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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/| WiMTWOETH AKT) HiLL'S k Jxercise Manuals. ; No. I. ARITHMETIC. rtcU^^T// y. ./a, iCI 3 2044 097 002 406 ». WENTWOETH & HILL'S Exercise Manuals. No. I. AEITHMETIO. BOSTON, U.S.A.: PUBLISHED BY GINN & COMPANY. 1892. EAtL^TU». 7d,^^c/ ^ <' ' .' . / \ ; Bntel-ed, according to Act of Congress, in the year 1886, by Geobox a. Wentwobth and George A. Hill, in the Office of the Librarian of Congress, at Waslilngtoa Ttpoorafht bt J. S. Cubbing & Co., Boston, U.S.A. Pbbsswobk bt Ginn & Co., Boston, U.S.A* PKEFAOE. r MHE objects to be attained in the study of Arithmetic are mental discipline and practical mastery of the subject. These objects are best secured by solving problems that are progressive in character and grouped under a few general heads. This collection of problems is not intended to supplant text-books in Arithmetic, but to supplement them. A great number and vari- ety of examples are given under each head, for the express purpose of enabling a teacher to select such as are specially adapted to the needs of his classes. The examples are, in the main, practical ; that is, similar to examples that occur in the ordinary affairs of life ; and many of them give accurate and interesting information. The authors will be glad to receive information in regard to errors, and suggestions for improving the work. * G. A. WENTWORTH, a A. HILL. April, 1887. CONTENTS. ♦ CHAPTER PAGE I. Integbal Numbebs 1 II. Decimal Fbagtions 38 III. Common Fbagtions 58 IV. Common Measubes 79 V. Pebcentage 124 VI. Pbopobtion 200 VII. Mensubation 222 VIII. Miscellaneous Exebcises 271 ARITHMETICAL EXERCISES. CHAPTER I. ^^^. INTEGRAL NUMBERS. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 51 66 48 36 25 17 18 57 15 44 19 91 46 63 31 42 52 82 24 31 8 21 27 42 30 72 45 50 49 25 91 28 23 36 48 36 25 81 82 81 38 13 33 63 70 8 39 82 32 17 19 14 41 80 64 90 61 14 7 71 47 26 21 35 57 45 75 9 55 27 9 54 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 48 52 8 16 33 54 55 68 • 23 13 48 35 9 61 43 48 52 46 67 5 9 99 6 42 17 26 52 85 27 8 78 43 25 7 51 57 29 28 67 7 38 19 9 67 68 85 9 64 83 83 9 26 41 92 4 25 79 64 23 49 75 94 17 35 9 57 18 14 7 39 88 87 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 51 46 30 25 32 47 18 24 91 33 64 75 56 63 72 81 17 26 57 31 28 63 90 9 48 31 45 82 19 21 15 8 23 70 61 55 36 42 50 81 14 35 44 21 36 8 14 27 25 52 49 38 41 57 19 27 48 39 7 9 17 82 25 13 80 45 91 42 36 82 71 54 2 Arithmetical exercises. Add: 37. 38. 39. 40. 41. 42. 43. 44. 45. 46. 123 516 321 225 871 213 421 222 624 448 205 341 75 716 215 327 87 85 231 526 310 236 184 348 64 98 116 376 785 379 79 110 769 519 371 716 615 584 923 87 118 196 815 96 296 825 379 972 84 999 47. 1234 368 5721 1050 4862 9215 48. 4321 6450 378 4291 5782 6431 49. 2345 3456 4567 5678 689 7890 50. 2783 345 1497 5840 9010 2709 51. 5207 3584 2671 987 3512 6705 52. 3426 783 5279 1085 9270 876 53. 2358 7291 5946 7368 5492 876 54. 9210 1029 291 3587 2785 8899 55. 12345 3276 4721 371 51028 61234 56. 23456 72564 3785 23584 987 96 57. 123456 258071 589347 258923 720145 396012 58. 580921 42364 527913 80235 726048 4386 59. 584321 92047 3681 927 1078 92569 60. 5203461 9350472 1456849 2604030 5876543 1234567 61. 2587609 3582764 1357908 4670253 8492056 4759841 62. 1357924 6804281 5975325 7101584 9276432 6789009 63. 8274108 3509270 4680259 3584672 9876543 5279614 64. 5791350 246801 1384650 2794589 6532108 7999888 65. 123 + 516 + 321 + 225 + 871 + 213 + 421 + 85 + 231. 66. 205 + 341 + 75 + 716 + 215 + 327 + 87 + 222 + 624. 67. 310 + 236 + 184 + 348 + 64 + 98 + 116 + 376 + 785. 68. 79 + 110 + 769 + 519 + 371 + 716 + 615 + 584. 69. 118 + 196 + 815 + 96 + 296 + 825 + 379 + 972 + 84. 70. 1234 + 4321 + 2345 + 345 + 5207 + 3426 + 2358. 71. 368 + 6450 + 3456 + 2783 + 3584 + 783 + 7291. 72. 5721 + 378 + 4567 + 1497 + 2671 + 5279 + 5946. 73. 1050 + 4291 + 5678 + 5840 + 987 + 1085 + 7368. 74. 4862 + 5782 + 689 + 9010 + 3512 + 9270 + 5492. 75. 9215 + 6431 + 7890 + 2709 + 6705 + 876 + 876. 76. 12345 + 23456 + 5 + 92583 + 23504 + 358 + 56789. 77. 3276 + 72564 + 23 + 4620 + 4368 + 9246 + 3587. 78. 4721 + 3T85 + 936 + 973 + 25 + 14376 + 296. 79. 371 + 23584 + 6543 + 25 + 9 + 845 + 89. 80. 51028 + 987 + 92840 + 9 + 36 + 29 + 7. 81. 61234 + 96 + 72104 + 17 + 378 + 7 + 12345. 82. 123456 + 580921 + 654321 + 5 + 345 + 584321. 83. 258071 + 42364 + 41058 + 24 + 6197 + 92047. 84. 589347 + 527913 + 3792 + 358 + 52718 + 3681. 85. 258923 + 80235 + 589 + 1497 + 6904 + 927. 86. 720145 + 726048 + 75 + 36725 + 871 + 1078. 87. 396012 + 4386 + 9 + 187348 + 89 + 92569. 88. 5203461 + 2587609 + 1357924 + 8274108 + 5791350 89. 9350472 + 3582764 + 6804281 + 3509270 + 246801. AILITMM£TI0AL £^£llOIS£d. Find from the table below the area and population in 1880 of : 90. The North Atlantic States. Nos. 1-9. 91. The South Atlantic States and District of Columbia. Nos. 10-18. 92. The Northern Central States. Nos. 19-29. 93. The Southern Central States. Nos. 30-36. 94. The Western States and Territories. Nos. 37-47. 95. The whole United States and Territories. Area In Area In No. Name, 8q. mllea. Population. ^0. 25. Name. 8q. mllea. Population, 1. Maine. 29,895 648,936 Iowa. 55,475 1,624,615 2, N.H. 9,005 346,991 26. Mo. 68,735 2,168,380 3. Vt. 9,135 332,286 27. Dak. 147,700 135,177 4. Mass. 8,040 1,783,085 28. Neb. 76,185 452.402 5. R.I. 1,085 276,531 29. Kan. 81,700 996,096 6. Conn. 4,845 622.700 30. Ky. 40,000 1,648,690 7. N.Y. 47,620 5,082,871 31. Tenn. 41,750 1,542,359 8. N.J. 7.455 1,131.116 32. Ala. 51,540 1,202,505 9. Penn. 44,985 4,282,891 33. Miss. 46,340 1,131,597 10. Del. 1,960 146,608 34. La. 45,420 939,946 11. Md. 9,860 934,943 35. Tex. 262,290 1,591.749 12. D.C. 60 177,624 36. Ark. 53,045 802,525 13. Va. 40,125 1,512,565 37. Cal. 155,980 864.694 14 W.Va. 24,645 618,457 38. Col. 103,645 194,327 15. N.C. 48,580 1,399,750 39. Nev. 109,740 62.266 16. S.C. 30,170 995.577 40. Ore. 94,560 174,768 17. Ga. 58,980 1,542,180 41. Wash. 66,880 75,116 18. Fla. 54,240 269,493 42. Idaho. 84,290 32,610 19. Ohio. 40,760 3,198,062 43. Mon. 145,310 39,159 20. Ind. 35,910 1,978,301 44. Wy. 97,575 20,789 21. 111. 56,000 3,077.871 45. Utah. 82,190 143,963 22. Mich. 57,430 1,636,937 46. Ari. 112,920 40,440 23. Wis. 54,450 1,315,497 47. N.M. 122,460 119,565 24. Minn. 79,205 780,773 . INTEGRAL NUMBEHd. 96. A laborer threshed 44 bu. of wheat, 114 bu. of rye, and 167 bu. of oats. How many bushels did he thresh in all? 97. A man bought a horse for $475, a carriage for $175, a harness for $78, and a whip for $2. What did he pay for them all ? 98. In 1880 the population of New York City was 1,206,299, and that of Brooklyn was 566,663. What was the population of both cities together ? 99. The Duke of Wellington's army at Waterloo consisted of the following British troops : infantry, 20,661 ; cavalry, 8735; artillery, 6877. There were also 33,413 Belgian and other allies. How many British troops were there in all ? What was the whole strength of his army ? 100. The army of Napoleon at Waterloo consisted of 48,950 infantry, 15,765 cavalry, 7732 artillery. What was the whole number ? 101. A bank had $38,463 in gold, $37,986 in bills, and $58,896 in cash items. Find the whole amount. 102. A horse-jockey bought a horse for $527, and a colt for $189. He sold them, gaining $25 on the horse and $49 on the colt. What did he receive for each animal? What did he receive for both together ? 103. Charles counts the kernels on 4 ears of corn. He finds on the first 460, on the second 454, on the third 486, and on the fourth 354. What was the total number ? 104. Kollins & Morse put 4 loads of coal in my cellar. The first weighed 2472 lbs., the second 2624 lbs., the third 2831 lbs., and the fourth 3046 lbs. What was the total weight ? 6 ARITHMETICAL EXERCISES. 106. What were the total expenses of Mr. Jones for one year, the items being as follows: rent, $192; groceries, $298; meat, $100; fish, $30; milk, $30; fuel, $40; clothing, $150; boots and shoes, $28; dry goods, $16; education of children, $22; taxes, $2; sundries, $29. 106. One factory employs 96 males and 64 females; another, 126 males and 54 females ; and a third, 102 males and 68 females. Find the number of persons employed by each factory ; the whole number of males ; the whole num- ber of females ; and the whole number employed. Males. Females. Total, First factory, 96 64 Second factory, 126 54 Third factory, 102 68 107. The egg product of a farm for one month was : Weeh, Hens' Eggs. Ducks' Eggs. First, 164 127 Second, 181 135 Third, 171 145 Fourth, 157 139 Find (1) the number of eggs laid each week ; (2) the total number laid ; (3) the total number of each kind laid. Ooose Eggs. 15 25 18 17 108. A stable-keeper's monthly consumption of oats for his horses was as follows : January, 1116 bushels. July, 810 bushels. February, 1008 " August, 837 " March, 1116 " September, 1170 " April, 1080 " October, 1197 " May, 1302 " November, 1116 « June, 1267 " December, 1177 " Find the amount for each quarter and for the year ? Mila. iRntUa. 44 78 54 96 26 46 36 70 39 72 37 58 INTEGRAL NUMBERS. 7 109. The distances between the chief cities on the Boston and Albany Line to New York, and the times of traversing them hj the f^t express, are as follows : Boston to Worcester, Worcester to Springfield, Springfield to Hartford, Hartford to New Haven, New Haven to Stamford, Stamford to New York, Find (1) distance from Boston to each of the other cities ; (2) the distance from New York to each of the other cities ; (3) the time required for the express to travel from Spring- field to each of the other cities. 110. A cattle-dealer has sold 17 oxen, 64 sheep, and 7 lambs; he has left 228 oxen, 475 sheep, and 49 lambs. How many animals of each kind did he have, and how many altogether ? 111. How many quarts of milk did Mr. Hall's cows yield during April, the daily score being as follows : 102 98 104 104 98 98 96 103 105 105 76 96 102 104 103 103 98 104 98 97 102 99 99 102 165 98 101 103 96 118 li;j. George has $5.98; Ellen has 69 cents more than George, but 23 cents less than Mary. How much money has Mary ? How much have they together ? 8 ARITHMETICAL EXERCISES. 113. A butcher sold one year : 72 ox-hides, weighing 4684 lbs., for $328 36 cow-hides " 1720 " • 104 185 calf-hides " 2432 " " 265 Total, hides, weighing for 114. A baker sold one week : 484 large loaves, weighing 942 lbs., for $38.72 424 small loaves, " 404 " " 16.16 146 graham loaves " 285 " " 11.68 Total, loaves, weighing lbs., for 115. The wine made one season from the vintage of four vineyards, in quantity, kind, and value, was as follows : Vineya/rd. Bed Wtne. Vcdrie. White Wine. Value. First, 3049 gals. , $2317 2784 gals. $1927 Second, 5419 " 3912 2095 " 1142 Third, 17148 " 9874 12904 " 6725 Fourth, 10838 " 8117 4191 " 3084 Total, 116. A butcher slaughtered one month 4 oxen. They furnished : Meat Hide and Tallow, Befase, Total The first. 624 lbs. 164 lbs. 454 lbs. The second , 538 " 154 " 412 " The third, 510 " 150 " 384 " The fourth 658 " 186 " 498 " • Total, INTEGRAL NUMBERS. 9 Subtract ; 117. 378 69 6830 2919 118. 976 588 2845 1438 119. 476 287 8456 2584 120. 800 177 8005 6324 121. 900 577 2004 1888 122. 801 375 4018 2508 123. 404 168 5030 1569 124. 506 177 6000 2318 126. 605 246 8004 3546 126. 801 628 8364 2576 in. 12345 1258 50607 38594 30927 27918 23504 12765 42060 31846 35620 16285 80000 36452 60305 48578 70004 28596 41035 18647 IV. 305070 123549 280491 173258 472085 214376 601407 342158 432000 120468 470062 358404 935026 476387 502801 315847 836425 478596 987054 5678023 1584318 7654321 6372918 3587025 1694916 4102030 1460928 5004006 2361238 1007008 925379 5000003 2409768 3000000 2756859 4001001 3579246 3050702 10 ABITHMETIGAL EXEECISES. 127. 128. 129. 130. 131. 132. 133. 134. 135. 136. 137. 138. 139. 140. 141. 142. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. 153. 154. 155. 33333 - 11111- 52431 - 63574 - 73650 - 94306 - 83104- 50402 - 71002 - 80042- 90132- 61213 - 81427 - 802041 710032 623004 534702 420573 625000 730004 800052 900006 800000 714320 904062 603004 521347 400100 824153 24444. 9999. 38657. 29885. 45796. 28579. 57685. 38765. 46854. 36758. 64574. 47658. 48569. - 358476. - 562849. - 246897. - 185943. - 236784. - 436128. - 347586. - 563479. - 741568. - 243685. - 185196. - 385794. - 485967. - 185698. - 138562. - 367594. 156. 157. 158. 159. 160. 161. 162. 163. 164. 165. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175. 176. 177. 178. 179. 180. 181. 182. 183. 184. 702106 645312 510340 423156 48005 90600 80050 50210 60032 73145 82006 92134 60030 50000 724350 531602 853047 940521 703642 621300 832005 960043 700321 634000 790005 800021 510203 612345 700400 268459. 287465. 386572. 185978. 34567. 28753. 27684. 18765. 48965. 27698. 37698. 28659. 15744. 27348. 386584. 473856. 256839. 563768. 426879. 384653. 465837. 378695. 465872. 287653. 294785. 385692. 286754. 347598. 285647, INTEGRAL NUMBERS. 11 Earnings of Boston Railroads. From the statistics given below, find the increase in gross earnings of each road for 1883 over 1882, and the net earnings for 1883. Qross Gross Gross Earnings, Earnings, Expenses, Name. 1882. 1883. 1883. 