauge shown in the illustration shows no pressure, the pointer standing at zero. * Exercise 7 1. How many pounds of pressure must be put in an auto* mobile tire to make it sufficiently hard? 2. A safety valve is placed in a boiler so that the pressure will not become too great and explode the boiler. Ask the janitor of your school building how many pounds of steam his boiler will carry before the steam forces its way out of the safety valve. 8. Most steam heating plants have low pressure boilers. Locomotives and engines have high pressure boilers. Ask an engineer how many pounds he aims to carry on his engine. 4. The pressure of the atmosphere is about 14.7 pounds per square inch. The steam gauge reads additional pressure above the pressure of the air. For example, if a steam gauge reads 14.7 pounds, we say the boiler is under two atmospheres of pressure inside and only one atmosphere of pressure on the outside. If the gauge reads 29.4 pounds, what would be the pressure on the inside and outside? PRACTICAL MEASURING INSTRUMENTS 276 UEASUKEMENTS OF THE EARTH'S SURFACE Short distances on land are measured by means of the aurveyor'a chain^ which W^9 is sixty-six feet long and has one hundred links. Sarreyor-. Ctoln Distances on the water, and loi^ distances by land, are Dteasured by observing the sun and other heavenly bodies, which seem to pass over the heavens and entirely around the world in twenty-four hours. Distance east and west measured in this way is called longi- tude. This old word meant length; and the ancient peoples who lived on the shores of the "loi^-east-and-west" Mediter- ranean Sea supposed that the lengOi of the world was east and west. They did not know that the world is round and they gave us the word longitude. It is customary to measure lon^tude from some great observatory, where the heavenly bodies are observed through the best instruments. Since the one at Greenwich ^in nij) near London, England, is the best known in the world, longitude is generally reckoned from that one. To make the distances east and west, imaginary lines are drawn north and south from the North Pole to the South Pole. These imaginary lines are called meridiana. All places between the poles along the same meridian have the same longitude. The Equator, which crosses every merid- ian at r^ht angles hajf-way between the poles, is the line from which distance is measured in degrees north and south. Imaginary circles to indicate latitude, or distance north or south from the Equator, are called paraUele qf latitude. 276 EIGHTH YEAR THE MEASUREMENT OF TIME Suppose it is noon at the place where you live and the sun is directly south of you. As the earth rotates from west to east, the sun seems to move westward and noon travels with the sun. Since the earth rotates on its axis once in 24 hours, the sun will seem to pass over 360° of longitude in 24 hours, or 15° of longitude in 1 hour. Exercise 8 1. If it is noon where you live, how long will it be before it is noon 15° west of you? 30° west of you? 45° west of you? 2. What time is it 16° west of you? 30° west of you? 45° west of you? 3. How long has it been since the sun was directly over the meridian 15° east of you? What time is it at a place 15° east of you? What time is it 30° east of you? For convenience, time must be reckoned from a certain meridian. This meridian has been chosen as that of Greenwich, England. All longitude west of this meridian to the 180th is called west longitude and all longitude east of this meridian to the 180th is called east longitude. STANDARD TIME 277 i. If it ia noon at Greenwich, what time will it be 15° west of Greenwich? 30° west of Greenwich? 5. If I set my watch at Greenwich and carry it west with me to longitude 90° west without re-setting it, how much too fast will it be? 6. Philadelphia is in about 75° west longitude. When it is noon at Greenwich, what time is it in Philadelphia? 7. Since there are about 60° of longitude between the extreme east and west coasts of the United States, what is the difference in time between a city in Maine and a city in western Oregon? Standard Tune All places on the same degree of loi^tude have the same local time, however far apart they may be north and south; but by far the greater amount of travel in the world is in an easterly or westerly direction, and to one traveling east or west the local time changes constantly. It is especially impor- 278 EIGHTH YEAR tant that railways shall have an unvarying standard of time for long distances. Hence a system of Standard Time has been adopted for this great country, by which its area has been divided into four great time sections, known as the Divi- sions of Eastern Time, Central Time, Mountain Time and Pacific Time. At all points in any one of these Divisions, the time is made artificially the same. When it is noon in the Eastern Division, it is 11 o'clock in the Central Division, 10 o'clock in the Moun- tain Division and 9 o'clock in the Pacific Division. Thus the Divisions are, successively, one hour apart. When travelers going east or west arrive at the boundary line of one of these divisions, they set their watches ahead or back, to correspond with the time in the next division. The Southern Pacific Railway makes no use of Mountain Time, but passes directly through from Pacific Time to Central Time. It will be noted that the Maritime Provinces of the Dominion of Canada make use of what is called Atlantic Time, which is the time of the meridian of Long. 60° W. This time is not employed in the United States. Exercise 9 1. When it is 12:15 a. m. at Chicago, what time is it in New York (Standard Time)? 2. When it is 4:32 p. m. at San Francisco, what time is it in Chicago? 3. When it is 9:45 at New York, what time is it at Denver? 4. Detroit is now under Eastern Time. How much differ- ence is there between the time in Detroit and the time at Cincinnati, which is in the Central Time belt but has practically the same longitude? INTERNATIONAL DATE LINE 279 6. BufiFalo, being at the line of division between Eastern Time and Central Time, makes use of botti. How far apart are clocks and watches found to be in a city so situated? Men- tion some other cities on the dividing lines of Standard Time Divisions? 