185. Eastern, $3,403,078 $3,584,506 $2,310,830 186. Boston & Maine, 2,768,326 2,915,943 2,070,760 187. Boston & Lowell, 2,083,241 2,127,305 1,512,134 188. Fitchburg, 2,418,431 ' 2,825,024 2,187,941 189. Boston & Albany, 7,348,276 8,103,947 6,158,904 190. Boston & Prov., 1,564,310 1,646,962 1,311,822 191. Old Colony, 4,126,258 4,249,179 3,020,738 192. K Y. & N. E., 3,302,789 3,568,953 3,163,525 Population of the ' largest cities in the United States. Find for each city the increase for each decade, and for both decades. Name, In I860. In 1870. In 1880. 193. Boston, 177,812 250,526 369,832 194. New York, 805,651 942,292 1,206,299 195. Brooklyn, 266,661 396,099 566,663 196. Philadelphia, 562,529 674,022 847,170 197. Baltimore, 212,418 267,354 332,313 198. Washington, 61,122 109,199 147,293 199. Cincinnati, 161,044 216,239 255,139 200. Chicago, 109,260 298,297 503,185 201. St. Louis, 160,773 310,864 350,518 202. New Orleans, 168,675 191,418 216,090 203. San Franmco, 56,802 \^^fin% ^^^?&^ 12 ARITHMETICAL EXERCISES. Consumption of sugar in the United States. Find for each year : (1) the total consumption ; (2) the increase over the preceding year ; (3) the excess of imported over domes- tic sugar consumed. Year. Imported sugar. Domestic sugar. 204. 1878, 614,170 tons. 71,500 tons. 206. 1879, 631,174 " 112,000 " 206. 1880, 730,519 " 88,822 " 207. 1881, 790,978 " 127,367 " 208. 1882, 866,517 " 76,373 " ToTis hay. Bu. com. Bu. oats. 209. A farmer harvested 27 256 189 His stock consumed 19 197 92 There remain Bu. corn. Bu. rye. Bu. oats. 210. A farmer raised in 1883, 487 133 274 in 1884, 461 ' 97 185 Difference Cds. oak. Cds. maple. Gds.pine, 211. A wood-dealer has for sale 275 318 462 He sells 128 77 219 There remain 212. A butcher had in his shop Monday evening. Lbs. beef. Lbs. mutton. Lbs. veal 1245 624 292 Tuesday he sells 426 204 114 He has left Wednesday he sells 231 218 73 He has left Thursday he sells 267 24 45 He has left INTEGRAL NUMBERS. 13 213. There are 96 scholars in a certain school; 49 of them are boys. How many are girls ? 214. A man owes $1217. If he pays $978, how much will he still owe ? 215. In 1880, the population of Boston was 369,832, and that of Baltimore, 332,313. What is the difference ? 216. The ^neid has 9892 lines, and the Iliad 15,683. How many more lines has the Iliad than the -^neid ? 217. The polar diameter of the earth is 41,707,620 feet, and the equatorial diameter is 41,847,426 feet. What is the difference ? 218. The art of printing was discovered about the year 1449. How long is it from that date to the year 1884 ? 219. What number must be added to 238,541 to make a million ? 220. By how much does the sum of 2853 and 4509 exceed the difference between 9241 and 1888? 221. A tank holding 250 gallons of water was filled by pouring 57 gallons into it. How many gallons of water were already in the tank ? 222. Shakespeare was born in 1564 and died in 1616 ; Milton was born in 1608 and died in 1674. How many years more did Milton live than Shakespeare ? 223. Mrs. Lincoln bought a sofa for $96, a rug for $19, an easy-chair for $67, and a mirror for $16. She gave to the salesman $200. How much should he give her back? 224. A farmer requires for his own use during the win- ter 22 tons of hay, 165 bushels of corn, and 110 bushels of oats. He has raised 85 tons of hay, 288 bushels of corn, and 191 bushels of cfttg, How mucla oi ^^^V Oi^xv. V^ ^^\ 14 ARITHMETICAL EXERCISES. Find the products of ; 226. 407 X 8736. 253. 230 X 6487. 226. 205 X 8347. 254. 203 X 6487. 227. 306 X 9287. 255. 3057 X 29,486. 228. 306 X 9674. 256. 7026 X 68,473. 229. 508 X 7536. 257. 5096 X 86,573. 230. 407 X 7659. 258. 5038 X 85,237. 231. 604 X 6429. 259. 6018 X 56,039. 232. 504 X 5938. 260. 4057 X 73,946. 233. 705 X 5319. 261. 4069 X 62,508. 234. 608 X 8437. 262. 6095 X 45,293. 235. 803 X 4928. 263. 8035 X 42,706. 236. 705 X 9183. 264. 8046 X 27,358. 237. 907 X 3719. 265. 5028 X 50,728. 238. 809 X 7536. 266. 2068 X 65,317. 239. 507 X 6825. 267. 6043 X 53,163. 240. 906 X 6392. 268. 4059 X 82,537. 241. 506 X 8765. 269. 7028 X 65,014. 242. 605 X 8746. 270. 3082 X 47,349. 243. 409 X 7654. 271. 5067 X 72,369. 244.. 308 X 9475. 272. 5073 X 71,386. 245. 708 X 4567. 273. 4075 X 36,425. 246. 406 X 7982. 274. 6072 X 46,382. 247. 605 X 3859. 275. 8032 X 28,743. 248. 507 X 6987. 276. 5067 x 52,389. 249. 574 X 1357. 277. 9054 X 87,536. 250. 329 X 1987. 278. 8024 X 79,531. 251. 506 X 7071. 279. 4368 X 98,476. 252. 476 X 2958. 280. 7896 X 98,476. INTEGRAL NUMBERS. 15 281. 48,637 X 50,206. 310. 75,968 X 98,765. 282. 30,604 X 23,579. 311. 35,279 X 54,628. 283. 50,604 X 60,208. 312. 26,513 X 47,824. 284. 23,456 X 60,403. 313. 49,382 x 62,835. 286. 29,046 X 70,809. 314. 39,627 X 72,693. 286. 34,567 X 50,403. 316. 49,387 x 56,428. 287. 20,704 X 30,807. 316. 52,764 x 81,635. 288. 40,503 X 45,678. 317. 36,947 X 74,836. 289. 35,279 X 60,403. 318. 15,629 X 24,813. 290. 30,504 X 56,789. 319. 47,395 X 82,519. 291. 43,568 X 50,608. 320. 67,215 X 92,308. 292. 67,895 X 70,503. 321. .58,368 X 75,479. 293. 40,706 X 54,632. 322. 27,050 X 90,070. 294. 50,703 X 78,956. 323. 14,896 X 80,090. 296. 69,425 X 80,504. 324. 65,038 X 88,909. 296. 30,705 X 89,567. 326. 85,700 X 98,476. 297. 50,790 X 57,009. 326. 65 839 X 42,600. 298. 25,417 X 76,532. 327. 64,870 X 20,300. 299. 27,938 X 36,845. 328. 77,869 x 97,800. 300. 37,625 X 83,246. 329. 98,653 X 55,700. 301. 38,564 X 52,736. 330. 75,060 x 91,400. 302. 41,769 X 58,463. 331. 46,054 X 78,000. 303. 25,748 X 83,469. 332. 62,900 X 98,653. 304. 56,123 X 81,753. 333. 48 X 25,380. 306. 47,539 X 84,317. 334. 32 X 26,490. 306. 36,729 X 69,487. 336. 437 x 36,090. 307. 54,973 X 72,436. 336. 528 X 45,070. 308. 23,895 X 25,637. 337. 6,219 X 43,170. 309. 64,952 X 83,769. 338. 3,458 X 75,640. V. 16 AEITHMETldAL fiXERCISE^. 339. S60 X 41,025. 366. 4,720 ix! 769,000. 340. 470 X 70,386. 367. 2,970 x 948,000. 341. 4,680 X 63,207. 368. 4,680 X 538,000. 342. 6,780 X 72,036. 369. 4,500 X 563,000. 343. 57,930 X 70,319. 370. 5,600 X 683,000. 344. 75,380 X 54,305. 371. 38,700 X 739,000. 345. 860 X 23,950. 372. 47,600 X 895,000. 346. 570 X 67,480. 373. 463,700 x 648,000. 347. 3,740 X 64,030. 374. 350,900 X 683,000. 348. 6,380 X 32,040. 375. 84,000 X 596,000. 349. 83,270 X 80,320. 376. 497,000 X 394,000. 350. 25,640 X 90,450. 377. 257,000 X 379,000. 351. 950 X 87,600. 378. 859,000 X 973,000. 352. 760 X 54,300. 379. 184,000 X 789,000.. 353. 4,830 X 25,600. 380. 639,000 X 738,000:. 354. 3,640 X 34,800. 381. 19,307 X 207,019:. 355. 8,090 X 60,500. 382. 407,079 X 604,807:. 356. 4,070 X 38,500. 383. 704,896 x 704,098:. 357. 474,700 X 65,300. 384. 407,091 X 376,546*:. 358. 3,600 X 84,700. 385. 79,004 X 47,3001 359. 83,600 X 96,700. 386. 65,430 X 37,600. 360. 54,800 X 96,700. 387. 50,103 X 65,030. 361. 90,600 X 34,800. 388. 943,600 X 67,490. 362. 80,500 X 56,300. 389. 80,460 X 392,000. 363. 4,960 X 724,000. 390. 10,023 x 5,412,384. 364. 3,580 X 649,000. 391. 13,560 x 145,800. 365. 3,290 X 645,000. 392. 19,380 x 198,780,, INTEGRAL NUMBERS. 17 393. If 6 car tickets cost 25 cents, what will be the cost of 60? of 600? of 6000? of 24,000? of 48,000? 394. A barrel of kerosene oil holds 42 gallons. How many gallons are there in 10 barrels ? in 60 barrels ? in 600 barrels ? in 12,000 barrels ? 396. 2000 pounds are a ton. How many pounds in 10 tons ? in 50 tons ? in 500 tons ? in 100,000 tons ? 396. If 4860 pounds of manure are spread over 1 acre of land, how many pounds are required for 5 acres ? for 7 acres ? for 8 acres ? for 9 acres ? 397. If an acre of corn is worth $27, what is the value of the corn raised on 12,106 acres? 398. A ship brought home 379 boxs of oranges, each containing 258 oranges. How many oranges are there in all? 399. An army consists of 18 regiments, each containing 950 men. Each soldier wears out 3 pairs of boots in a year. What will it cost to provide this army with boots for 2 years, at $4 per pair? 400. On New Year's Day a man stopped drinking, and began to give his wife every week the sum of $2, which was the amount he used to spend on the average for drink. She saved the money, and at the end of the year she bought with it a sofa for $35, an easy-chair for $17, and 5 parlor chairs, at $6 each. After paying for these things, how much money did she have left ? 401. A clock strikes 156 times a day. How many times does it strike in a leap year (366 days) ? 402. A railroad 57 miles long cost $ 10,390 a mile. What was its entire coat ? 18 ARITHMETICAL EXERCISES. 403. Multiply the sum of eighty-five and ninety-three by their difference. 404. A train starts at 7 o'clock in the morning, and travels at the rate of 33 miles an hour. How many miles will it have travelled by 2 o'clock in the afternoon ? 406. If a swallow destroys daily 500 insects, how many will it destroy in 4 months of 30 days each ? 406. Light travels 185,000 miles a second. How many miles will it travel in eight minutes of 60 seconds each ? 407. A dozen dozen is called a gross. How many steel pens are there in 27 gross ? 408. If the rate of a steamer is 15 miles an hour, how many miles will it pass over in 8 days of 24 hours each ? 409. A butcher bought 42 sheep, at $6 each, and 16 calves, at $9 each. What was the cost of the sheep? the calves ? both together ? 410. A certain book contains 184 pages. Each page contains 32 lines, and each line has on the average 11 words. How many words are there in the book ? 411. A wholesale dealer bought 144 boxes of eggs, each box containing 72 dozen. How many eggs did he buy ? 412. There are 24 hours in 1 day. How many hours are there in 1 month of 30 days ? in 1 year of 365 days ? How many hours has Louis lived, who is 9 years 2 months and 6 days old ? 413. A man earns $75 per month, his wife $37, and his son $48. How much will all three earn in one year ? 414. Multiply each number from 10 to 20 by 10, 11, 12, etc., to 20, and arrange the factors and their products in a table like ihe Table of Multiplication. IKTEO&AL KUHBERS. 19 Fii id the quotients of : 415. 36 H -2. 443. 882 +.6. 471. 6951 -K 7. 416. 46 ^ -3. 444. 875 -H 7. 472. 4560 -*- 8. 417. 68 -H -4. 445. 384 ^ -8. 473. 5310 ^ 9. 418. 75 H -5. 446. 711 H -9. ' 474. 3656 ^ 8. 419. 84^ -6. 447. 623 H -7. 475. 5937 -^ 2. 420. 91 H -7. 448. 936 H -8. 476. 5930 : 3. 421. 72 H -8. 449. 860- ^4. 477. 3715 -^ 4. 422. 90 H -9. 450. 945 H -3. 478. 4123 ~ 5. 423. 86- ^5. • 451. 716^ -2. 479. 5633 -s- 6. 424. 92- h4. 452. 443 H -3. 480. 9984 ^ 7. 425. 87- h3. 453. 275 H -4. 481. 7436 ^ 8. 426. 95- h5. 454. 412- f-5. 482. 5179-1-9. 427. 73- h-2. 455. 419- h-6. 483. 9265 H- 8. 428. 49- ^3. 456. 592- ^-7. 484. 6345 ^ 8. 429. 57- ?-4. 457. 390- h-8. 485. 4187 ^ 9. 430. 82- 5-5. 458. 868- h9. 486. 3009 -f- 8. 431. 69- ^6. 459. 594- ^-7. 487. 5372 : 2. 432. 79- h7. 460. 583- 1-4. 488. 8547 -^ 3. 433. 95- ^8. 461. 819- h5. 489. 5180 -^ 4. 434. 39- ^-9. 462. 725- h-6. 490. 9745 -5- 5. 435. 87- h7. 463. 9374- h2. 491. 5670 -i- 6. 436. 77- h4. 464. 7846- 1-3. 492. 8538 -*- 7. 437. 88- H-3. 465. 9736- r-4. 493. 4783 -^ 2. 438. 99- h5. 466. 6836- h5. 494. 8626 -f- 3. 439. 862- h2. 467. 8142- f-6. 495. 9581 -4- 4. 440. 714-- -3. 468. 9002- f-7. 496. 7394 -»- 5. 441. 876- -4. 469. 6776- h8. 497. 8325 -^ 6. 442. 840 -. -5. 470. 4212- h9. 4^^, . ^^^^-v"! 20 AEITHMETICAL EXfiJlOISES. Divide by 2 ; by 3 ; and so on to 9 : 499. 9437. 601. 6392. 500. 5179. 502. 8765. Divide by 20 ; by .30 ; and so on to 90 : 503. 4791. 506. 9572. 504. 6783. 506. 8327. Divide by 200 ; by 300 ; and so on to 900 : 507. 9759. 609. 9985. 608. 9684. 510. 9564. Find tbe quotients of : 511. 7,468 H- 63. 612. 4,687 H- 73. 513. 6,874^84. 614. 8,746 -f- 94. 616. 8,913 -^ 25. 516. 9,138 -^ 35. 517. 5,389 -^ 46. 518. 3,895 ^ 56. 619. 6,958-^67. 620. 9,586 ^ 77. 621. 5,869-^-88. 622. 8,695 h- 99. 523. 59,384 -f- 21. 624. 93,845-^31. 625. 38,459 -^- 42. 626. 24,637 -T- 52. 527. 84,593 -^ 63. 628. 45,938 H- 73. 629. 630. 631. 632. 633. 634. 635. 636. 637. 638. 639. 640. 541. 642. 543. 544. 546. 646. 74,958 49,587 95,874 58.749 87,495 72,463 56,789 67,895 78,956 89,567 95,678 45,678 56,789 67,895 78,956 89,567 95,678 56,789 -h84. -f-94. ^25. -^35. -^46. -^56. -^67. -^77. ■^88. -ir 98. -5-29. -f-39. ^14. -f-15. -^16. -f-17. ^18. -^19. INTEOfiAL iruMBGilS. 21 547. 278,356 H - 22. 676. 54,289 ^ -407. 648. 802i005 H - 34. 577. 42,895 -. 1-512. 549. 415,920- f 46. 578. 28,954- K-613. 650. 502,080 -. - 58. 579. 89,542 - J- 724. 651. 758,213 H - 16. 680. 95,428 - i-836. 652. 329,457 - i- 14. 681. 79,382 -«- 947. 563. 278,356 - ■r- 32. 682. 93,827 - h958. 564. 802,005 - H 44. 683. 84,596 - 1-675. 566. 415,920 ^ - 56. 684. 45,968 - h583. 656. 502,080 - ■r- 68. 586. 59,684 - h768. 657. 758,213 - h 17. 686. 96,845 - ^859. 558. 329,457 - h 13. 587. 68,459 - h964. 559. 278,356 - H. 42. 688. 73,821 - 1-485. 660. 802,005 H - 54. 589. 38,217 - 1-576. 661. 415,920 - ^ 66. 590. 82,173- r-658. 662. 502,080 - h 78. 691. 21,738- h783. 663. 758,213 -. !- 18. 692. 17,382 - 1-877. 664. 329,457 - h 17. 593. 94,658 - 1-987. 665. 278,356 - ■r- 52. 694. 46,589 - h999. 566. 802,005 -. h 64. 595. 654,321 - 1-305. 567. 415,920 - H 76. 696. 888,333 - 1-326. 668. 502,080 H - 88. 697. 678,901 - h958. 569. 758,213 - h 19. 698. 496,432 - h434. 570. 329,457 H - 18. 599. 563,497 H h567. 671. 83,216 H -101. 600. 718,584 H -432. 572. 32,168 -'. -102. 601. 654,321 H h407. 573. 21,683 H -203. 602. 888,333 1 -528. 674. 16,832 H -205. 603. 678,901 H h964. 676. 68,321 -i -306. 604. 496,432 -i -572. 22 ARITHMETICAL EXERCISES. 606. A straw-shop can make 350 hats a day. How many days will it take to fill an order for 28,000 hats ? 606. How many times can 239 be subtracted from 4302? 607. What number multiplied by 79 will give the same product as 279 multiplied by 653 ? 608. How many 6-pound packages of buckwheat flour can be made from 15,000 pounds of the flour ? 609. A salt dealer put up 44,000 pounds of salt, in boxes holding 20 pounds each. How many boxes were required ? 610. A society of 3240 persons went on a excursion. How many cars were required to carry them, allowing 72 to each car ? 611. How many weeks will it take a man to dig a ditch 864 feet long, if he can dig 48 feet a day ? 612. The dividend is 3856, the quotient 142, the remain- der 22. Find the divisor. 613. If 8 dozen shirts cost $192, how much is this a dozen ? How much for each shirt ? 614. A ship sailed from Liverpool to the Cape of Good Hope, a distance of 7000 miles, in 50 days. What was her average daily rate? 616. The New Testament contains 260 chapters. How many days will it take a person to read through it, if he reads a chapter every morning and 3 every evening ? 616. A mile contains 5280 feet. How many times will a wheel 11 feet in circumference turn in going a mile ? 617. If sound travels 1060 feet a second, and a cannon Is fired at a distance of 16,960 feet, how many seconds will intervene between the flash and the report ? INTEGRAL NUMBERS. 23 618. The area of British India is 1,004,616 square miles, and the population 150,767,861. How many persons are there to a square mile ? 619. A railroad is 81 miles long, and cost $1,000,000 lacking $55. What did it cost per mile ? 620. A page of a book contains 36 lines and 2052 let- ters. How many letters on the average are there in a line? 621. The dividend is nine hundred and eighty-seven, the quotient fifty-four, and the remainder fifteen. What is the divisor ? 622. A shoe dealer bought 4 dozen pairs of shoes for $96, and sold them at $3 a pair. What was his profit ? 623. I bought 14 watches for $756. What must be my selling price in order to gain $6 on each watch? 624. In Iowa, in 1880, 260,192,840 bushels of corn were raised. The area planted was 6,847,180 acres. What was the average yield per acre in bushels ? 626. One day a fruit peddler sold 288 oranges. His profit on each dozen was 3 cents. How many cents was his profit on them all ? 626. A man agreed to dig a ditch through a meadow for $200. It took him 80 days to do the work. How much did he receive a day ? 627. A cider merchant made 12,000 gallons of cider, which he put into casks holding 42 gallons each. How many full casks did he have ? 628. How many days will 72 bushels of oats last 12 horses, if each horse is allowed 6 quarts a day? One bushel contains 32 quarts. 24 ARITHMETICAL EXERCISES. 629. 68,179,600 pounds of pork were exported from the United States in the year 1882. How many barrels of 200 pounds each were exported ? 630. In 1880, 25,519,200 bushels of osAs were raised in Ohio. The number of acres sown was 911,200, and the total value of the oats was $8,676,528. What was the average yield per acre, and what was the average value per bushel ? 631. A man bought 9 cows for $378, and sold them for $4 more for each cow than he gave. What did he pay for each cow, and how much did he receive from the sale of all of them ? 632. The total cost of publishing 3600 copies of a pam- phlet was $282. If 1400 copies have been sold, at 12 cents each, how many more copies, at 10 cents each, must be sold to pay expenses ? 633. How many States of the size of Rhode Island could be made out of the State of New York, and how much would be left over ? (For data, see page 4.) 634. How many States as large as New York could be made out of Texas, and how much would be left over? (See page 4.) 635. If as many persons die in 33 years as are equal to the entire population, how many persons on an average die annually out of every million ? 636. In how many hours will a cistern holding 3330 gallons be filled by a pipe that discharges into it 185 gal- lons an hour ? Also, in how many hours, if another pipe at the same time allows the water to run out at the rate of 74 gallons aij hour ? INTEGRAL NUMBERS. 25 637. In New Jersey, for the year ending July 31, 1883, there were made 186,400,000 bricks, worth $1,480,700. What was the average value per thousand ? From the following data from the census of 1880, find for each State the average yield of tobacco per acre, and the average value per pound : Pounds No. of produced. acres. Total value. 638. Connecticut, 15,487,660 10,070 $2,323,149 639. Pennsylvania, 34,854,108 29,729 3,485,411 640. Maryland, 18,841,830 26,726 1,318,928 641. Virginia, 78,421,860 118,821 6,273,749 642. North Carolina, 35,724,385 63,229 3,215,195 643. Kentucky, 149,017,855 224,087 10,431,250 644. Tennessee, 24,319,890 38,603 2,188,790 645. Ohio, 38,434,587 35,439 2,306,075 From the data given below, and taken from the census of 1880, find for each State the average yield of cotton per acre, and the average value of the cotton per pound ; Pounds No. of produced. acres. Total vcUue. 646. N. Carolina, 184,734,000 933,000 $18,473,400 647. S. Carolina, 266,696,000 1,441,600 29,336,560 648. Georgia, 454,166,900 2,786,300 45,416.690 649. Florida, 35,727,200 251,600 3,215,448 650. Alabama, 378,932,400 2,460,600 37,893,240 651. Mississippi, 391,300,000 2,275,000 39,130,000 652. Texas, 550,873,000 2,395,100 49,578,570 653. Arkansas, 232,243,000 1,080,200 23,224,300 654, Tennessee, 165,688,600 816,200 14,911,974 26 ARITHMETICAL EXERCISES. Write all the prime numbers between : 655. 1 and 50. 665. 600 and 550. 656. 50 and 100. 666. 550 and 600. 657. 100 and 150. 667. 600 and 650. 658. 150 and 200. 668. 650 and 700. 659. 200 and 250. 669. 700 and 750. 660. 250 and 300. 670. 750 and 800. 661. 300 and 350. 671. 800 and 850. 662. 350 and 400. 672. 850 and 900. 663. 400 and 450. 673. 900 and 950. 664. 450 and 500. 674. 950 and 1000. Eesolve into prime factors : 675. 225. 685. 504. 695. 960. 705. 1725. 676. 315. 686. 672. 696. 1152. 706. 27,525. 677. 392. 687. 704. 697. 1296. 707. 11,256. 678. 441. 688. 756. 698. 1728. 708. 87,147. 679. 495. 689. 792. 699. 2240. 709. 1176. 680. 616. 690. 1056. 700. 1624. 710. 2750. 681. 968. 691. 240. 701. 2925. 711. 2555. 682. 1089. 692. 486. 702. 2254. 712. 7755. 683. 405. 693. 729. 703. 71,001. 713. 5544. 684.. 448. 694. 768. 704. 1261. 714. 7581. Find the G.C.M. of : 715. 342, 665. 719. 1500, 1565. 723. 1650, 960. 716. 720, 1720. 720. 6409, 7395. 724. 1712, 1872. 717. 2272, 3522. 721. 5187, 5850. 725. 3708, 3264. 718. 252, 1000. 7»2. 394, 672. 726. 2523, 1798, INTEGBAL NUMBEBS. 27 727. 2067, 3146. 728. 1908, 2736. 729. 384, 1296. 730. 406, 622. 731. 1025, 1575. 732. 7455. 4723. 733. 2883, 2356. 734. 2486, 736. 3003, 736. 5550, 737. 4067, 738. 1392, 739. 5325, 740. 4242, 4407. 2574. 4551. 5146. 2048. 8307. 6565. 741. 742. 743. 744. 746. 746. 747. 4833, 4972, 6916, 3861, 1442, 19^6, 1742, 6237. 4407. 5850. 4653. 7245. 2340. 2386. a' \ Find the L.C.M^f: 748. 7, 8, 15, 21, 24. 749. 8,9,16,24,27. 750. 4, 7, 12, 21, 34. 751. 12,16,21,35,42,60. 752. 12, 14, 20, 24, 30. 763. 15, 27, 36, 54, 60, 80. 764. 6, 9, 15, 25, 36, 40, 54. 755. 8, 12, 18, 24, 28, 30. 756. 10, 15, 18, 24, 28, 40. 757. 16, 14, 12, 32, 50, 75. 758. 14, 21, 24, 36, 49, 60. 759. 15, 18, 24, 40, 50, 90. 760. 16, 14, 20, 24, 32, 35. 761. 6, 6, 7, 8, 9, 10, 11, 12. 762. 8, 20, 34, 50, 56, 70, 85. 763. 4, 9, 10, 14, 15, 18, 21. 764. 14, 18, 24, 35, 42, 68. 765. 12, 16, 24, 36, 54, 144. 766. 24, 16, 20, 8, 30, 25, 12. 767. 15, 12, 128, 30, 16, 320. 768. 508, 889. 769. 517, 564. 770. 124,341,372. 771. 312, 260, 390. 772. 112, 200, 72. 773. 195,234,225. 774. 454,478,227. 776. 544,170,850. 776. 1025, 1575, 315. 777. 3003,2574,1287. 778. 242, 22, 286. 779. 112, 196, 588. 780. 252, 170, 84, 72. 781. 175,140,65,560. 782. 132, 144, 154, 288. 783. 100, 96, 87, 128. 784. 144, 96, 176, 168. 786. 708,177,354,826. 786. 760, 364, 336, 1736. 787. 720,396,252,540. 28 ARITHMETICAL EXERCISES. Miscellaneous. 788. If a bushel of corn is worth 72 cents, what is the value of 100 bushels ? of 10,000 bushels ? of 40,000 bushels? 789. One man is worth $3240, another 10 times as much, and a third 10 times as much more. What are they all three worth ? 790. A cabinet-maker made 14 tables at a cost of $7 each; he sold them at $11 each. How much money did he make ? 791. A jeweller sold 17 clocks, at $ 14 each. He received for pay 24 ten-dollar bills. How much money should he return ? 792. A boy can point 13,679 pins in an hour. How many can he point in 6 days, working 9 hours each day ? 793. If I buy 60 horses, at $130 apiece, and sell 18 of them at $175 each, and the rest at $115 each, do I gain or lose, and how much ? 794. How much more will a man earn in a year, at $25 a month, than at $22.60 a month ? 796. A farmer sold 33 cans of milk, at 62 cents a can, and 16 cans, at 58 cents a can. If he is paid $25, how much is still due? 796. In the siege of Gibraltar (1779-1783) the English fired 67,163 round shot, and the French, 176,741. If the average weight of each ball was 18 pounds, how many pounds of iron were fired ? 797. A treasury clerk receives $ 126 a month, and spends $87. How much will he save in one year ? INTEGRAL NUMBERS. 29 798. My daily paper costs 2 cents on each week day and 5 cents on Sunday. What will it cost for one year having 365 days, 52 of which are Sundays ? 799. A pound of platinum is worth $85. The yearly production of platinum in South America is 550 pounds, and in the Ural Mountains 4180 pounds. What is the value of the total yearly production ? 800. Fill out the account of the following sale : 9 chamber sets, at $ 65 each, $ 15 " " " $58 " Total, $ Cash paid, $875 Still due, 801. A grocer bought 214 barrels of extra flour, at $8 each, 78 barrels of ordinary flour, at $6 each, and 43 bar- rels of sugar, at $ 16 each. Make out an account of the purchase, and find the amount of his bill. 802. A trader sold 4 dozen straw hats, at $2 each, 2 dozen seal-skin caps, at $ 11 each, and 7 dozen beaver hats, at $6 each. He received $125 cash on the bill. How much is still due him ? 803. A stock farmer estimates roughly the value of his stock, as follows : 175 cows, at $46 each ; 87 calves, at $8 each ; 10 pairs of oxen, at $ 140 a pair ; 4 bulls, at $ 80 each ; 215 sheep, at $12 each ; and 160 hogs, at $11 each. How many animals has he in all, and what are they all worth? 804. If the annual sale of dime novels in this country is 600,000 copies, how much money is expended on them in one year ? 30 ARITHMETICAL EXERCISES. 806. John's father on his sixteenth birthday began to give him half a dollar a week, to use as he pleased. If John spends on the average 10 cents a week, and saves the rest, how much money will he have on his twenty-first birthday ? 806. A good cow yields 168 pounds of butter a year. If it takes 216,000 cows to supply London with butter, how many pounds of butter are consumed annually in that city ? 807. A farmer has 6 cows that give each 12 quarts of milk daily for 8 months in the year. He sells the milk for 6 cents a quart. How much does he receive for the milk, counting 30 days for each month ? 808. A factory employs 220 men, 87 women, and 64 children. Their average weekly wages are: men, $8; women, $5; children, $3. What is the amount of their wages for the year ? ^ 809. A fruit seller bought 15 dozen melons, at 10 cents apiece, receiving 13 for each dozen. Ten of the lot were bad, and the rest he sold at 15 cents apiece. What was his profit ? 810. Do not kill birds. They destroy the small insects which devour our crops. Certain kinds of birds, as swal- lows and tomtits, eat as many as 500 insects a day. How many insects will 25 such birds eat in 1 day ? in 1 month ? in 1 year? 811. The female cockroach lays in the ground on the average 90 eggs. Each egg may give birth to a white worm, which, during the three or four years that it lives in the ground, devours the roots of at least 150 plants. How many plants are saved by a child who kills 260 cock- roaches ? INTEGRAL NUMBERS. 81 812. The mole is a useful animal, for it eats insects which destroy the roots of plants. If a mole kills 3 insects a day, and each insect is able to destroy 18 plants worth 15 cents each, how much money may the mQle save for the owner of the plants in a year ? 813. How many years from the Deluge, B.C. 2348, to the end of a.d. 1884 ? 814. Two boys spend a week walking together in the White Mountains. On Monday they walked 20 miles ; on Tuesday, 13 miles; on Wednesday, 18 miles; on Thursday, 26 miles ; on Friday, 22 miles, and on Saturday, 9 miles. How many miles did they walk during the week ? 815. I sold a piece of land for $2176, and thereby lost $75. What did the land cost me ? 816. An orchard contains 89 apple-trees, an equal num- ber of pear-trees, 78 peach-trees, an equal number of plum- trees, 17 cherry-trees, and 1 mulberry-tree. How many trees are there in the orchard? 817. One day a dealer in toys sold 127 marbles. The next day he sold as many more. He then had 46 left. How many had he at first ? 818. A man has 6 teams, and each team can haul 4 cords of wood a day to market. How many days will it take him to haul 720 cords to market ? 