6. If El Paso should make use of Mountain Time it would have the time of what meridian? Would this be near the local time of the place? The International Date Line When ME^ellan's men returned to Spain from their voyage around the world, they found that they were a day behind in their time. There must be some place, then, where people travelling west or east can chaise a day in time. It would be very incon- venient for this change to be made in any thickly populated area of the world. The nations of the world have agreed upon such a line passing along the 180th meridian with a few variations as shown in the map. A person travelling west adds a day to bis calendar when he crosses ther international date line. If he travels east, he goes back a day on his calendar when he crosses this line. Exercise 10 1. If a ship crosses the international date line going west at 11:50 p. m. Saturday, how long will it be Sunday on board the ship? 2. If a ship crosses the international date line going east at midnight Sunday, how lon^ will it be Sunday on the ship? CHAPTER VII THE METRIC SYSTEM Weights and Measures Over a century ago, in the time of the French Revolution, a conunission of able men was formed to devise a convenient system of weights and measures to replace the clumsy systems then in use in the countries of Europe. They proposed the metric system, a scheme so scientific in plan and so convenient in its use that it has grown in favor over the world, until now it is used around the globe, except among the English-speaking peoples. Even in the United States and in the British Empire it is in use in a limited way, being employed very generally in scientific laboratories and is recognized by law. ' The need for a more general knowledge of this system in this country is growing from day today, in view of our increas- ing trade with the nations which use it exclusively. Without mastering it we cannot readily understand the trade catalogues of their business houses or the bills sent us for articles purchased; nor can we make them readily understand our own price lists and bills of goods sold to them without writing these in terms of the metric system. No ambitious pupil of the present day can afford to slight the metric system in his study of arithmetic. This commission measured very carefully a portion of the meridian running through Paris and estimated, from this measurement, the distance from the North Pole to the Equator. They then took one ten-millionth of this distance as the stand- ard measure for length and named it the meter. Since they wished to base their scheme upon a decimal ratio, they selected the Greek prefixes deka, meaning ten; hekto, 280 THE METRIC SYSTEM 281 meaning hundred; kiloy meaning thousand, and myria, meaning ten thousand, for the multiples of any unit of measure, and the Latin prefixes deci, meaning 3^; centij meaning xiirj ^^^ ndUi, meaning xo^nrj ^^^ *^® fractions of any unit of measure. Instead of learning an entirely new set of names for each table as we have to do in our dumsy English system of weights and measures, all we have to do in the metric system is to learn one new unit for each table, and, by prefixing the roots, the new tables can be formed. Metric Table of Length 10 miUimetera (mm) =1 centimeter (cm.) 10 centimeters. 10 decimeters. . 10 meters 10 dekameters. 10 hektometers 10 kilometers. . = 1 decimeter (dm.) = 1 meter (m.) = 1 dekameter (Dm.) ^ 1 hektometer (Hm.) = 1 kilometer (Km.) = 1 myriameter (Mm.) The following is an illustration of a decimeter divided into 10 equal parts called centimeters (cm.). Each of these centi- meters is also divided into 10 equal parts called millimeters (mm.). Along the base of the ruler is shown a scale in inches. This shows that a decimeter is slightly less than 4 inches. A meter =39.37 inches. nTTTTm mTTTm ^ 2cm. ocm 4cm 5cm 6cm 7bm 6cm 9aTi lOcm TTTNT ± tin 2in 3in Exercise 1 1. A meter stick is how many times as long as the decimeter shown above? 2. If you have access to a work shop, construct a meter stick from another as a model or use the scale in your book. 282 EIGHTH YEAR 3. A meter equals how many centimeters? 4. A dekameter is equal to how many meters? 6. A kilometer is equal to hew many meters? 6. Change 355 millimeters to centimeters. Since 10 millimeterB » 1 cm., 355 mm.s=355 ^l]n.-^10 mm. » 35.5, the number of cm. This shows the convenience of the metric system in chang- ing from one unit to another — ^we merely move the decimal point to the right or left the required number of places. 7. Change 8750 mm. to meters. 8. Change .5 km. to Dm. 9. Change 345 meters to km. 10. A rod in our English system is equal to how many meters? 11. Find the length and width of your school room in meters. 12. Measure the length and width of your desk in centimeters. 13. Draw a line on the blackboard a meter in length without looking at a meter stick. Now measure it and see how many centimeters you have missed it. 14. Measure the lengths of Objects in your school room after you have first estimated their length, using the different units meter, decimeter and centimeter in your estimates. 16. A kilometer is equal to what decimal fraction of a mile? In France they estimate the distance between two cities in kilometers instead of miles as we do here. Metric Table of Square Measure The square centimeter is one of the most common of the units of square measure in scientific work. As shown in the exact reproduction at the left, it is a square 1 cm. on each side. Find the number of square centimeters in a square inch. I laouARc KZNTVICTCR THE METRIC SYSTEM 283 100 sq. millimeters (sq. mm.) — 1 sq. centimeter. 100 sq. centimeters (sq. cm.) = 1 sq. decimeter. 100 sq. decimeters (sq. dm.) =1 sq. meter (sq. m.). For measuring land the following units are used: 1 sq. meter = 1 centare (ca.)* 100 centares ~1 are (a.). 100 ares =1 hectare (Ha.). A hectare is equal to about 2.471 acres. Exercise 2 1. What is the area of the top of your desk in square centimeters? 2. Draw a square meter on the floor without using a meter stick. Use the meter stick to check your estimated square meter. 3. A friend of mine in Argentina writes that he has planted 20 hectares of wheat. How many acres of wheat has he planted? 4. What part of an acre is an are? 6. Reduce 45675 sq. mm. to square meters. (Remember that the multiplier is 100 in square measure instead of 10.) 6. Make 5 problems that involve square measure. Metric Table of Volume 1000 cu. millimeters (cu. mm.) = 1 cu. centimeter. 1000 cu. centimeters (cu. cm.) = 1 cu. decimeter. 1000 cu. decimeters (cu. dm.) = 1 cu. meter. In measuring wood a cubic meter is called a stere. A cubic centimeter is a cube 1 cm. long, 1 cm. wide and 1 cm. high. The exact size of a cubic cm. is shown in the illustration at the right. Find the nmnber of cubic centimeters in a cubic inch. 1 cu. cm. is what part of 1 cu. in.? 284 EIGHTH YEAR Exercise 3 1. Make a cube 1 decimeter long, 1 decimeter wide and 1 decimeter high. An. open cubical box may be made by making I each line in the pattern shown at the left ^ 1. decimeter long. The four sides may be turned up at the dotted lines and the comers HdiM sewed or pasted together with some kind of gummed paper. 2. In a stere are how many cubic centimeters of wood? 8. A shipment of guanacaste wood from Central America forms a pile two meters high, 1 meter broad and 30 meters long. How many decasteres does it contain? 