819. The area of England is 50,535 square miles ; of Scotland, 29,167 square miles ; and of Wales, 8,125 square miles. How many more square miles are there in England than in Scotland and Wales taken together ? 820. Four loads of hay together weighed 9169 pounds. The first weighed 2007 pounds ; the second, 1963 pounds ; the third, 2614 pounds. What was the weight of the fourth ? 32 ARITHMETICAL EXERCISES. 821. I have 272 stamps, and my brother has 25 more than I. How many have we together ? 822. A man was born in 1817. When will he be 75 years old ? ■ 823. For the fiscal year ending June 30, 1881, the ex- ports and imports of the United States were as follows : Exports. Imports. Merchandise, $902,367,346 $642,664,628 Specie, 19,406,847 110,575,497 What was the trade balance in favor of the United States ? 824. A farmer took $1000 with him to market. He bought a horse for $225, a pair of oxen for $170, a bull for $90, and a carriage for $145. On his way home a part of his remaining money was stolen. When he reached home he found he had only $ 60 left. How much of his money was stolen ? 825. John bought an arithmetic for 45 cents, a reader for 37 cents, a penholder for 4 cents, and a quire of paper for 15 cents. He gave the shopkeeper a two-dollar bill. How much change should he receive back ? 826. A farmer sold for $490 a horse which cost him $647, and for $310 another horse which cost him $225. Did he gain or lose on the two horses, and how much ? 827. A man bought 3 houses. He paid for the first, $6260; for the second, $3585; and for the third, as much as for both the others. He sold them all for $15,979. How much did he lose by the transaction ? 828. If 110 sugar-canes yield 6 pounds of sugar, how many pounds will be obtained from 1,233,210 canes? 829. How many solid squares, with 8 men on each side, can be formed out of a million of men ? INTEGRAL NUMBERS. 83 880. At an election 3795 persons voted, and one of the candidates received 709 votes more than the other. How many voted for each candidate ? 831. Shem was 98 years old at the time of the Flood, B.C. 2348, and 600 yjears old when he died. Abraham was bom, B.C. 1996. How old was Abraham when Shem died ? 832. Two trains start from the same place at the same time. One travels at the rate of 35 miles an hour, the other at the rate of 25 miles an hour. How far apart will they be after 7 hours, if they travel in opposite directions ? How far apart if they travel in the same direction ? 833. Multiply one million and one by three hundred thousand and three. 834. A merchant began business with $20,000, and retired after 17 years* trading. He made $5600 each year for the first 6 years, lost $8476 the next year, and made $ 7320 a year for the remainder of the time. How much was he worth when he retired from business ? 836. A man owns 3 houses. The first is worth $3333, the second is worth 3 times as much as the first, and the third is worth 3 times as much as the first and second together. What is the value of the 3 houses ? 836. A certain number exceeds nine dozen and nine by 168. Another number falls short of 189 by eight dozen and eight. Find the product of these two numbers. 837. If 19 oxen cost $1330, and an ox is worth 14 sheep, what is the price of a sheep ? 838. A man paid $931 for 49 acres of land, and $98 for fencing it in. He then sold it for $25 an acre. What was his profit ? 34 ARITHMETICAL EXERCISES. 839. If a woman can make 5 yards of ribbon a day, working 12 hours each day, how many hours must she work in order to make 840 yards ? 840. Overall makers in Boston receive 5 cents a pair when made at home, and 50 cents a dozen when made in the shop. If a girl make 2400 pairs at home, how much more will she receive than if she make them in the shop ? 841. There were in Ohio, in January, 1883, 774,253 milch cows, valued at $27,098,855. What was the aver- age value of a cow ? 842. A grocer bought 5 firkins of butter, containing respectively 42 pounds, 46 pounds, 55 pounds, 38 pounds, and 49 pounds. What was the average number of pounds to a firkin ? 843. The attendance at the high school one week was as follows: Monday, 116; Tuesday, 109; Wednesday, 84; Thursday, 96; Friday, 111; Saturday, 120. What was. the daily average attendance for the week ? 844. If 336 bees weigh an ounce, and 4032 bees fill a quart, how many ounces will a swarm weigh that just fills 2 quarts ? 846. How many States, each as large as Massachusetts, could be formed out of Texas, and how much would be left over ? (See page 4.) 846. If four new States were formed out of Texas, having the respective areas of New York, New Jersey, Pennsyl- vania, and Ohio, what area would still be left? (See page 4.) 847. Lake Erie covers 9600 square miles. How much larger is it than the States of Massachusetts and Rhode Isl&nd taken together? (See page 4.) INTEGRAL NUMBERS. 35 848. Of what number is 1188 both divisor and quo- tient? 849. What number between 400 and 600, besides 475, will divide 211,850 without a remainder? 860. A confectioner puts up 4000 pounds of assorted candies in 1-pound, 2-pound, and 6-pound packages, of each size an equal number. How many packages did he put up all together ? 851. A dealer in horses bought 40 horses at $125 apiece, and sold 15 of them at $ 105 each. At what price apiece must he sell the others in order to clear $600 by the transaction ? 862. Mr. Gage owns a farm valued at $ 8500, and his life is insured for $10,000. He has also the following stocks : 60 shares Atchison R.R. stock, at $94 a share. 35 " Boston & Albany R.R. stock, at $196 " " 18 " Bell Telephone stock, at $214 " " His other personal effects are valued at $2400. What are his total assets ? A 863. A wholesale grocer wishes to put up for market, in packages of equal weight, 4000 pounds of oatmeal and 3144 pounds of cracked wheat. He also wants to have as few packages as possible. What is the least number of pack- ages he can have, and what is the weight of each pack- age? 854. Half the sum of two numbers is 412, and half their difierence is 40. What are the numbers ? 865. A certain school is attended by 112 boys and 147 girls. What is the smallest possible number of classes which can be formed, each class to contain the same number of scholars, and to consist entirely of boya ot ^h^ai^'^ cX. ^-^^1 86 ARITHMETICAL EXERCISES. 856. What is the smallest number of dollars that can be divided into piles, either of $5 each, or of $4 each, or of $2 each? 857. A man paid $1450 for a farm, $325 for drainage, $80 for fencing, and $420 for labor. The gross proceeds for one year amounted to $2975. With the profits he buys sheep at $5 each, and cows at $23 each, of each the same number. How many animals of each kind does he buy ? 858. On July 1, 1871, the debt of the United States, less cash in the treasury, was $2,292,030,835. By July 1, 1885, it had been reduced to $1,386,555,523. What was the average reduction per annum for the whole of this period ? 859. The foreign immigration into the United States during the 10 years ending June 30, from 1876 to 1885 inclusive, was as follows : 1876, 169,986. 1881, 669,431. 1877, 141,857. 1882, 788,992. 1878, 138,469. 1883, 603,322. 1879, 177,826. 1884, . 518,592. 1880, 457,257. 1885, 395,346. What was the total number, and what was the average for each year ? 860. The revenue and expenditure of the United States in dollars, as estimated by the secretary of the treasury and in actual amount, for the fiscal year ending June 30, 1885, were as follows : Estimated. Actual Amount. Revenue, 330,000,000. 323,690,706. Expenditure, 243,000,000. 260,226,935. How far was the secretary out of the way in each estimate? What was the surplus for the year ? INTEGRAL NUMBERS. 37 861. A house-builder bought a house for $2637, and spent $247 in repairing it; he then sold it for $3000. What did he gain ? 862. Harry is reading a book of 524 pages ; he is now at page 228. How many pages has he still to read ? If to-morrow he reads 78 pages, and the next day as many more, at what page will he then be ? How many pages will then remain to be read ? 863. One spring supplies 119 barrels of water in 7 hours; another, 390 barrels in 15 hours; and a third, 324 in 18 hours. In how many hours will the three springs together fill a cistern holding 1647 barrels ? 864. A clerk agreed to work for a yearly salary of $1460. How much was that a day? He was discharged at the end of 5 months. How much is still due him, if he has already received $85 ? 865. A publisher sold 1500 copies of a book for $1020, and thereby made a profit of $ 150. Find the cost, the selling price, and the profit per hundred copies. 866. A button-hole maker earned in one month of 26 working days $52. She did 800 button-holes a day, and is paid at the rate of 25 cents per hundred. How many button-holes did she do during the month ? 867. Mr. Fernald never gets home to supper till after 6 o'clock. His wife once kept an account for 30 days, and found that he was 15 minutes late 7 times, 18 minutes late 5 times, 20 minutes late 8 times, 25 minutes late 5 times, and half an hour late 5 times. What is Mr. Fernald's average time of getting home to supper ? CHAPTER II. DECIMAL FRACTIONa 1. Decompose the following numbers into their different orders of units : 0.6. 12.308. 9.123456. 0.14. 17.150. 36.008090. 0.543. 43.7209. 567.0086. 0.4305. 67.8070. 157.00007-. 0.0567. 1.21037. 589.40027. 0.0031. 0.01567. 0.5679357. 0.0507. 0.00896. 0.5612389. 0.4925. 0.04236. 0.0000768. 2.35. 0.00009. 0.0317897. 4.654. 0.00900. 0.0100059. 2. Read the numbers in the preceding exercise, pro- nouncing first the integral part, and then the decimal part. 3. Write the following numbers : three hundredths ; four hundred two thousandths ; three thousand two hundred twenty-five ten-thousandths ; twenty-seven thousand two hundred twenty-six hundred- thousandths ; ninety-seven and two hundred eighteen thousandths ; fifteen hundred- millionths ; one million and seventeen ten-millionths ; one million seventeen ten-millionths ; eighty-three thousand and twenty-seven thousandths ; eight thousand four ten- thousandths. PECIMAL FRACTIONS. 39 4. What place after the decimal point is the place of thousandths? hundred-thousandths? hundredths? mil- lionths? ten-millionths ? ten-thousandths? 5. In a decimal number, what is the name of the order of units written in the first decimal place ? in the third ? the fifth? the seventh? the fourth? the second? the sixth ? 6. Multiply by 10, 100, 1000 the numbers: 3.05; 4.538; 8.5. 7. Divide by 10, 100, 1000 the numbers: 32.8; 318.4; 4.825. 8. Reduce 40,000 cents to dollars. Reduce 75 dollars to cents. Add: 9. 10. 11. 12. 17.24 52.38 30.709 27.6090 42.73 367.4 0.80063 0.0046 12.06 0.172 96.40 3.4603 96.32 6.0053 0.210 0.034 9.60 9005.079 46.90050 56.90 13. 5678.0036 + 12.897 + 0.11593 + 0.612 -f 1.651. 14. 0.60105 + 0.00015 + 412.685 + 0.115 + 1.61 + 0.18. 15. 2.012 -f. 0.191 -f- 0.768960 + 71.02. 16. 707.60149 -f- 0.0000619 + 810.5 -f- 0.320 -f 0.0409. 17. 4.37805 -f 0.04459 + 600.2. 18. 806.78943 + 0.897601 + 1.2 + 8.97641 +0.006-f 8.654. 19. 7089.7642 + 8.9645 -f- 9.8764 + 102.67 + 789 + 1.870. 20. 0.501276+286. 78-f8.791+0.64218-f54.897+0.8964. 21. 0.305412+210.0015 + 2000.56 + 0.00001 + 4. 22. Eighteen and seventeen hundredths ; seven hundred seventy-seven ten-thousandths; seven and four hundred thirty-two thousandths. 40 ARITHMETICAL EXEECISES. Add: 23. One and eighteen ten-thousandths; two and four hun- dred ten-thousandths; eighty-five ten-thousandths; three hundred sixteen thousandths ; ninety-five hundredths ; one thousand eight ten-thousandths ; seventeen hundred-thou- sandths ; four and four thousand eighty-nine hundred- thousandths. 24. Fourteen ; fourteen tenths ; fourteen hundredths ; fourteen thousandths ; fourteen ten-thousandths ; fourteen hundred-thousandths ; fourteen millionths ; fourteen ten- millionths ; fourteen hundred-millionths. 25. 12 eagles ; 44 dollars ; 168 dimes ; 6927 cents. 26. 87 thousand-dollar bills ; 1260 hundred-dollar bills; 378 gold eagles ; 5500 dollars ; 42317 dimes ; 98 cents. 27. A shoemaker presented the following bill for his services. Correct the mistake in the addition. 1884. May 15. 1 pair of custom boots, $ 14.50 June 17. 1 pair of congress boots, 4.75 July 19. 1 pair of children's shoes, 2.26 Aug. 7. Repairing, 1.87 Oct. 9. 1 pair of fancy slippers, 3.40 Dec. 4. 1 pair of ladies* boots, 6.75 Total, 134.52 28. The separate items of an account on four pages of a ledger were as follows. What is the whole amount ? $2.45 $2.40 $4.72 $19.27 13.60 5.17 15.25 6.42 9.70 91.60 37.40 12.33 8.85 217.70 25.60 3.07 10.80 7.48 200.45 2.69 DECIMAL FRACTIONS. 41 '29. A newsboy's sales on Monday amounted to $1.68 ; on Tuesday, to $2.04 ; on Wednesday, to $2.46 ; on Thurs- day, to $1.88 ; on Friday, to $0.95 ; and on Saturday, to $3.24. What was the amount for the week ? 30. I bought a field for $877.50, and paid $88.27 for fencing and draining. At what price must I sell the land in order to make $125.50 ? 31. By selling a cow for $32.60 I lost $4.67. For how much should I have sold her to gain $8.50 ? 