4. How many cubic meters of earth are removed to make an excavation 12 meters long, 8 meters wide and 1.5 meters deep? 6. What will be the cost of teaming in the removal of 2500 cubic decimeters of gravel at $1 per cubic meter? 6. A cubic meter is equal to about 1.3 cubic yards. How many cubic yards would there be in the excavation described in Problem 4? Metric Table of Capacity The cubical box described in Problem 1 of the preceding exercise if made correctly will hold exactly 1 cubic decimeter. This is taken as the unit of capacity and called the liter (lee-ter). A liter is equal to about 1.057 quarts. lOmilliliters (ml.) =1 centiliter (cl.) lOcentiliters =1 deciliter (dl.) lOdeciliters =lliter (L.) lOUters =ldekaliter (Dl.) lOdekalitera =1 hektoliter (HI.) lOhektoUters =lkiloUter (Kl.) THE METRIC SYSTEM 285 Exercise 4 1. How many cubic centimeters are there in a liter? 2. If milk costs 8 cents per liter, what is the cost of a deka- liter of milk? 8. Reduce 8 dekaliters to deciliters. 4. An aquarium 2 meters long, 1^ meters broad and 1 meter deep contains how many liters? 6. A bin in a certain granary is 4 meters long, 3 meters broad and 176 centimeters deep. How many hektoliters does it contain? 6. A hektoliter is equal to about 2.837 bushels. How many bushels of wheat will the bin described in Problem 5 hold? 7. Change 245 liters to hektoliters. 8. Make 4 problems involving the metric table of capacity. Metric Table of Weight If a cubic centimeter of distilled water be weighed at a temperature of 39° F. it will weigh exactly a gram. 1000 of these grams make a kilogram (or kilo for short). A kilogram, then, is the weight of a cubic decimeter or liter of distilled water at the temperature of 39° Fahrenheit. 10 miUigrams (mg.) 10 centigrams 10 decigrams 10 grams 10 dekagrams , 10 hektograms , 10 kilograms = 1 centigram (eg.) = 1 decigram (dg.) = 1 gram (g.) = 1 dekagram (Dg-) — 1 hektogram (Hg.) = 1 kilogram (Kg.) =1 m3rriagram (Mg.) 10 myriagrams =1 quintal (Q.) 10 quintals =1 Metric Tan (MT.) 286 EIGHTH YEAR Exercise 6 A kilogram is equal to about 2.204 pounds. 1. A gram is equal to how many centigrams? 2. A kilogram is equal to how many grams? 8. How many grams are there in a metric ton? 4. How many pounds are equal to a metric ton? 6. Linseed oil is only .935 as heavy as distilled water. How many grams will a liter of linseed oil weigh? 6. Gasoline is only .7 as heavy as distilled water. How much will a Uter of gasoline weigh? 7. I weighed myself on a standard metric scale in a phy- sician's office and found my weight 74 kilograms. Find my weight in pounds. 8. The average weight^ of boys 13^ years old is 38.48 kilograms. Find their average weight in pounds. 9. The average weight of girls 13^ years old is 40.24 kilograms. Find their average weight in pounds. 10. How many pounds do you weigh? Express this weight in kilograms. 11. A farmer in Argentina measures his wheat by the hekto- liter. A hektoliter = 2.837 bushels. A bushel of wheat weighs 60 pounds. From these facts find the weight of a hektoliter of wheat in kilograms. 12. A cubic decimeter of gold weighs 19.3 kilograms. How many pounds avoirdupois weight does a cubic decimeter of gold weigh? 13. A cubic foot of water weighs 62.5 pounds. How many kilograms are there in the weight of a cubic foot of water? 14. Make three problems which involve the metric table of weights. iFrom Table B, Rowe's "Physical Nature of the Child." THE METRIC SYSTEM 287 Exercise 6 Prom the information already given in connection with the metric system find the following equivalents: 1. A meter =? feet? 6. A quart =? cu. in.? 2. An inch =? cm.? 7. A cu. meter =? cu. ft.? 8. A mile = ? km.? 8. A pound = ? grams? 4. An are =? sq. yd.? 9. A cu. in. =? cu. cm.? 6. A gallon =? liters? 10. A rod =? meters? Exercise 7 1. At 40 cents a meter, what will be the cost of 2.5 deci- meters of ribbon? 2. A book is 4 centimeters thick between the covers: It contains 400 pages. How many leaves are there in 1 millimeter of thickness? 3. Sound travels in dry air at the rate of 1087 feet in a second. How many meters does it travel? 4. How many seconds would elapse between the flash and the report of a gun if I was a kilometer away? 6. Lead is about 11.4 times as heavy as distilled water. How many pounds will a liter of lead weigh? 8. A bale of hay weighs 40 kilograms. Find its weight in pounds. 7. A field is 40 rods long. How many meters long is the field? 8. What is the cost of 150 decimeters of cloth at $1.25 per meter? 9. I am 5 feet 10 inches tall. Find my height in centi- meters. Find your height in centimeters. CHAPTER vni EFFICmNCT IN THE HOME A Southern Colonial Bungalow' When one decides to build a house, he is interested in seeing two things : an exterior view of the finished bouse and a floor plan, showing the arrangement and sizes of the various rooms. The floor plan of the Southern Colonial Bungalow is ehottn in 0>6 flluBtration on the next page. Exercise 1. A Study of the Floor Plan 1. What are the outside measurements of the house, excluding the front porch? 2. Read the azes of the various rooms from the floor plan. 3. How lai^e ia the front porch? 4. How many chimneys are shown in the plan? 5. Would you make any changes in the plani if you were going to build this house? 'Acknowledgment is made to the "Gordon-Van Tine Homee," Daven- ■ '' a p. 109), aud for the EFFICIENCY IN THE HOME 289 Exercise 2. Cost of the House 1. The basement excavation was 1.8 yards deep. Find the number of cubic yards of earth that was excavated. See the floor plan for the dimensions of the house. The basement isr the same size as the house, exclusive of the front porch. 2. In excavating for the basement of the house, there were 200 cubic yards of earth removed. Find the cost of excavating at 25 cents per cubic yard. 3. In the foundation the following materials were used: 42 perch^ of stone at $5.00 per perch; 40 cubic yards of poured con- crete at $5.50 per cubic yard; and block and foot- ings costing $195. Find the total cost of the foundation. 4. The contractor charged for 120 square yards of cement floor at 80 cents per square yard. Find the cost of cementing the base- ment. 6. The plastering was estimated at 600 square yards at 36 cents per square yard. How much did the plastering cost? 6, The carpenter labor amounted to 833 J hours at 60 cents per hour. Find the total amount paid the carpenters. *A perch =24i cubic feet. Po^c n ft: L^E^ ■5" 290 EIGHTH YEAR 7. The rear chimney was 35 feet high and cost $1.30 per linear foot. Compute the cost of this chimney. 8. The other items in the cost of the construction of the house were: Lumber $669.00; miUwork $239.00; hardware $132.00; paint (material and labor) $190.00; brick for porch work $80.00; fireplace (chimney, hearth, stone, etc.) $105.00; wiring $14.00; and hot-air beating plant $129.00. . Find the total cost of these items. 9. Find the total cost of the house as shown by the various items described in Problems 1 to 8 inclusive. 10. Find the total cost of the excavating, the foundation and the cement floor of the basement.. These items amounted to what per cent of the total cost of the house? 11. The cost of the carpenter labor was what per cent of the total cost of the house? 12. The total cost of the lumber, millwork and hardware was what per cent of the cost of the house? Exercise 3. Furnishing a Home 1. What size rugs would you buy for the living room and the dining room? What are the advantages of rugs over carpets? 2. Would you buy rugs for the two bed rooms? If so, what size would you buy? 3. How many shades would be needed for the bungalow? 4. Would you put linoleum on the kitchen floor? Linoleum is made in 6-ft., 9-ft. and 12-ft. widths. Which one of these widths would be used on the kitchen with the least waste? 6. Make out a list of the various articles of furniture which you would buy to furnish this home and the approximate cost of each article. Find the total cost of these furnishings. EFFICIENCY IN THE HOME 291 6* An expert in interior decorations and home furnishings suggested the following as a model list of furniture for this five-room bungalow. Find the total cost of furnishing the bungalow in this manner: Living Room (Antique Mahogany) Davenport, with damask, valour or tapestry covering flOO . 00 Chair to match 55 . 00 Sofa table to go with davenport if used in front of fireplace 37. 50 Overstuffed arm chair with velour, tapestry or damask covering . . 50 . 00 Occasional chair or rocker in cane or upholstered 18 . 50 Sofa, and table at each end of sofa, each 12 .00 Living room table, 30"X54" 45.00 Book case, 4' wide 40 .00 Best Grade Wilton Rug, 10' 6"X 13' 6" 122.00 Dining Room (Tudor Wahiut) 7^ gjjow how you would ^^«* *7^^ furnish this house with an Serving Table 38.00 Extension Table 58.00 Cabinet 60.00 Arm Chair 22.00 Side Chairs, 5 at $13.50 67 . 50 WUton Rug, 11' 3"X 13' 0". .110.00 Chamber No. 1 (American Wahiut) Bed— Full size $42.00 Spring and Mattress 38 . 50 Chest of Drawers 66.00 Dresser 65.00 Night Stand 8.00 Side Chair and Side Rocker, ea. 9 . 00 Wilton Carpet, 9' X 11' 46.00 Chamber No. 2 (Ivory Enamel) Bed— Full size $48.00 Spring and Mattress 38 . 50 Chest of Drawers 36.00 Toilet Table 47.00 Night Stand 10.00 Toilet Table Bench 10.00 Side Chair and Side Rocker, ea. 11. 75 Wilton Carpet 9'Xll' 46.00 allowance of $800 to cover all expenses for furnishmgs. Get prices on furniture from the local dealer in making your estimates. 8. Furnish the house on an allowance of $500. 9. Which would be the better plan if your allow- ance were too small: to buy a full equipment of cheap furniture or to buy fewer pieces of higher-priced furni- ture? 10. What articles would you provide for the front porch? Estimate the cos^ of these articles* 292 EIGHTH YEAR Exercise 4 The house plan shown in this illustration is the one for the house shown on page 109. 16-0 1. Compare this plan with the plan of the bungalow. Which one would you prefer for a home? Why? 2. Estimate the cost of furnishing this house, listing the various articles and their prices as in the preceding exercise. 3. Discuss size of rugs, number of windows, etc., for this plan as outlined in Exercise 1. Exercise 6. Expenses of a Home 1. How many tons of coal would be needed to heat this home for a year? Get estimates from owners of houses of about the same size. • 2. How much does coal cost in your community? Estimate the cost of the coal at that price. EFFICIENCY IN THE HOME 293 8. Compare the cost of burning hard coal and that of soft ooal for a house of this size. 4. If the kitchen range were a coal stove, how many tons would be needed to supply the stove per year? Find the cost of the coal for cooking purposes for a year. 6. If gas is used in your community, find .the cost per month for the average family. What is the total gas bill for a year? 6. If estimates for both coal and gas can be obtained, compare the costs to see which is the more economical. 7. Secure actual data from the homes in your community and estimate the cost of lighting a home for a year. 8. Estimate the table expenses^ for a family of 4 to 8 persons per month? Campfire Girls In order to encourage girls to become efficient as home managers, honors are granted to Campfire Girls for the following achievements: 1. Save ten per cent of your allowance for 3 months. 2. Plan the expenditures of a family under heads of shelter, food, clothing, recreation and miscellaneous. 8. Have a party of ten with refreshments, costing not more than one dollar. 4. Market for one week on $2.00 per person. 6. Market for one week on $3.00 per person. 6. Give examples of 5 expensive and 5 inexpensive foods having high energy or tissue-forming value. Do the same for foods having little energy or tissue-forming value. Choose one of the above achievements to work out and report on it to the class at a later date. *A review of the section on Food Values at this point will be of assistance in planning the food for the family, use. A very elaborate and profitable treatment can be made of this topic. 294 EIGHTH YEAR Exercise 6. Keeping the Family Budget Efficiency in a business enterprise demands that the income and expenses of every department be known. Likewise effi- ciency in the home demands that the home managers apportion the family incomes in the most advantageous manner. A large business corporation made out a suggestive budget for the benefit of their employees. They suggested that the daily expenses be entered on an account sheet similar to the following: Budget Estimate for a Family of Five Date Food 30% Shelter 20% Operating Expenses 10% Clothing 15% Contingency 25% 1 2 3 4 5 6 7 8 9 10 • . etc. to the close dof each month. EFFICIENCY IN THE HOME 295 Under food they included meat, groceries, vegetables, bakery and dairy products, and any meals at hotels or restaurants. Shelter included rent or payments on owned home, interest on mortgage, taxes, fire insurance, and upkeep of the house. Operating expenses comprise heat, light, fuel for cooking, ice, hired help, laundry, telephone and replacement of home fur- nishings. Contingency includes savings, educational expenses, church dues, club dues, concerts, personal expenses and expenses for health and recreation. 1. If the family income is $75 per month, find the amounts that should be included under the various headings of the suggested family budget. 2. Find the amounts for family incomes of $100, $125 and $150 per month. 3. Keep a family budget at home for a month and see how the amounts expended for the various apportionments compare with the percentage of the suggested budget. 