32. The main line of a railroad is 114.38 miles in length. There are four branches whose lengths in miles are respec- tively, 9.17, 22.05, 11.44, and 12.15. What is the entire length of the road ? ' 33. A lady bought at a dry-goods store 4 dozen buttons, for $1.20 ; 1 comb, for $0.87 J ; 1 bottle of rose water, for $0.70; 6 towels, for $1.98 ; 1 belt, for $1.12} ; 1 sack, for $16.25; 1 purse, for $2.75; and 1 penknife, for $0.45. What was the amount of her bill ? Find the difference between : 34. 174.29 and 49.62. 41. 3.125 and 1.9375. 35. 14.5389 and 5.870. 42. 8.425 and 5.3875. 15.136 and 0.89764. 43. 1.25 and 0.175. 0.5475 and 0.4212. 44. 2.834 and 2.786. 0.875 and 0.525. 45. 3.245 and 1.2375. 0.275 and 0.198. 46. 1.1 and 0.0009. 5.25 and 3.875. 47. 10 and 0.000010. 48. From thirteen hundred one and one hundredth take eleven hundred eighty-nine and twenty-five thousandths. ^ 49. From the sum of three hundred nineteen dollars /^twenty-five cents and fourteen dollars one cent take two hundred eighteeft dQllars seven cents. 42 ARITHMETICAL EXERCISES. \ * m 50. From the sum of 3.0045, 19.028, and 32.4009, take the difference between 63.4 and 9.004. 51. Find the difference between two and four hundred fifty-seven thousandths minus one and sixty-eight hun- dredths, and fourteen and ^ve tenths minus seven and eighty-eight thousandths. 52. How much greater is the sum of seven thousand four hundred sixty-seven and one thousandth than the dif- ference between five and nine hundred-thousandths'? 53. Subtract 387 cents from $387. 54. Subtract 24,000 cents from $8400. Find the following differences : 55. 53.0718-61.89712. 61. 64.89767-50.81789. 56. 1.05689-0.6873045. 62. 90.3217-72.02134. 57. 54.91204-46.00036. 63. 90.6438-89.76432. 58. 15.10246-0.54056. , S4. 2.959656-1.5645. 59. 0.2001234-0.01069. 65. 15.896-12.0716897. 60. 0.040621-0.0213. 66. 9.03-0.90003. 67. A lady bought a sewing-machine for $37.50. She gave in exchange her old machine, valued at $9.75, and the balance in money. How much money did she pay ? 68. The Boston and Maine Railroad Company, in 1883, operated 203.84 miles of road, of which 58.76 was double track. How much was single track ? 69. The distance from New York to Chicago by the New York Central and Lake Shore route is 982.24 miles. The distance from New York to Buffalo is 441.75 miles. What is the distance from Buffalo to Chicago ? DECIMAL FBACTIONS. 43 70. John bought a cap for $1.63, a pair of boots for $3.75, and a pair of skates for $2.10. He gave the sales- man a ten-dollar bill. How much ^loney should be given back ? 71. At night the mercury of the thermometer stood at 44.7 degrees; in the morning it stood at 28.8 degrees. How many degrees did it fall during the night 7 72. Before a storm the mercury in a barometer fell from 80.292 inches to 29.347 inches. How many inches did it fall ? 78. New Year's Day my father gave me $3.50; my mother, $2.25; and my two aunts, $0.80 each; and I bought a present for my sister, costing $4.25. How much money have I left ? 74. One pound of dry oak-wood when burnt yields 0.022 pounds of ashes. What part of the pound disappears in the air? 76. An ice-house contained 1000 tons of ice. The owner sold at different times, 242.765 tons, 87.125 tons, and 166.375 tons. He then found that he had 480.042 tons left. How much had been lost by melting ? 76. The revenues of the United States for the fiscal year ending June 30, 1883, were: customs, $214,706,496.93; internal revenue, $144,720,368.98; other sources, $38,860,- 716.04. The expenditures for the same period were $265,408,137.54. What was the surplus for that year? 77. The heights of the barometer observed on four successive mornings were as follows : 29.74 inches, 29.62 inches, 29.4 inches, and 29.55 inches. What was the average height for this period ? 78. How much must be added to nine thousandths in order to obtain the whole number nine? How much in order to obtain nine thousand ? 44 ARITHMETICAL EXERCISES. Find the products of: 79. 5.27 X 4.83. 88. 4.36 X 219000. 80. 4.36 X 2.19. 89. 7.43 X 0.067. 81. 1.89 X 0.76. 90. 2.06 X 21.716. 82. 2.38 X 3.47. 91. 4.36 X 0.0219. 83. 5.62 X 0.213. 92. 5.62 X 0.0213. 84. 2.78 X 0.547. 93. 2.78 X 0.0213. 85. 5.27 X 0.00483. 94. 7.19 X 1.012. 86. 18.9 X 0.000076. 95. 6.78 X 11.007. 87. 52.7 X 48300. 96. 5.69 X 30.800. 97. Three hundred twenty-seven ten-thousandths by four hundred eight thousandths. 98. Four millionths by nine ten-thousandths. 99. Three hundred seventeen millionths by one hundred seventy-nine ten-thousandths. 100. Thirty-four thousand five hundred sixty-four mil- lionths by fifteen hundred-thousandths. 101. Four hundred ninety-five millionths by eight hun- dred four ten-thousandths. 102. Nine hundred twenty-five dollars sixteen cents and eight mills by three and seventeen thousandths. 103. Twelve hundred seventy-five dollars by twelve hundred seventy-five ten-thousandths. 104. 7896.01 X 6.8970. 110. 0.7639x763900. 105. 0.44068x0.0024. 111. 0.0009 X 0.0983, 106. 0.18961x1.15. 112. 380.460 X 23.40. 107. 42.6008 X 0.204. 113. 84.459 X 0.54. 108. 0.78964 X 1.2565. 114. 78.924 x 3.6100. 109. 5.78934x0.0763. 115. 7642.8 X 6.564. DECIMAL FEACTIONS. 45 Find the quotients of : 116. 1.7503-5-7.61. IIT. 39.538 -*- 0.53. lie. 392.37-^31.9. 119. 5.2441 -f- 22.9. 120. 228.75-^30.5. 121. 89645 -f-1.05. 122. 3.162 -*- 79.05. 123. 27.09 -^0.047. 124. 5.765 -^2.5. 125. 0.736 ■^200. 126. 9.216 ■i- 0.0256. 12T. 0.817 H- 0.9147. 128. 78.1 • ■*■ 1.071. 129. 918 ■*- 914.71. 130. 213 • 4- 91.614. 131. 17.5 ■ ■^ 1.15. 132. 24.8 ■ : 400. 133. 300 -5-0.015. 134. Multiply sixty-two hundredths by sixty-two hun- dredths, and divide the product by four ten-thousandths. 136. Divide five hundred seventy-nine by seventy-five thousandths, and from the quotient subtract eighteen hun- dred-thousandths. 136. Multiply 3.15 by 0.315, and divide the product by 2.5. 137. Divide five thousand six hundred by twenty-eight hundredths, and to the quotient add fifteen and nine hundredths. 138. Divide fifty dollars seventy-five cents by forty-six, and add five cents to the quotient. 139. 110.925 -J- 1.53. 140. 1109.25-^0.0153. 141. 0.39237 -J- 3190. 142. 0.39538 H- 5300. 143. 0.52441 -V 229C0. 144. 0.78895-15.5. 145. 20973.6-^0.8739. 146. 9110.64^2900. 147. 0.03486 -^- 4.98. 148. 175.030-^76100. 149. 0.62825 -f- 1.75. 46 AEITHMETICAL EXEECnSES. Miscellaneous. 151. Add five and 394 thousandths; 85 ten-thou- sandths ; seventy-five and 19 hundredths ; 10G9 ten- thousandths; five hundred eighty-nine and 300 ten- thousandths ; 108 ten-thousandths. 152. Subtract 325 thousandths from 325. 153. The subtrahend is four hundred eight ten-thou- sandths, the minuend is ninety-five hundredths. Eequired the remainder. 154. Simon Day bought six horses : for the first he paid $107.09; for the second, $87; for the third, $ 98.02 ; for the fourth, $53.75; for the fifth, $83.25; and for the sixth, $115.95. Required the cost of all. 156. Two men starting from the same place travelled in opposite directions, one going 595.25 miles ; the other, 789.01 miles. , How far apart were they, and how much farther did one travel than the other ? 166. From five trees 76 bushels of apples were gathered ; one bore 12.07 bushels ; another, 15.25 ; another, 17.01 ; another, 16. What was the yield of the fifth? 157. John Greene had $ 1000 deposited in a bank ; he paid for rent, $150 ; to the butcher, $125.13 ; to the gro- cer, $148.10; to his tailor, $30; for taxes, $37.80; and gave $60.75 for charities. What sum remained to his credit in the bank ? 168. A man earned in a week, $6.07; in another, $7.03; in another, $11.25. He paid from this for board^ $7.08; for boots, $3.25; for car-fare, $0.75; and for fo^hrs, pi. 2^. How much remained ? DECIMAL FRACTIONS. 47 159. A man made 15.09 rods of fence in one day, 17.2 the next, 12 the next, and 16.4 the next ; a hurri- cane carried away 13.9 rods and displaced 12.12 rods. How many rods of perfect fence remained ? 160. A meat bill for the several days of the week was $4.25, $3, $4.18, $3.06, $2.17, $5.03. On Wednesday $5.18, on Friday $3.01, were paid. What was the balance due after Saturday's purchases ? 161. A merchant, from a bin of coal containing 70 tons, sold at different times 15.05, 18.9, 25.01 tons. After these sales he put in 13.08 and 0.25 tons. How many tons were there then in the bin? 162. Abraham Arnold began farming with $1784. He bought a horse for $87.25, farm implements for $385, fur- niture for $490.75, repaired his house at an expense of $275.01, bought stock for his farm to the amount of $409.17; he then received a legacy of $1350.40. How much money had he left after all his bills were paid? . 163. A drover bought four horses. For the first he paid $97.25; for the second, $25 more than for the first; for the third, the sum of the cost of the first and second ; for the fourth, $240,825. He sold them all so as to gain the difference between the cost of the first and last. What was his gain, and what did he receive for the whole ? 164. Hiram James owes to one man $ 1000 ; to another, $75.02; to another, $198.75; and to a fourth, $325.50. How much money will he need to pay these debts and have $2189.84 to begin business? 165. The difference between two cargoes of coal is 3754.0009 tons, and the smaller cargo has 2789.01 tons. Required the number of tons in the larger ca.Tgfi, 48 ARITHMETICAL EXERCISES. 166. What is the cost of 8.5 yards of cloth at $0.75 per yard? 167. How many yards of cloth at $0,125 per yard can be bought for $45,625? 168. Eleven and seventy-five hundredths tons of coal cost eighty-two dollars and twenty-five cents. What will be the cost of twenty-one and four-tenths tons? 169. A five-dollar bill was given to pay for 16.4 pounds of sugar at $0,125 per pound. What change should be given back? 170. A case of five dozen collars cost $8.70. For what must they be sold apiece to bring $ 10.20, and what will be the gain on the whole? 171. A grain merchant spent $303.75 for equal quanti- ties of rye at 60 cents, and corn at 75 cents per bushel. How many bushels of each grain did he buy ? 172. A man bought 80 yards of cotton cloth for $18.40, and had made from it 2 dozen shirts. Find the price of the cloth per yard, and the cost of a shirt, if the expense of making the 2 dozen shirts is $6.80. 173. A person has spent $1300 during the first 7 months of a common year ; how much must he diminish his daily expense in order that his total expense for the year may not exceed $2000? 174. A person wishes to have made 5 dozen shirts from material which costs 25 cents a yard. It takes 2.5 yards for a shirt, and he hires a woman to make them, paying her $ 2 a week. She makes 2 shirts every 3 days. Find the total expense, and the cost of one shirt. DECIMAL FRACTIONS. 49 176. On the first of Maxch a man bought 148 yards of cloth at 55 cents a yard. Fifteen days later the same cloth fell 4 cents a yard, and he purchased then 200 yards. He wishes to sell the whole so as to gain $ 11 ; what must be the selling price per yard ? 176. Paul planted 17 dozen peach-stones which he bought at the rate of 3 cents a hundred. He raised 119 peach-trees, which he grafted, and sold at 6 cents apiece. He grafted upon quince-stalks 150 pear-scions, which he sold all together for $ 11.27. Find the cost of the peach- stones, the price of a single pear-tree, and the amount of his two sales. 177. Barrel-hoops are made from young trees. If from a cord of these trees 720 hoops can be made, how many cords will be required for 60 barrels, 30 hoops to a barrel, and what is the value of a cord of wood fit for hoops, reckoning the hoops at $ 15 a thousand ? 178. A sheep-raiser shears his sheep at an expense of 3 cents a head. The sheep average 8 pounds of wool, which he sells for 22 cents a pound, and finds that his net profit after paying for the shearing is $2595. How many sheep had he ? 179. A field of wheat of 8.5 acres produces 300 sheaves per acre, and two sheaves of wheat furnish a bundle of straw weighing 10 pounds. What is the value of the whole straw, at_ the rate of $ 12 per ton ? (A ton is 2000 pounds.) 180. A horse requires 10 pounds of hay a day besides his grain. A man who owns 3 horses* has harvested 5 acres of grass, obtaining 5000 pounds of hay an acre. For how much can he sell his crop, if he reserves enough to last his horses a year, and sells the rest at $15 ^ tc^x^l 50 A.RITHMETICAL EXERCISES. 181. A farmer carries to market 64 sacks of wheat which weigh 120 pounds each. He sells these at the rate of $2.50 for 100 pounds. With the money^he purchases a horse, and has $45.50 left. What does "lie pay for the horse ? 182. Powder contains in every 100 parts by weight 75 parts of saltpetre 12.5 of sulphur, and 12.5 of charcoal. How. much of each of these substances is required to make a ton of powder ? (2000 pounds.) 183. Find the time which a locomotive with the velo- city of 27 miles an hour would take to make the distance passed over in 13.25 hours by another locomotive, having the velocity of 43.5 miles an hour. 184. A stick 4.5 feet long standing upright casts a shadow 10 feet long. What is the height of a column which at the same time casts a shadow 75 feet long ? 185. Seventy-five hundredths of a piece of cloth was sold for $86.40 at the rate of $1.60 a yard. Find the length and value of the whole piece. 186. A man wishes to exchange 6 barrels of vinegar, each containing 29 gallons, at 36 cents a gallon, for wine valued at $3.00 a gallon. How many gallons of wine should he receive ? 