4. Another expert on home economy suggested the following classification: Rent, 25%; food, 25%; clothing, 15%; education, 10%; luxuries, 5%; miscellaneous expenses, 10%; savings, 10%, Find the monthly apportionments of this budget for an income of $125. 5. Compare the apportionments for the two budgets. Which is the most suggestive and helpful to a home manager? 6. Bring to the class any other budgets for distributing the family income among various headings and compare these budgets with those presented in this chapter. 7. Does the location (in a large city, a small city, or the country) affect the per cents apportioned among the various items of a budget? Show why. 296 EIGHTH YEAR EFFICIENCY IN BUSINESS The boys and girls in the upper school grades are the coming business men and women. If you study the things that lead to efficiency in business, you will find that scientific pi and economy in management are the essential factors. The printing trade is here used for illustration only, lessons will apply to other industries as well. The Exercise 7 Mr. Franklin, with $5000 to invest in the printing business, rented floor space 50'x28'. The accompan3ring diagram will show how this space was laid out, by an expert, to insure the greatest working corwenience, the proper proportion of expenditures in equipment and the highest utility of space. After a careful study of the floor plans, Mr. Franklin pur- chased the material and furniture listed on the following page, which it was found would give him a complete and well-pro- portioned working outfit. EFFICIENCY IN BUSINESS 297 Wood and Steel Equipment $ 850.00 Machinery, including Motors 1,830.00 Type, Spaces and Quads, Borders, Ornaments, Brass Rule, Iron Furniture, Quotation Quads, etc 1,435.00 Miscellaneous material such as Quoins, Mallets, Planers, Brushes, Benzine Cans, Ink, Knives, Roller Supporters, Composing Sticks, Galleys, and all the small tools necessary in a printing plant 110.00 1 Office Desk 55.00 1 Counter (built in) 42.00 1 Show Case 62.00 1 Typewriter 85.00 4 Chairs (average, $7.75) 31.00 Total What balance did he have remaining as working capital? There was still another necessary preparation for the safe conduct of the business, viz., the establishment of a cost system to include the overhead charges (see page 62) and a properly classified schedule of wages for the three separate departments of the work as below shown :^ Composing Room wages $0.50 per hour Overhead charges — Rent, Heat, Light, etc 1.00 per hour Net cost per working hour .$1.50 per hour Press Room wages (Gordons) 30 per hour Overhead charges — Rent, Heat, Light, Power, Insurance, Taxes, etc 65 per hour Net cost per working hour $0.95 per hour Bindery wages — Girls 21 per hour Overhead charges — Rent, Heat, Light, Insurance, Taxes, etc 24 per hour Net cost per working hour $0.45 per hour *The "cost system^* enabled Mr. Franklin, at the end of each week, auicklv to determine whether the business of each department was con- aucted at a vrofit, or, if at a losSy to make the necessary correction and thus avoid further risk and loss. 298 EIGHTH YEAR Mr. Franklin ordered his paper from a wholesale paper house, by the ream, in sheets of various sizes, weights and grades, including the standard lines specified in the second column of the problems below. Let us now find the largest number of circulars 5"x7" that can be cut from a sheet 2l"x36"^ Solution: 3 7 2Zx30 = 21 0x7 Note that 5 is canceled into 36, 7 times, the fraction being discarded. Show the amount of waste in square inches. Find the number of circulars, or pieces of paper of the sizes given in the first column, that can be cut vrith the least waste from the sizes given in the second column, and show the amount of waste for each in square inches. 1. Si'xll" from 17''x22'' 2. 4' X bl' from 22' x 28' 8. Si'xll" from 22'x34' 4. 4|' x 8' from 24' x 36' 6. 6 J' x 9' from 25' x 38' r Exercise 8 1. For 9. certain job of printing, 2 reams of book paper were needed, weighing 80 pounds to the ream, and costing 8 cents per pound. The composition (type setting) required 8 hours, the press work 6 hours and the bindery work 3 hours. What was the net cost based on the "working hour" rates given in the table on page 303? ^In arriving at the amount of paper required for a job, printers by the use of cancelkition are able to see at a glance the sized sheet they may have in stock from which they can cut with the least waste. 6. 6i' X 9' from 26'x29' 7. r xlC from 28' X 42' 8. 8' xlOl" from 32' X 44' 9. 9' xll' from 35' X 45' .0. 9' xl2' from 38'x50' EFFICIENCY IN BUSINESS 299 2. If the printing office added 20% for profit, what was the total cost of the job to the customer? 3. Mr. Howe, a merchant, ordered 6000 handbills, size 6^"x9", for Ms anniversary dry goods sale. How many reams of paper were required for this job if cut from sheets 25"x38"? 4. If the paper cost 6 cents per pound and weighed 60 pounds to the ream, what did the paper cost? 6 If the composition required 1^ hours and the press work 2 hours, what was the cost of these two items at the net prices given in the table? 6. If Mr. Franklin added 20% for his margin of profit on the job, what did the 6000 handbills cost Mr. Howe? 7. A High School Glee Club ordered 500 programs for their annual entertainment, size (before folding) 6 J"x9", printed on both sides from stock weighing 100 pounds to the ream. How many sheets 25"x38" were required, and what was the cost of the paper at 10 cents per pound? 8. If the composition required 5 hours and the press work 4 hours, what was the charge to the Glee Club, counting in the office charge of 20%? 9. A graduating class ordered 1500 programs, size 4"x6". What paper size given in the table cut to the best advantage, and how many sheets were required? 10. A School Board ordered 2000 letterheads, size 8|"xll". If these were cut from sheets 17''x22'', of paper stock costing 9 cents per pound, and weighing 90 pounds to the ream, the composition requiring 1 hour, and the press work 2 hours, and 20% was added for profit, what was the total charge for the job? 11. Find some printed program, estimate its cost based on the tables given, submit your figures to your local printer, and see how near you have reached the correct amount. SUPPLEMENT The purpose of this section is to provide additional work in simple equations to supplement Chapter III of Part I, and to give material for additional work in measurements in con- nection with Chapter IV of Part II. . While this section is intended to be optional, it offers valuable training in preparation for algebra and geometry and should be used when time permits. I. SIMILAR FIGURES Similar figures are figures having the same shape. All squares are similar to each other because they all have the same shape. In the same way all circles are similar. All rectangles are not similar to each other. Rectangles A and B are similar to each other because they have the same shape, each being twice as long as wide. Rectangles B and C. are not similar because C is 5 times as long as it is wide and B is only 2 times as long as it is wide. Exercise 1. Ratio and Proportion Ratio and proportion are very convenient tools to work with in discussing similar figures. It will be to our advantage, then, to master the uses of these tools before going further into the study of similar figures. The ratio ol one number to another is the number of times the first contains the second. 300 SIMILAR FIGURES 301 The ratio of 15 to 3 is the number of times 15 contains 3, which equals 5. The ratio of 15 to 3 may be expressed as follows: 15 : 3 reads "the ratio of 15 to 3" or -^. The fraction is an excellent way of expressing a ratio because it indicates the division idea of a ratio. -^, the ratio of 15 to 3 = 15-^ 3 = 5. A statement that two ratios are equal is called a proportion as 15 : 5 = 24 : 8. The four numbers in this proportion are called the terms of the proportion. The first and last terms of a proportion are called the extremes and the second and third terms are called the means, 15 and 8 are the extremes of the above proportion and 5 and 24 are the means. What is the product of the extremes, 15 and 8? What is the product of the means, 5 and 24? How does the product of the means compare with the product of the extremes of the proportion? See if the same relation exists between the products of the means and extremes in the following proportions: 1. 10 : 5= 8 : 4. 6. 18 : 6 = 15 : 5. 2.60:15 = 12: 3. 6.30:6 = 25: 5. 3.48: 8 = 12: 2. 7.15:7=45:21. 4. 4: 2 = 36:18. 8. 6:5 = 18:15. If we should try a very large number of these proportions, we should find that the same relation holds true. This relation may be e;cpre3sed in the PRINCIPLE: In any proportion the product of the means is equal to the product of the extremes. If one term of a proportion is unknown, by means of this principle the unknown term can be found. Let X represent the unknown term.^ « ^By putting the value of the unknown term in place of X after it has been found and ^en finding whether the product of the means equals the product of the extremes, a check upon the correctness of the work is shown. 302 EIGHTH YEAR 40:X=24:3 24 XX or 24X= product of the means. 40 X 3 = 120= product of the extremes. Therefore: 24X=120 (Check: 40 : 5= 24 : 3) 120 = 120 Exercise 2 Fmd the value of X in each proportion: 1. 27:12=X: 8. 6. 21 : 18= 56: X. 11. 9: 3=X: 6, 2. 14:X = 26:13. 7. X: 28= 10: 7. 12. X: 12 = 20: 5. 3. 35: 7 = 15: X. 8. 3.5:2.5 = .21: X. 13. 16: 6=X:18. 4. X: 7=36: 6. 9. 9 : 5=X:10. 14. 21:X=14: 8. 6. 18:12= X: 6. 10. 8: X= 16: 8. 16. f : f = X: f. PRINCIPLE: In similar figures the corresponding dimensions are proportional. c If the triangles ABC and M N O are similar (that is, the same shape), the corresponding dimensions are proportional: AB:MN = CD:OP. Exercise 3 1. Suppose A B = 16 inches ; N M = 10 inches ; C D = 6 inches. Find O P. Solution: Put those values in the above proportion: 16 : 10 = 6 : X. 16X=60 (the product of the extremes = product of means). X=^ or 3f . Therefore: O P or X=3f in. k SIMILAR FIGURES 303 2. Two rectangles axe similar. The base of the first is 12 inches, the base of the second is 8 inches and the altitude of the second is 6 inches. What is the altitude of the first? Caviion: Be sure to keep the right order — ^base of 1st : base of 2nd — alt. of 1st : alt. of 2nd. 3. In the iabove triangles A B = 16 inches, MN = 10 inches and A C = 7 inches. Find the side M O. Exercise 4. Similar Triangles 1. To measure the height of a tree. Method: Measure the shadow A B of the tree. Set up a stick F D whose length you have measured, so that it is perpendicular to the surface of the ground. Measure the shadow of this stick. The triangles ABC and D E F are similar. The shadow of tree A B : shadow of stick D E = height of tree A C : height of stick F D. 2. If A B = 30 feet; D E = 22 inches and D F = 36 inches, find the height of the tree. Caviion: Both expressions in the same ratio must be ex- pressed in the same unit of measure. 3. A tree casts a shadow 42 feet long. At the same time a stick 5 feet high casts a shadow 3 feet long. How high is the tree? 4. Another method of measuring the height of the tree . is to construct a large right triangle out of strips of lumber. Make it so that the legs of the right triangle are 3 and 4 feet long. If equal legs are put on this triangle it is much easier to make the accurate measurements. 304 EIGHTH YEAR Move the triangle back and forth until a person with his eye at B can just see the top of the tree along the edge D B. Measure the distance from B to the tree. ABE and D C B are similar triangles. The length of the legs of the triangle measuring instrument must be added to A E to give the whole height A E. 5. Suppose A B = 50 feet, B C = 3, feet and D C=4 feet, what is the height of the tree? Allow 3 feet for the legs. 6. To measure the distance across a pond. Measure B C, D C and E D. Triangles ABC and D C E are similar. ThenBC : DC=AB : ED. Suppose BC = 150 feet; DC =90 feet; and E D = 50 feet. Find A B. 7. To measure the width of a stream. Select some object such as a tree on the opposite bank at B. Set a stake at A and lay ofif a line A D. Lay ofif D C as nearly par- allel to A B as possible. Set a stake at any point O in the line A D. Move back along the line D C until the stake at O is in line with the tree at B. Set a stake at this point C. Measure A O, O D and D C. The triangles A O B and C O D are similar. By means of this pair of similar triangles we get the pro- portion: AB : CD=AO : O D. 8. If CD = 100 feet, A = 50 feet and O D = 25 feet, find A B, the width of the stream. SIMILAR FIGURES 305 9. A boy desiring to measure the width of an impassable riVer flowing through level land drew on the edge of the bank, parallel with the stream, a base line, at each end of which he drove a stake to which he attached the end of a ball of twine. At one end of the base line, with an instrument, he sighted a small spot in a rock on the opposite bank, and noted the angle made by the line of sight with the base line. He then turned his instrument to an equal angle on the other side of the base line, and had an assistant carry the twine a long way along the line of sight. At the other end of the base line he sighted the same spot in the rock, then turned his instrument to an equal angle on the other side of the base line, and had his assistant carry the second ball of twine along the line of sight. From the point where the strings crossed, he measured straight to the base line, and announced the measure as being that of the width of the stream. Was this correct? Explain your answer. 