187. A person bought 2.5 pounds of candles at 28 cents a pound, 1.5 pounds of coffee at 36 cents a pound, 3.75 pounds of brown sugar at 8 cents a pound, 1.25 pounds of tea at 80 cents a pound. He gave a five-dollar bill in payment. How much change should he receive ? 188. A merchant buys eggs for $28.50 at the rate of $1.90 a hundred. How many dozen, and at what price a dozen, does he sell them to gain $2.75 upon his purchase?. DECIMAL FRACTIONS. ' 51 189. A workman who makes $3.25 a day saves $300.00 a year. He rests Sundays and eight other days. How much does he spend a day ? 190. It is estimated that one pound of butter can be made from 10.5 quarts of milk, and that a good cow will furnish annually 300 pounds of butter. How many quarts of milk will the cow give in a year, and what will be the income, supposing that the butter is sold at the rate of 28 cents a pound ? and which is more profitable, to make but- ter or to sell milk at 2.5 cents a- quart? 191. A bushel of wheat weighs 60 pounds. It is found that 3.5 bushels of wheat furnish 141 pounds of flour, and 141 pounds of flour furnish 183.2 pounds of bread. How much flour and how much bread will a hundred pounds of wheat make ? 192. A man receives a salary of $1500 a year. He estimates his expenses as follows: rent, $28 per month; groceries, $9 per month ; provisions, $17 per month. He places the cost of fuel and light at $95 for the year; that of clothing, at $200; and all other items, at $300. If his estimates are correct, how much money will he have left at the end of the year ? 193. A owes B $360. To pay the debt he leases B a house at a rent of $24 a month. How many months can B occupy the house before the debt is cancelled ? 194. A company of 16 men and 15 women dine to- gether. The cost per each person was $4, but the men pay the whole bill. How much does each man have to pay? 195. A board 'is 15 inches wide at one end and 9 inches at the other. What is its average 'wiMclI 0.018 0.020 0.027 0.113 0.093 0.085 0.690 0.603 0.539 0.120 0.100 0.095 0.190 0.145 0.169 0.110 0.098 0.118 0.393 0.253 0.302 52' AEITHMETICAL EXERCISES. 196. Below are the prices per pound of certain com- modities in Massachusetts for the years mentioned, as given in the Report of the Massachusetts Bureau of Statis- tics of Labor for 1884. Find to two decimal places the purchasing power of one dollar in pounds of each com- modity for each year named. Price per pound in the year. No. Article. 1860. 1872. 1878. 188S. 1. Flour, superfine, $0,039 $0,055 $0,044 $0,041 2. Corn meal, 0.023 3. Rice, 0.075 4. Tea, Oolong, 0.548 5. Sugar, granulated, 0.103 6. Beef, for roasting, 0.110 7. Pork, salt, 0.110 8. Butter, 0.218 197. The log-book of a steamer recorded the following distances in miles made by the steamer for 5 successive days: 316, 344, 278, 214, 363. What was the average rate for the 5 days ? 198. The lowest price of bar iron in 1882 was $56 per ton. In 1852 the lowest price was $ 34 per ton. How much more money would 20,000 tons of bar iron cost in 1882 than in 1852 ? 199. A fruit-seller sold 24 dozen oranges at 25 cents per dozen, 36 dozen at the rate of 2 dozen for 25 cents, and 15 dozen at 40 cents per dozen. What did he receive for them all, and what was the average price per dozen ? 200. A father, dying, left $ 15,200 to each of his chil- dren. One of them dies, and his part was then divided among the survivors, thereby increasing their portions to the amount of $ 19,000. How many children did the man have, and how much money did he leave ? DECIMAL FRACTIONS. 53 The following illustrations of the conditions of the labor- ing classes in Europe are taken from the first annual report of the Commissioner of Labor, Washington, D.C. Find for each case the annual surplus or deficit. 201. Outlay. Rent . . Bread . . Coffee . . Milk . . Macaroni Vegetables, Clothing, etc Fuel, etc. . Total , . etc Italian Stone-Cuttee. $24.00 106.85 18.15 33.85 36.50 113.15 71.20 19.00 Income. Earnings of father Earnings of son Earnings of girl Earnings of boy Total income . Total outlay Surplus or deficit $260.00 83.30 40.00 52.00 202. Italian Glass-Wobkeb. Outlay. Rent f 16.00 Bread 62.05 Milk and coffee . . . 47.45 Fish 10.95 Meats 9.36 Groceries ...... 142.45 Clothing 42.00 Fuel and light . . . . 12.00 Religion, etc 18.00 Total Zncome. Earnings of father Earnings of sons • Earnings of mother Earnings of girl . Total income . . Total outlay . . Surplus or deficit • fl45.25 146.00 90.00 25.00 203. Outlay. Board (with room) . . ? 149.24 Clothing 29.05 Beer and billiards . . 43.80 Incidentale 30.60 Shoemakee, Leeds, England. Income. Total earnings • . Total outlay . . Surplus or deficit . .$330.72 54 ARITHMETICAL EXERCISES. 204. COLLIEB, LlEQE, BELGIUM. Outlay. Rent i f 24.00 Bread 87.60 Meats 18.25 Coflfee, milk, etc. . , • 43.80 Beer and spirits , , . 43.80 Groceries 76.65 Clothing 62.00 Fuel and light .... 15.00 Total Income. Earnings of father . . $156.00 Earnings of mother . . 87.00 Earnings of daughter . 58.00 Earnings of two children 72.50 Total income .... Total outlay .... __^_^ Surplus or deficit . • • 205. Mill Superintendent, Halifax, England Outlay, Rent f 62.40 Bread 73.00 Meat and fish .... 89.43 Butter, etc 65.70 Fruits 33.80 Tea and coffee .... 27.37 Milk 20.07 Groceries, etc 1.12.00 ' Light . . . Fuel . . . Clothing . . Incidentals . Total outlay Total earnings Surplus or deficit f7.20 23.40 76.00 39.26 719.72 206. Caepet- Weaves, Halifax, England. Outlay. Rent $24.96 Bread and flour . . . 49.27 Meats 73.00 Lard, butter, etc. • . . 40.15 Tea and coffee .... 18.20 Milk 19.42 Beer and ale .... 23.73 Groceries 146.66 Club dues 1.44 Fuel and light Clothing . . Carpet . , Incidentals . Total Outlay Earnings of father Earnings of mother Total income . . Surplus or deficit . ? 16.50 37.40 1.55 23.30 375.00 113.36 DECIMAL FRACTIONS. 55 207. Female Weaveb, South GsBMAinr. OuUay. Board and lodging . . 1 67.05 Clothing 16.20 Beer 17.62 IncidentalB 8.90 Total outlay Total earnings . Surplus or deficit 124.68 208. CABPEiirTEB, Cologne, Gebmaitt. Ovilay. Rent $28.80 Bread 51.10 Coffee 13.52 Milk and eggs .... 21.84 Meats 17.47 Groceries 72.40 Beer 36.75 Fuel and light .... 15.60 Clothing . . Incidentals . Total outlay Earnings of father Earnings of mother Total income . . Surplus or deficit . 136.50 20.08 268.32 31.20 209. The gold coinage at the Philadelphia Mint in 1884 was as follows: 71 double-eagles, 76,905 eagles, 191,048 half-eagles, 1106 three-dollar pieces, 1993 quarter-eagles, and 6206 dollars. What is the total value of this coinage ? 210. Find the total value of the silver coins made at the Philadelphia Mint in 1884 the number of pieces being as follows: 14,070,875 dollars, 5275 half-dollars, 8876 quarter-dollars, 3,366,380 dimes. 211. From the report of the Massachusetts Bureau of Statistics of Labor for 1883 it appears that the average annual income of the working-girls of Boston is $269.07, and the average annual necessary expenses, $261.77. At this rate, how long would it take a girl to save $ 100, sup- posing that she spends only $4 a year for books, amuse- ments, and other items ? 212. How many bushels of potatoes, at $0.65 each, are required to pay for a piano costing $260? 56 ARITHMETICAL EXERCISES. 213. The account between farmer A and grocer B for one year was as follows : A sells B, B sells A. 60 bushels potatoes, at f 0.85 4 barrels flour, at $6.25 460 quarts milk, " 0.05 16 gallons molasses, " 0.67 314 dozen eggs. " 0.18 200 pounds gran, sugar. " 0.07 250 pounds butter " 0.27 80 " brown " " 0.05 12 barrels apples, " 1.25 45 '• coffee. " 0.32 2 bushels pears. " 1.50 14 " tea. " 0.65 When they settle the account, which has to pay money to the other, and how much ? 214. A man has in his pocket-book on Monday morn- ing $96.42. During the six days of the week he spends the following amounts: $5.27, $2.48, $18.05, $0.94, $11.73, $31.16. On counting his money at the end of the week, he finds that he has only $16.50 left. How much has been lost or stolen ? 215. A gentleman bought an estate for the round sura of $10,000. If the buildings on the estate are worth $2400, and the estate contains 190 acres, what did he pay per acre for the land ? 216. A lady bought 16 yards of cloth at 70 cents per yard. She paid $5 cash, and the rest in butter at 20 cents per pound. How many pounds of butter did she pay ? 217. A has $672; B, $1260; 0, $1512. They buy horses at the same price, paying for each horse the highest price that will allow each man to invest all his money. How many horses did each man buy ? 218. When potatoes are worth $0.77 per bushel, and corn $1.10, how many bushels of corn should a farmer receive in exchange for 50 bushels of potatoes ? DECIMAL FRACTIONS. 57 Add the following ; 219. 220. 221. 222. $901.45 $787.61 $41,321.04 $458,010.13 2,890.35 6,055.12 275,963.24 1,603,420.76 1,840.30 5,086.12 214,708.67 1,419,033.76 2.768.22 11,999.86 577,546.37 4,293,514.77 3,368.67 13,591.38 620,661.34 4,427,162.22 2.331.03 8,904.12 276,457.29 3,110,104.48 2,266.00 9,924.00 445,831.54 3,997,466.22 808.26 3,329.37 282,046.62 1,200,458.14 1,795.10 5,077.36 173,514.03 1,473,918.65 1,927.86 10,393.16 622,552.30 2,672,149.69 3,229.80 6,873.13 205,504.53 2,469,757.38 150.99 7.83 6,436.83 118,819.19 1,983.80 5,240.53 205,923.97 1,562,165.38 3,758.46 10,470.24 474,325.40 3,188,873.24 7.649.04 7,081.51 440,820.75 1,848,745.68 4.738.23 14,842.50 836,247.62 4,426,440.60 3,736.65 8,047.49 339,656.31 2,314,563.02 1,106.77 . 8,824.88 471,416.39 2,014,899.00 2,004.54 7,389.47 522,548.00 1,846,713.28 2,757.10 8,079.61 270,949.80 2,997,528.75 2,328.52 119.69 7,871.97 3,060,991.86 3,012.58 122.58 834,809.76 1,370,265.87 6,082.40 144.77 482,301.33 518,143.59 4,509.44 118.18 671,921.65 137,948.73 6,784.60 98.52 457,991.20 2,187,505.90 3,942.00. 107.01 418.79 1,132,088.55 CHAPTER III. COMMON FRACTIONS. Find by cancellation the quotients of: ^ 68 X 5 X 4 ^j 14 X 16 X 5 10x8 * * 20x2x7* 2 102 X 9 X 8 ^2 18 X 3 X 6 ' 3 X 6 X 12 ' ' 9 X 60 ' 3 18 X 3 X 36 j3 42 X 4 X 3 X 1 6x8x9 * * 6x5x8 - 138 X 20 X 15 -- 300x6x32 4. — — • 14. 8 X 5 x 30 4 X 12 X 16 g 212 X 85 X 22 ^g 90 X 24 X 9 '5x11x17x4 ' 8x18x3* ^ 1165 X 7 X 12 X 4 ^g 12 X 720 X 64 14 X 6 X 20 * * 16 X 48 X 4 ' ^ 72 X 9 X 1799 14 X 2 X 3 X 20 • 6x27x514* * 8x9x5 g 212 X 133 X 28 ^g 6 X 24 X 56 38 X 14 X 14 ' * 4 X 7 X 16 ^ 270 X 48 X 16 ^^ 135x3x41 64 X 45 X 36 5 X 45 X 246 jQ 4350 X 48 X 9 32 X 32 X 203 X 68 12 X 4 X 54 * ' 406 X 34 X 8 COMMON FRACTIONS. 59 Reduce to whole or mixed numbers : 21. ^. 22. ^. 23. ^. 24. ^. 25. i^. 26. ^^. 27. ff|. 28. ^^, 29. i4|i. 30. ^4f^. 31. ms. 32. -4^ 33. 1^ 34. 1^ 35. i^W 36. 87. 38. 39. 40. 171 • Reduce to improper fractions : 46. 15|f. 47. 90^. 48. 79^. 49. 23^. 60. 329|f. 61. 924|J, 62. 89|4. 53. 3^. 54. 23tti. 65. 79|i. 56. 67. 58. 59. 60. 13W 41. 13|. 42. 28^. 43. lOf. 44. 5ifi. 46. 8|f. Reduce : 61. 8, 12, 13, 19, 20 to fractions with denominator 12. 62. 5, 11, 14, 17, 24 to fractions with denominator 15. 63. 6, 8, 14, 13, 25 to fractions with denominator 16. 64. -J-, f , f , f , -J- to fractions with denominator 24. 66* ft W> "A"' "A"» i ^^ fractions with denominator 60. 66. -f , "I, -j^, 1^, -^ to fractions with denominator 36. 67. f, 5^, 3f , 4J^, 6^ to fractions with denominator 18. 68. 3 J, 4f , 3^, 4^, 6-j^ to fractions with denominator 30. 69. 4f , 3f , 4f , 3^, 7-j^ to fractions with denominator 40. 70. 9 to fractions with denominators 4, 8, 7. 71. 33 to fractions with denominators 3, 5, 8. 72. 29 to fractions with denominators 11, 13, 20. 73. 37 to fractions with denominators 12, 14t, !?>• 60 ARITHMETICAL EXERCISES. Reduce to lowest terms by the method of factoring : 74. 75. 76. ST- 82. m 83. m 77. If. 81. m- 84. 85. 86. 87. 88. 89. 98 TTT 68 rft tor HI II* "5 256 90. iM 91. iM 92. HI 93. H^ 94. iff T^ 96. Iff 96. m 97. iff 98. 99. 100. 101. 102. 103. 104. 105. 574 1080 ff* Mi 6 m 221 ttt 824 Reduce to lowest terms by the method of the G.C.M. 106. 107. 108. 109. 110. 111. 112. 113. MM MM MM iM+ MM im MM MM 114. 115. 116. 117. 118. 119. 120. 121. 8 12 mi mi MM MM mi 22. 23. 24. 25. 26. 27. 28. mi mi mi MM 29- tWt 130. 131. 132. 133. 134. 136. 136. 137. mu nm mu iMi mn 5001 urn Reduce to simple fractions : 138. i off off. 146. 139. f off offf. 147. 140. f offf of-j^y. 148. 141. I off of If. 149. 142. f off ofSf. 150. 143. f of If of f of 4f .' 151. 144. f of2f off of 5f. 152. J 45. 3%- of f of 4|f of 3|. 153. *ofAofMof3fof|f. MofTMrof41of;^. f of5f of^offfofS. ffofl6|ofAof70J^. fofT^of^ofSfofSf.' f off of ^ of 9. 3^ of 19 of 4f of If. ^ofTofTiVofM. GOUUON FBACTIONS. 61 of: 62. fx5f. 63. ^X7|. Find the produc 164. fx|. 166. f XtV- 156. |X^. 167. f X^. 168. -HXM- 169. fXfi- 160- T*irX|i. 161. IfXM- 178. ix2^X|. 179. ^X3^xf 180. sfx^xM- 181. 2iXfX3|. 182. 3^X^X5^. Find the quotient of : 8^ t^f 196. ^ 64. H^Xl6f. 66. I X 18|. 66. l^XH- 67. 2^Xf 68. I X 6^. 69. -A-XTf 183. 184. 186. 186. 187. 89. t-i-|. 90. |^|. 91. i^^. 92. i4 94- H^M- 96. if^if. if- 197. H 198. ^ 199. f^ 200. 5f 201. 7| 202. 3f 203. 6^ 212. i^-^loflOi. 213. 4|i-^-Jof25f 214. |i-^|ofl2|. 216. if-^^of3f 216. 3|-^-||of7f li- 15 217. 218. 219. 220. 221. 170. 9|X8^. 171. Tt^xM^. 172. 19ixl6|H- 173. 23ix3Jf 174. 17|X||f. 175. -Bf*Xitt- 176. 4^X17^. 177. 