10. By placing a mirror on the ground and moving up or back until the top of the object to be measured is seen in the mirror, the height pf any object can be found. ABC and B D E are similar triangles and C A distance from the eye to the ground; A B, the distance from one's feet to the mirror = D E, the height of the object : B D the distance of the mirror from the object. If AB = 10 feet; C A = 5 feet; B D = 25 feet, find DE. Have pupils find other methods of measurements involving the use of similar triangles. ^\a^/i\.rvltfW 306 EIGHTH YEAR n. CONES AND PYRAMIDS A p3rramid is a solid having for its base a triangle, rectangle or other polygon, and having for its lateral faces triangles meeting at a point called the vertex. Triangular Pyramid Quadrangular P3rramid Cone A cone is a solid having for its base a circle, and bounded by a curved surface tapering uniformly to a point called the apex. Construct a hollow quadrangular prism out of cardboard. Construct a hollow quadrangular pyramid with a base and altitude equal to the base and altitude of the prism. Fill the pyramid with sand and see how many times it must be emptied into the prism to fill it. You will find that it takes 3 pyramids full of sand to fill the prism. The volume of the prism is equal to the product of the area of the base times the altitude. The volume of a pyramid is ^ of the product of the area of the base times the altitude. In the same way it can be shown that the volumes of a cone is one-third of the volume of a cylinder of the same base and altitude. PRINCIPLE : The volume of a pjrramid or of a cone is equal to one-third of the product of the area of the base times its altitude. Exercise 6 1. What is the volume of a cone having a base 7 inches in diameter and a height of 9 inches? Solution: 3.5X3.5X9X3.1416 Volume = ^ t, find the volume of a pyramid having a base of 64 square feet and an altitude of 6 feet. 8. A marble cylindrical shaft 1 foot in diameter imd 10 f^t high is capped by a marble cone having the same diameter at the base. The altitude of the cone is equal to its diameter. Find the volume of the shaft and cone. 4. The Pjrramid of Khufu, in Egypt, has a square base, measuring 750 feet on each side, and its height was originally 482 feet. Find in cubic yards its contents as originally com- pleted, according to these figures. A globe or sphere is a solid bounded by an evenly curved suri'ace every point of which is equally distant from a point within called the center. m. SPHERES A cubical block of wood may be made into a sphere having its diameter equal to the width of the cube. The wood that is removed lies chiefly at the comers and along the edges of the cube. If very exact weights are made of the cube and of the sphere, the sphere will be found to we^h .5236 as much as the cube. Since the volume of the cube is equal to the cube of its edge and the diameter of the sphere is equal to the edge of the cube. PRINCIPLE: The volump of a sphere is equal to .SSaS times the cube of Its dUmeter. [Se: page 243.] Exercise 6 1. Find the volume of a sphere 4 inches in diameter. Solution: .5236X(4X4X4)=33.5104, number of cubic inches in volume of sphere. 308 EIGHTH YEAR 2. Find the volume of a sphere 6 mches in diameter. 8. If the earth were a perfect sphere exactly 8000 miles in diameter, what would be its volume in cubic miles? ' 4. A globe 3 feet in diameter is how many times the size of a globe 1 foot in diameter? 6. A wood turner makes a wooden ball 3 inches in diameter from a 3-inch cube. What part of the wood is wasted in making the ball? 6. Measure the circimiference of a regulation baseball. Find its diameter. How many cubic inches are there in the volume of the baseball? Surface of a Sphere If a croquet ball be sawed into two equal halves and cord be wrapped around the curved surface and then around one of the flat circular surfaces where the ball was sawed, it is fpund that it requires twice as much twine for the curved surface of one of the halves as for the circle. It therefore requires four times as much cord for the whole surface of the sphere as a circle of the same diameter. Since the area of a circle =7rr*, the area of the surface of a sphere =4xr2. 7. Find the surface of a sphere 8 inches in diameter. Solution: Area of surface of a sphere =47rr*. 47rr2=4X3.1416X(4X4) =201.0624. The area of the surface of this sphere «" 201.0624 sq. in. 8. Find the surface of a sphere 5 inches in diameter; 6 inches in diameter; 10 inches in diameter. 9. The radius of the earth is approximately 4000 miles. Find the approximate number of square miles in the earth's surface. 10. Find the number of square inches of leather in a r^^- ation baseball cover. (Use measurements found for Problem 6.) EQUATIONS 309 IV. SIMPLE EQUATIONS Exercise 1 An equation is a statement of the equality of two quantities. For convenience in writing equations, letters are generally used to stand for the unknown numbers. For example, if we wish to solve the following problem, we will find it convenient to use an equation: 1. A newsboy sold twice as many papers today as he did yesterday. During the two days he sold 96 papers. How many did he sell each day? We may let the letter X stand for the unknown number of papers sold yesterday. Then 2X stands for the number of papers sold today. X H-2X = the total number sold. But 96 = the total number sold Therefore X +2X = 96. or3X=96. The expression 3X =96 is an equation because it is a statement of the eqiiality of 3X and the number 96. If 3X = 96, X =96-^ 3, or 32. and 2X = 2X32, or 64. Solve the following problems by using equations: 2. A farmer bought 20 rods of chicken wire fencing. He wished to make a lot twice as long as it was wide. Find the number of rods in the length and width of the chicken lot. Suggestion: Let X= the number of rods in the width. Remember that there are four sides to be considered in getting the perimeter of the lot. 3. Mary is twice as old as her brother. The sum of their ages is 21 years. Find the age of each. 4. A real estate dealer bought a lot on which he built a house costing three times as much as the lot. If the total cost of the house and lot was $5200, what was the cost of each? 310 EIGHTH YEAR 6. The sum of three numbers is 84. The second is twice as large as the first and the third is twice as large as the second. Find the three nimibers. 