9i X 7^. f X i^ X 8^. 6f X ^ X 6|. * X f X 6f . HxfxH- 204. 19f-s-|J. 205. n^-i-u. 206. 4|-s-6J. 207. 5J^11|. 208. 2||-T-7f 209. 3ii-i-9f 210. 14|-!-4|. 211. 71^2^. iof2f + f ^ of 1^ ^ It of If . 62 ARITHMETICAL EXERCISBf. Change to equivalent fractions with least common denominator : 222. I I f. 228. I ^, if, H- 223. I I, f • 229. I I ^, a. 224. -y, ^, -J-, Ys. 230. -J^, -^i •^, -J-, -j^. 226. -J-, J, f, -f. 231. -I, f , 1^, 1^, -jI^. 226- i. 1. ii. «• 232. I, ^, I, iJ, I, i|. 227. f. A. M. M- 233. I, f, -f, tS;^, -tf, ^. Arrange in order of magnitude : 234. i, A. i- 238. T^. T^. If. 242. |, ||, f^. 286. t, i|, f 239. I, f , if. 243. -H. A. H' 2»6. I, H. A- 240. I, f, ^S^. 244. |, H- A- 287. ^, -f, T^. 241. T>j, ^, :^. 245. f f ^. Express in the simplest form the value of : 246. i + i + t 259. || + ^ + J + ^. 247. f + i + f 260. 1^ + 1 + 1^ + ^. 248. l + i + A. 261. fl + ^ + l^ + lf. 249. T«r + f + l- 262. 3|+li + 2i. 260. ^ + f + T(V- 263. 5Tlj+5| + 2f. 251. i + ^ + U- 264. 7Tly + 6| + 10f. 252. f + f + f. 265. 4f + 2i + 3i. 253. •J + f + ^. 266. lT!^ + 5^ + 2if. 254. f + ^ + ^ + ^. 267. 6i+7| + 8| + 9f 266. fi + | + ^ + ||. 268. Sf+7i + 8i + 9f 256. l + ^ + if + TVj. 269. 7f + 8| + 5if+7ii. 257. If + A + lf + H. 270. 5i + 6|+7^ + 9H- ^58- :f^^-# + if + M- 271. 9|+10f+llf + 5i^. OOUUON FKACTIONS. 63 Find the value of : 272. 18 -f 288. |f-A- 304. 6f - 3|. 273. 10 -f 289. ff-A- 306. 7|-3^. 274. 9-^. 290. |-f . 306. 8f-f 275. 11 -T^. 291. |f-|f- SOT. 7|--^. 276. 8-2iV- 292- f-M- 308. 23^^-19^. 277. 23-11. 293. a-U- 309. le^^^-litf. 278. 18— H- 294. li-if- 310. 18^1 -17,^. 279. 6-^. 295. ^-U- 311. 29,11^ - 9-ii^. 280. 5-H- 296. tVit-A- 312. 20J-16|. 281. 19 -H. 297. tV-rfr- 313. 16^-13|. 282. |-f 298. l-f 314. 5tV-2H. 283. ^-f. 299. ^-^. 315. 7^-6^ 284. f-f 300. if-T^. 316. 2^-1,^^. 286. H-A- 301. li-^. 317. 4f-lf 286. ■A'-f 302. 3^-2|. 318. 27^-6^. 287. H-if- 303. 7^-5^. 319. 16^-91- 320. I of -Lfi - tV of 28J- 321. B^ + 8i-3^-2^ + 5\ + 6^-l6^. 322. |xVVx&?x9f X2ix63. 323. 6i X llf X 16T*r X Vff X ^ X T^. -.^ 27 874 i 81A 326 5i:z2i ^ li±M V ^i±li 64 A&ItBMETICAL EXERCISES. 7 Express as common fractions in their simplest form : 327. 0.8. 331. 0.032. 336. 0.0425. 328. 0.125. 332. 0.004. -336. 0.46875. 329. 0.3125. 333. 0.0625. 337. 0.00256. 330. 0.15625. 334. 0.7168. 338. 0.000375. Express in the form of decimal fractions : 339. 340. 341. 342. 343. 344. 345. 346. A. tinftr- 17 Tuinnr- loooo* 347. |. 348. f 349. ^. 350. If. 351. ^. 352. ^. 353. 4^. 354. ■^. 355. 356. 357. 358. 359. 360. 361. 362. TTST TTff 81 TSTT 1 1 Express as decimal fractions : 371. |. 372. i. 373. ^. 374. ^. 375. ^. 376. ^. 377. ^. 378. If 379. y|y. 380. -g^j-g-. 381. 382. 383. 384. 385. Keduce to common fractions : 391. 0.16. 396. 0.623i. 392. 0.116. 393. 0.416. 394. 0.288. 395. 0.083. 397. 0.7045. 398. 0.0046. 399. 0.0054. 400. 0.0227. 363. 364. 365. 366. 367. 368. 369. 370. 11 1600 1 T 28 8 T5T 386. ^. 387. fj. 388. 389. i TOT T9T 390. :^. 401. 0.0054. 402. 0.0916. 403. 0.02439. 404. 0.42857i. 405. 0.076923. common fractions. 65 Miscellaneous Exercises. (Including sabjects treated in the preceding chapters.) 406. What part of 25 is f ? 407. What is i of 17i ? I of 39| ? 408. Which is the greater, |J or ^ ? 409. What is 3^ of 94 ? 94 is -^ of what number ? 410. One-fourth, one-third, and three-sevenths of a num- ber added together make 60. What is the number ? 411. In France 1225 wolves were killed in 1882, for which the government paid $29,000. What price wfiis paid per head ? 412. What fractions are equal to -|, and have for nume- rators the numbers 6, 51, 33, 39, 48? 413. What is ^ of 70 ? 70 is -^ of what number ? 414. If j\ of a ship is worth $27,000, what is the whole ship worth ? 415. If a girl knits f of a stocking per day, how long will she take to knit 45 pairs of stockings? 416. Two horses together cost $575. What is the cost of each, if one of them cost f as much as the other ? 417. Elsie gave $f per yard for 9 yards of gingham, and $2J for lining and trimming. If she had bought her dress ready-made, it would have cost $8.00. What did she save by making it herself ? 418. Simplify gxi^-^^. 419. What is the value of 9 boxes of raisins, each con- taining 27^ pounds, at 18 cents per pound? 66 ABITHMETICAL EXERCISES. 420. A tailor, after cutting 8|- yards from a piece of cloth, found that there were 17|- yards left. What was the entire length of the piece ? 421. 68 is (I + I) of what number ? 422. For hemming linen handkerchiefs, 2\ cents a dozen is paid. When work is good, a girl hems 75 dozen a day. How much does she earn in a week ? 423. A workman gets $3.25 a day, and spends on the average $2.10. How much will he save in a year of 365 days, counting out 52 Sundays and 4 holidays ? 424. Jane has $12.50, and Susan has $0.50. What part of Jane's money is Susan's money ? 425. If 3| yards of cloth are required to make a shirt, how many shirts can be made from a piece of 56 J yards ? 426. A dry-goods dealer bought 520 yards of cloth at $1.75 per yard, and sold f of it at $2 per yard. For how much per yard must he sell the remainder in order to make a clear profit of $250 by the transaction? 427. Divide 5.4306 by 18, and 0.50025 by 29, and add the quotients. 428. How many pairs of trousers, each pair requiring 2|- yards, can be made f^om a piece of doeskin containing 33i yards ? 429. A grocer bought a hogshead of sugar weighing 744 pounds at 7-J- cents per pound, and sold it at 7-J- cents per pound. What was his profit? 430. If 3^ yards of cloth are required to make a shirt, how many shirts can be made from 12 pieces, each measur- ing 47^ yards ? COMMON FRACTIONS. 67 431. What is the value of 7 pieces of cloth, each con- taining 34f yards, at $2.82 per yard? 432. If a boy drops 5 cents in a money-box every day, how much money will he find in it at the end of one year ? 433. A farmer was offered $300 for the apples in his orchard, but preferred to gather them himself. He sold 164 barrels of bald wins at $1.50 each, 29 barrels of russets at $1.75 each, and 300 bushels of cider apples at 15 cents a bushel. Calling his labor worth $50, did he gain or lose by declining the offer, and how much ? 434. I sold 1^ of a lot of land, and then ^ of what re- mained. After the second sale there remained 13^ acres. How much land was there to begin with ? 435. A locomotive passes over -j^ of a route in 3^ hours. In what time will it pass over the entire route ? also in what time I? -J? y\? 436. A workman spends -^ of his income in food, -J- in clothing and lodging, -^ in other expenses, and saves at the end of the year $318. What was his income ? 437. Simplify |-i + T\-A-i 438. Two men are 21^ miles apart ; when they meet, one has travelled 5 miles more than the other. How far has each travelled ? 439. A boy being asked to find the value of 8^+2J + 3f +4^, gave as his answer 18. How great an error did he make ? 440. Simplify f-i+^-T^+i • 441. Find the value of (l - M^ + M ] ■*■ ^' 68 ARITSMETICAL EXERCISES. 442. A man bought a cargo of potatoes. After selling -J of them to one party, J to another, and -J- to a third, he had 220 bushels left. How many bushels were there in the cargo? 443. The metre is equal to 3^^ feet, very nearly. Express 1 foot as a fraction of a metre. 444. A lady wishing to purchase a piano-cover finds it will require 2|- yards of plush at $3^ per yard, the same quantity of lining-flannel at $|- per yard, 1 J yards of satin at $1-J- per yard, 1^ yards of fringe at $1J per yard. The cost of making will be $5. Find the cost of the piano- cover. 445. Mr. Gay sold 86 barrels of baMwjn apples for $1|- per barrel, 24 barrels of porters at $2^ per barrel, and 69 barrels of greenings at $1.90 per barrel. He bought a horse for $125, and spent the remainder for cows at $54 each. How many cows did he get, and how much money had he left ? 446. Excursion tickets from Boston to Fabyan's and return cost $ 7f . Board at Fabyan's is $ 3^ per day. To the summit of Mt. Washington, $3.00; to Profile House and Flume, $3.00. What will it cost Mrs. Smith to take these excursions, if she remain at Fabyan's one week ? ^ 447. Simplify ^ of Itf +li of Sj-lj of Sj , 448. A mason built 6^ yards of wall on Monday, 4|- yards on Tuesday, 4|- yards on Wednesday, and 7|- yards on Thursday. How much has he earned in this time, if he is paid $0.80 per yard? 449. Seven cars carried respectively 24-|-, 18|-, 15|-, 28, 17^%, 32-J^, 27^^ tons of coal. Required the average number of ton's carried by each car. COMMON PEACTIONS. 69 460. Simplify HXi^Xlf^XHf. 451. Whicli is the greater, ^ or ^^, and what is the difference between them? 462. Divide the difference between 200,000 and 200,000,000 by 666. 463. Reduce the following fractions to decimals, and then add the results : -^^ - sAffoo^ ^ f • • • • • 454. Reduce 0.87 — 0.259—0.56 to a common fraction. 465. If Mr. Jones can plant a certain field in 10 days, but with the assistance of his son can do it in 6 days, how long would it take his son alone to plant the whole field ? 456. One gas-jet burns |- as much as a second, and this burns J as much again as a third. How much gas will the first burn while the third burns 1000 cubic feet ? 457. A farmer bought a barrel of flour for $7.50, a plough for $ 12, and 36 pounds of sugar at 7^ cents a pound. How many bushels of -potatoes at 60 cents a bushel will pay the bill ? 458. Find the total product of each principal crop pro- duced in Ohio, in 1880, from the following data : Average yield No. of acres. per acre Indian corn, bushels. 3,198,400 37.5 Wheat, 2,845,170 17.5 Rye, 29,600 14.7 Oats, 911,400 28. Barley, 54,030 26.3 Potatoes, 124,400 85 Tobacco, pounds, 35,489 1083 Hay, tons, 1,782,581 I.'i^ 70 ARITHMETICAL EXERCISES. 459. A liberty pole is divided into 4 parts. The first part is ^ of the whole, the second is J, the third is |, and the fourth is 11 feet long. What is the entire length of the pole ? 460. A furniture dealer bought 140 hair mattresses at $18.15 each. He wishes to sell them so as to -make on the whole number $180. He has already sold -f- of them at $18.50 each. How much apiece must he get for the others ? 461. Two-thirds of the wood in a large pile have been sold, at $7 per cord, for $2940. How many cords remain, and what is the value of the wood remaining ? 462. The diameter of the moon is ^^ that of the earth. The diameter of the sun is 110 times that of the earth. What fraction of the sun's diameter is that of the moon. 463. Simplify 1^X9^x31x9^^ i^x 3^x121x2^X3/^ 464. How many pound, half-pound, and quarter-pound packages, of each an equal number, can be made from a chest of tea containing 89 J pounds ? 465. A man owning -^ of an estate, sold -^ of his share for $120|-. What is the value at the same rate of -^ of the whole estate ? 466. What is the value of -j^ of -j^ of a vessel, if a per- son who owns -^ of it sell -J- of -J- of his share for $350? 467. If gunpowder is composed of 33 parts of nitre, 7 of charcoal, and 5 of sulphur ; how many pounds of each will be required to make 30 pounds of powder? 468. If a silver rupee in Calcutta be worth $-J^, what must you pay in American money for a sandal wood fan valued at 3 rupees ? COMMON FRACTIONS. 71 469. Find the L.C.M. of 18, 24, 28, 30, 56, 70, and the G.O.M. of 184,851 and 256,496. 470. Find the L.C.M. of 12, 15, 22, 40, 55, 72, and the G.O.M. of 215,441 and 860,343. 471. Simplify 10^-4f-6^+7f+8|-6|f. 472. A man owns -^ of a ship. If he sells -J of his share, what fraction of the whole will he still have ? 473. Three persons divide the cost of a musical entertain- ment in such a manner that the first pays ^ of the whole, the second -J of what the first pays, and the third pays the remainder, which is $50. What is the amount of the bill? 474. The rates of the express and mail trains on a rail- way are 40 and 28 miles respectively. What time is saved by taking the former for a journey of 192 miles? 475 . Simplify ^-^Si-^~ 5^ + 252^. 476. If i of 14 of an estate be worth $300, what will -^ of it bring at the same rate ? Ti 477. A farmer put f of his corn into one bin, and the rest into another. He sold -J of wh^ was in the first bin and "I of what was in the other. The/'est he kept for his own use. How much did he keep, the whole quantity being 480 bushels ? 478. If ^ of a piece of work be done in 25 days, how much will be done in W^ days? 479. A cistern holding 6000 gallons is supplied with water by 2 pipes. One of them will admit 100 gallons in 1 J hours, the other, 200 gallons in 4-^ hours. If both pipes are opened when the cistern is em^ty, in how many hours will it be filled ? 72 ARITHMETICAL EXEECISES. 480. I bought of a merchant tailor 5f yards of broad- cloth for the sum of $20.12J-. On measuring it, I found that there were only 4J- yards. How much ought the tailor to pay me back? 481. Find the value of 11.0071-0.30103 + 19-14.09-0.0982+6.774. 482. A boy spends \ of his money for a dictionary, -J- for a geography, and -J- for a pair of skates. These purchases amount to $1-^ more than -J- of all the money he has. What sum is paid for each article ? 483. If a young man spend in four months as much as he earns in three, how much can he lay by annually, on the supposition that he earns $ 250 J- every six months ? 