6. A farmer has a farm of 80 acres. He has a certain number of acres in oats; twice as many acres in pasture and hay as in oats; and five times as many acres in com as in oats. How many acres has he in each? 7. The area of a rectangle is 56 square inches and the width is 4 inches. Find the length. Let X=the length. Then 4 times X or 4X=the area. 8. The area of a field is 80 square rods. The length is 32 rods. Find the width, using an equation as shown in Prob- lem 7. Exercise 2 As shown on page 49, an equation may be represented by a balance. The two sides will therefore balance or remain equal if we take the same quantity or number from both sides or if we add the same numbers to both sides. Suppose we wish to find the value of X in the equation XH-6 = 19. If we take away 6 from the left side, we shall have left merely the un- known number X. But if we take 6 from the left side, we must also* subtra-ct it from the right side to keep both sides of the equation equal to each other. X-f6 = 19 Subtracting : 6 = 6 X = 13 If we wish to find the value of X in the equation X— 3=5, we must add 3 to the expression X— 3 to make it equal to X because X— 3 means three less than X, the unknown number. If we add 3 to the left side of the equation, we must also add 3 to the right side to keep both sides of the equation equal. EQUATIONS 311 X-3=:5 Adding: 3=3 X =8 Find the value of X in the following equations: 1. X+5 = 12. 11. X+11 = 15. 2. X-4= 9. 12. 3X-- 5=13. 8. 2X+3 = 17. 18. 5X+ 2 = 27. 4. 3X+1 = 10. 14. 2X- 6=12. 5. 2X-2= 8. 16. X-13=19. 6. 6X+4 = 19. 16. 9X+ 4=49. 7. 2X-5 = 11. 17. 3X- 2=13. 8. X+7 = 15. 18. 4X+ 3 = 21. 9. 4X+3 = 19. 19. 7X- 5 = 16. 10. 7X-3 = 11. 20. 5X+ 6 = 26. Exercise 3 1. The sum of two consecutive numbers is 27. What are the numbers? Suggestions: Let X=one number. Then the next (consecutive) num- ber is X-fl. The two numbers X+X-fl =27 or 2X+1 =27. Solve the equation 2X-}-l =27 for the value of X. 2. John is 4 years older than Louise. The sum of their ages is 24 years. Find their ages. 8. Two newsboys made 45 cents selling papers. One made 7 cents more than the other. How much did each make? 4. A farmer bought a horse and a cow for $185. The horse cost $55 more than the cow. How much did each cost? 6. The sum of two numbers is 80. One is 20 larger than the other. Find the two numbers. 6. A lawyer received $26.60 for collecting a debt on a commission of 5%. Find the amount of the debt. Equation: $26.60= .05 XX. 312 EIGHTH YEAR Per Cents of Food Substances in the Various American Food Products Protein Fat Cmrbo- hydrates Ash (mineral) Water Refuse White bread 9.2 8.9 9.8 9.2 16.7 6.4 1.0 26.8 3.3 3.0 2.5 16.7 16.5 14.5 13.7 16.9 3.2 13.7 16.1 14.9 . 6.0 1.8 1.4 7.1 7.0 1.3 1.4 1.4 0.9 1.3 0.7 0.9 0.7 1.0 0.4 8.0 0.4 "0.3 0.8 1.0 0.7 0.6 0.5 0.9 0.2 0.3 1.9 4.3 2.3 11.5 8.6 3.8 6.6 4.6 5.8 7.5 5.2 19.5 6.9 1.3 1.8 9.1 1.9 7.3 1.2 85.0 35.3 4.0 .5 18.5 16.1 7.8 23.2 25.5 27.5 2.1 6.8 18.4 3.0 1.3 0.1 0.6 0.7 0.5 0.1 0.2 0.3 0.1 0.4 0.2 0.4 0.2 0.2 0.4 0.3 0.1 "0.3 0.4 1.2 0.5 0.1 0.4 0.6 0.1 "2.6 0.3 3.0 30.2 33.7 8.3 4.9 41.6 25.6 31.3 33.3 29.1 26.6 53.1 52.1 73.1 75.4 66.2 77.9 •••••••• 3.3 5.0 4.8 4.5 'i".i 4.3 "*"".4 3.3 14.7 21.9 22.0 16.9 7.7 4.8 8.9 5.7 10.8 4.6 3.9 2.6 2.5 2.2 79.0 88.0 100.0 70.0 81.0 96.0 10.8 14.3 14.4 5.9 8.6 12.7 7.0 2.7 4.6 70.6 74.2 68.6 9.6 3.6 0.6 45.9 22.9 4.3 6.2 6.2 18.6 6.8 1.1 1.6 2.1 1.0 2.1 .9 3.0 ^ 3.8 0.7 0.7 0.5 0.8 0.7 0.8 0.7 3.1 1.3 0.7 0.8 0.9 1.1 0.8 0.9 1.7 1.0 0.9 0.9 0.5 0.6 1.1 0.4 0.5 0.4 0.8 0.4 0.4 0.1 ""0."3 0.6 0.4 0.3 0.4 0.4 0.6 0.1 0.3 1.2 2.4 3.1 1.1 2.0 0.4 1.4 1.1 0.8 1.1 .0.7 1.6 .6 35.3 35.7 5.9 12.6 7.7 13.6 11.0 30.8 87.0 91.0 74.0 51.7 58.2 50.3 44.0 50.7 89.0 45.4 42.4 52.9 88.3 62.6 55.2 68.5 74.6 70.0 77.7 78.9 62.7 66.4 44.2 94.3 81.1 80.5 56.6 12.3 11.4 63.3 48.9 58.0 62.5 63.4 76.0 85.9 37.5 44.8 13.8 18.8 13.1 2.7 2.6 .6 21.1 5.4 1.4 1.8 1.4 6.9 1.0 16.4 17.5 14.3 16.6 3.3 33''7 22.7 35.6 20.0 20.0 20.0 15.0 10.0 30.0 20.0 50.0 lO 15.0 40.0 25.0 35.0 25.0 30.0 27.0 10.0 5.0 59:4 50.0 10.0 10.0 45.0 49.6 86.4 15.0 25.0 62.2 52.4 53.2 24.5 58.1 Graham bre&d - Soda crackers Corn meal Oat meal Buckwheat Butter Cheese Milk Buttermilk Cream Beef Veal Pork..._ Mutton. Sausage ^ Soups Chicken Turkey Fish Oysters Potatoes Sweet potatoes Beans Peas Beets Cabbage Onions Turnips Parsnips Squash ... , , . Tomatoes Cucumbers Lettuce Rhubarb Rice Tapioca Sugar Molasses . Honey Candy — Apples Bananas Grapes Lemons Oranges Pears Strawberries Watermelon Muskmelon Dates — dried Figs — dried Raisins — dried Almonds Brasilnuts Butternuts Chestnuts Cocoanuts Hickory nuts Filberts Pecans.... - Peanuts Knfflish walnuts INDEX PAGE Addition . . 6-10, 14-18, 156-8 Angles 135-136 Applied decimal problems 38 Applied fraction problems 41-44 Applied insurance problems . 109 Applied measurement problems, 140-141, 149-154 Applied percentage problems, 66-68 Approximation problems . . 178 Bank discount .... 188, 189 Bank draft 191 Bankrupt (broken bench) 180 Banks and banking 179 Barometer 264 Bills of exchange . . .211 Bonds 199-a02 Book binding 153 Book paper 152 Boy scouts 140, 141 Boy's cash account 120 Business forms .... 113 Business transactions ... 77 By-products 67 Cabling money .... 213 Calories 73 Campfire girls 293 Cashier's memorandum . 126 Checking accounts 182 Checks 183, 210 Clearance sales .... 80 Colonial bimgalow 288 Commercial discounts 81 Commissions .... 92, 174 Compound interest 187 Cones 306 Cotton 69,70 Coupons 201 Customs duties .... 100 Daily products . . . 63-65 PAGE 121 169 36 39 37 36 Day book and journal Decimals 34, addition of division of multiplication of . . . subtraction of . Discounts 79, 175 Division drills, . 4-22, 103-107 Efficiency in business . 296 Efficiency in the home 288 Electric meter .... 270, 271 Emergency remittances . . 212 Equations . . . 48, 309 Exchange . . . . 190 Express money order . 208 Express rates .... 130, 131 Family budget . . . 294,295 Federal reserve banks 181 Food products 71 Food values . . . 72-76, 312 Foreign money and travel, 215-217 Fractional equivalents 46 Fractions — Conmion decimal . addition of division of multiplication of review of subtraction of Freight rates Gardening . Good roads Graphs . bar . circle . distribution line pictorial 23 34 25,26 30 29 23, 167 26 131, 132 . 141 . 250 . 255 258,259 . 261 . 260 256,257 . 255 House building and furnishing, 289 313 314 Hygr Insur ace fire life Incoi Indoi Insur Inters Inter Inter. Invei Inves Inroi Irrig! Lines Makj Makj Metr tal tal: tat tal tal Mixe Mom Mon Moti Mult Nati< National expenses National revenues Overhead charges . Paper and printing Parallelogram . Parcel post Partial payments' Pay roll Percentage . . . Perimeter . . To avoid fine, this book should be returned on or before the date last stamped below BOM- -40 99 . 100 62, 297 149-154 . 142 127-129 89 125-126 45, 77, 170 . . 138 Thermometer . Time drafts Trapezoid . Travelers* checks Triangles Trust companies Type sizes . Weather reports Wireless Writing numbers 145- PAOI . 207 133, 219 180 245 61 306 300 2 118 137 207 113 186 127 235 pli. . 160-164 i 164-166 ' . . 191 . 199 ! . , 247 ! . .301 . 4-22 . 159,164 ' . . 307 . . 221 • . . 179 '. 194-198 2, 158, 159 95, 176 . 212 . 262 191-193 . 144 . 218 148, 226, 231 . 179 . 161 266-268 . 214 3