484. A merchant tailor has 16 dozen shirts made from cloth costing 12 cents per yard. The bosoms cost him 50 cents each, and he pays for making, 35 cents apiece. It requires 8J yards of cloth for 3 shirts. How much will he gain if he sells the shirts at $ 20 per dozen ? 485. A piece of work must be finished in 36 days, and 15 men are set to do it, working 9 hours a day ; but after 24 days it is found that only three-fifths of the work is done. If 3 additional men be then put on, how many hours a day will they all have to labor in order to finish the work in time ? 486. What must be added to ■}■ of -J in order that the sum may be equal to -^ of 3 J ? 487. A can do a piece of work in 7 hours, and B can do it in 8 hours. If they work at it for an hour alternately, A beginning, in how many hours will the work be finished ? 488. The sum of two numbers is 774|, and their differ- ence 178|-. What is their product? COMMON FRACTIONS. 73 489. George can gather 5 bushels of cranberries in three days ; Henry, 7 bushels in nine days ; Rufus, 11 bushels in twelve days. In how many days can they together gather 121 bushels ? 490. If -j- of a roll of carpeting is worth $78.50, what is the whole roll worth ? 491. Two men undertake to do a piece of work for $14. One could do it alone in 6 days, the other in 7 days. With the help of a boy, they finish it in 3 days. How should the money be divided ? 492. What number exceeds the sum of its fourth, fifth, and sixth parts by 161? 493. A farmer bought 7 bullocks for $480, and after keeping them 16 weeks, at a cost of $3.15 per week each, he sold them for $117 each. Did he gain or lose, and how much ? 494. What will be the expense of giving to each of 175 poor children a sandwich, a cream-cake, and an orange, the sandwiches being 5 cents each, the cakes 40 cents a dozen, and the oranges 25 cents a dozen? 495. The circulation of the Boston Herald for the week of the presidential election, ending Nov. 9, 1884, was as follows: Monday, 110,620; Tuesday, 180,487; Wednes- day, 302,030; Thursday, 198,642; Friday, 182,788; Sat- urday, 160,400; Sunday, 104,960. Find the total circu- lation for the week, the average for the week, and the total value at a cent and a half a copy. 496. From a tank full of water f of the water was with- drawn. Then 35 gallons were added, when the tank was exactly half fulL What is the capacity of tl[i^ ^^-ukl 74 AEITHMETICAL EXERCISES. 497. Mrs. Snow, having $50, wished to purchase h dress. She bought 24 yards of silk at $ 1^ per yard, 1^ yards of silesia at 18 cents per yard, 5^ yards of cambric at 8 cents per yard, 2 spools of silk at 12 J cents each, 1 spool of twist for 5 cents, 1^ dozen buttons at 42 cents per dozen, and -J- of a yard of velvet at $2 per yard ; she paid $15 for making the dress. How much money had she left? 498. What is the freight on 5600 bushels of oats, of 32 pounds each, from Chicago to New York, at $0.60 per 100 pounds ? 499. What is the value of 15 pieces of broadcloth, each piece containing 44^ yards, worth $3-J- per yard? 600. A trader bought wheat at $1.25 per bushel, and sold it at $1.17 per bushel. How much did he lose oa every dollar he paid ? 501. How many bushels of potatoes at $-J per bushel will pay for 12J- bushels of wheat at $ 1.20 per bushel? 502. A grocer bought a hogshead of molasses containing 128 gallons at $0.64 per gallon. He paid $2.08 for cart- age and lost 16 gallons by leakage. At what price per gallon must the remainder be sold to gain -J- of the entire cost? 503. From a piece of calico containing 35|- yards there have been sold at different times 12| yards, 2^ yards, 2^ yards, and 8|- yards. How many yards remain ? 504. A father and his son undertake a piece of work which they can do in 15 days by working together. They work together 6 days, and the son then finishes the work in 30 days. How many days would it take them each tq do the piece of work ? COMMON FRACTIONS. 75 605. Find the G.C.M. and L.C.M. of 471, 1256, and 1727. 606. Find the value of 34 X I nnnr 607. Reduce to decimals -Ar, -Mr. and -^1 — z2_. 608. Simplify 10 - 7.889 + 13.0052 — 2.99372 ; and also fiimplifj 10 - 13.0052 + 7.889 + 2.99372. 609. Find the value, correct to seven decimal places, of 17.824 - 11.63172 + 9.883 - 1.16857142 + 12.3. 610. If 5 pounds of copper are melted with 4^ pounds of tin, how much copper will there be for each pound of tin ? How much copper will there be in 1 pound of the alloy ? 611. If gun metal be composed of 90^ parts of copper to 9j^ parts of tin by weight, how much tin and how much copper are there in 1 pound of gun metal ? 612. How many minutes will it take a pipe, supplying water at the rate of 2|- gallons per minute, to fill a cistern holding 62|- gallons ? 613. Simplify ^ of ^~^~|^ X (3^ + i - 2,^). 514. A gas chandelier in a public hall consumed 2700 cubic feet of gas in 86 hours. The cost of the gas was $6.75. Find (i.) the price of the gas per 1000 feet, (ii.) the cost of the light per hour, (iii.) the number of cubic feet of gas consumed in 5J- hours. 515. One man does -f of a piece of work, and another man does -J- of it. What fraction of the work remains to be done? 76 ARITHMETICAL EXERCISES. 516. Three masons working together built a wall in 12 days. The first, working alone, could have built it in 32 days, and the second in 36 days. If $ 96 is paid for build- ing the wall, how much should each inason receive ? 617. If 19 pounds of silver are alloyed with 31 pounds of copper, how many pounds of each- of these metals are there in 191 pounds of the alloy ? 518. Three brothers buy a farm, the first taking -^ of it, the second ^, and the third the remainder. The third paid $1722 for his part, which measured 42 acres. What did each of the others receive, and what did he pay ? 519. Bell-metal consists of 4 parts of copper to 1 part of tin. What will a bell weighing 12,400 pounds cost, if the copper costs 19 cents per pound, and the tin 22J- cents per pound, and the cost of making, etc. is $500 ? 520. A tailor cuts 9-32j. yards of cloth from a piece measuring 44^ yards. How many vests, each requiring 1^ yards, can he make with the remainder ? A. 521. The sum of ^ and -^ of a number is 16}^. What is the number? Koo Q- T^ 0.203x0.0004x16 522. Simplify — — — — . ^ ^ 0.008x0.0029 523. Find the total annual cost of a house, of which the rent is $ 864, the gas-rate is -^ of the rent, the water-rate is J of the gas-rate, and the expense of clearing the side- walks from snow is f of the water-rate. 524. Find the value of -M^^ . *X|X18| 625. How many tons of ore must be taken from a mine that, after a loss of \^ in roasting, and -j^ of the residue in smelting, there shall remain 506 tons of pure metal ? COMMON FRACTIONS. 77 626. A laborer has to spend 45^ cents per week on bread wben it is at &}- cents a loaf. If the price rise to 7 cents a loaf, how much less bread must his family eat in a week, that it may cost him the same as before ? 627. A freight train leaves a station, and travels at the rate of 10 miles an hour ; after 4 hours another train fol- lows from the same station, travelling 16 J miles an hour. How many miles must the second train travel before it comes up with the first ? 628. A farmer has his sheep in two pastures ; the num- ber in one is three-fifths the number in the other. If there be 480 in the whole flock, how many are there in each pas- ture ? KOQ Q- riw 0.304 X 0.002 x 1.8 629. SimpllfV ^r-TTTTTTTr 7^-7^7^?: • ^ ^ 0.0009x0.038 630. A gentleman, by his will, gave \ of his property to his eldest son, ^ to the next, -^ to the third, and the rest to the youngest. The portion of the youngest was $47,400. What was the value of the entire property ? * 531. A can do a piece of work in 3^ hours, B in 3if- hours, and in 4 J- hours. In how many hours can they do it, working together? If $3 is paid for doing the work, what is each man's share? 632. The amount of starch in potatoes is ^ of their weight, but the amount that can usually be extracted is only -j^. How many pounds weight of starch can be obtained from 100 pounds of potatoes, and how much is lefb in the potatoes after the process of extracting is ended? 533. A man walking 18 miles finds that the distance he has walked in 1 hour 40 minutes is -f of the remaining difits^nc^. Find his rate of walking. 78 AEITHMETICAL EXERCISES. 634. A grocer mixes equal weights of raw Java cofifee, costing 24 cents per pound, and Rio coffee, costing 14J cents per pound. The loss in weight by roasting and grinding is -J-. At what price per pound must he retail the mixture in order to make a gross profit of 2 cents per pound ? 635. Green coffee when roasted loses -J- of its weight. A dealer buys raw coffee at 22|- cents per pound, and sells it roasted at 30 cents per pound. What will be his gain or loss in filling an order for 1000 pounds of roasted coffee, if the cost of roasting be $ 2.25 ? 636. When flour is worth $ 7.35 per barrel (196 pounds), what ought to be the price of half-pound loaves of bread, assuming that 4 pounds of flour make 5 pounds of bread, and allowing to the baker a profit just equal to the cost of the flour? 537. If grapes yield f of their bulk of wine, and wine yields -^ of its bulk of alcohol, and a quart of alcohol weighs If pounds, how many pounds of alcohol can be made from 100 bushels of grapes? 638. A farmer planted -J of a field with corn, -J with potatoes, and the rest, amounting to 2^ acres, with oats. He harvested 660 bushels of corn, 1080 bushels of potatoes, and 105 bushels of oats. What was the yield of each in bushels per acre ? 639. If an iron bar, when heated from 0® to 1® of the centigrade thermometer, expands by T-g^inr ^^ ^^ length, what will be the length in feet at 30° of a bar whose length at 0° is 101 feet ? CHAPTER IV. COMMON MEASURES. TABLES. I. Length. 12 inches (in.) ■» 3 feet 6} yards, or 16J feet = 320 rods, 1760 yards, 1 _ or 5280 feet J ' 1 foot (ft.). 1 yard (yd.). 1 rod (rd.). 1 mile (mi.). 1 lii^e 1 palm 1 hand 1 span Measures sometimes itsed for Special Purposes. 3 in. 4 in. 9 in. 1 cubit = 18 in. 1 pace = 2J ft. 1 chain = 4 rds. 1 link =* xir chain. 1 fathom 1 furlong 1 knot 1 league 6 ft. J mi. 6086 ft. 3 knots II. Surface. 144 square inches (sq. in.) 9 square feet 30J square yards 160 square rods 640 acres # = 1 square foot (sq. ft.). • 1 square yard (sq. yd.). ' 1 square rod (sq. rd.). • 1 acre (A.). ■ 1 square mile (sq. mi.). Measures sometime used for Special Purposes. 1 rood « 40 sq. rds. 1 square of flooring or roofing = 100 sq. ft. 1 section of government land ■» 1 mile square. 1 township oi land * 36 bc\. m\W. 80 ARITHMETICAL EXERCISES. III. Volume. 1728 cubic inches (cu. in.) = 1 cubic foot (cu. ft.). 27 cubic feet — 1 cubic yard (cu. yd.), 128 cubic feet — 1 cord. Measures in use for Special Purposes. 1 cord foot = J of a cord = 16 cu. ft. 1 board foot = a board 1 foot square and 1 in. thick. IV. Capacity. Dry Measure. 2 pints (pt.) => 1 quart (qt.). 8 quarts = 1 peck (pk.). 4 pecks -» 1 bushel (bu.). Liquid Measure, 4 gills (gi.) = 1 pint (pt.). 2 pints « 1 quart (qt.). 4 quarts — 1 gallon (gal.) Apothecaries* Measure^ Used for compounding medicines, is as follows 60 minims (H^l) = 1 dram {ni Ix). , 8 drams = 1 fluid ounce (fl. dr. viii). 16 fluid ounces = 1 liquid pint (A- oz. xvi). Comparison of Units of Volume and Capacity. 1 bushel = 2150.42 cu. in. = 1.25 cu. ft. nearly. 1 cubic foot = 0.8 of a bushel, nearly. 1 gallon =231 cu. in. = -j^ of a cu. ft., nearly. 1 cubic foot = 7} gallons, nearly. 23 dry quarts = 27 liquid quarts, nearly. 1 bushel, heaped measure = 5 pecks, nearly. 1 British imperial bushel =1.032 United States bushels. 1 British imperial gallon = 1.2 United States gallons. 1 British quarter = 8 imperial bushels. 1 cubic foot of water weighs 62} pounds, nearly. i gallon of water weighs 8 J pounds nearly. OOMMOK MEASUBE8. 81 V. Weight. Troy Weight 24 grains (gr.) — 1 pennyweight (dwi.^ 20 pennyweights — 1 ounce (oz.) 12 ounces — 1 pound (Ih.). Avoirdupois WeigJiL 16 drams (dr.) — 1 ounce (oz.)« 16 ounces • — 1 pound (Ih.). 100 pounds — 1 hundredweight (cwt.). 2000 pounds - 1 ton (t). The long ton is still used in the United States Custom Houses and in wholesale transactions in iron and coaL 112 pounds avoirdupois — 1 long hundredweight 2240 pounds avoirdupois =» 1. long ton. 1 pound avoirdupois — 7000 Troy grains. Apothecaries' Weight. 20 grains Troy — 1 scruple (3). 8 drams — 1 ounce (J). 3 scruples - 1 dram ( 3 ). 12 ounces — 1 pound. VI. Time. 60 seconds (sec.) — 1 minute (min.). 60 minutes — 1 hour (hr.). 24 hours — 1 day (dy.). 7 days — 1 week (wk.). 366 days ■- 1 common year (yr.). 366 days — 1 leap-year. The day of this table is the mean solar day^ or average interval between two successive passages of the sun across the meridian. Average length of the year — 365 dys. 5 hrs. 48 min. 50 sec, nearly. Thirty days have September, April, June, and November; February has twenty-eight alone; all the rest have thirty-one; But leap-year, coming once in four, gives February one day more. Every year divisible by 4 is a leap-year, except those centennial years in which the number of centuries is not divisible by 4 ; thus^ 1888 and 2000 are leap-y ears, but 1887 and 1900 w^ \io\.\^«^-^'fcw>i. 82 ARITHMETICAL EXERCISES. VII. Akgulab Measuee. 60 seconds {f^) = 1 minute {f), 60 minutes = 1 degree (°). 90 degrees « 1 right angle. 360 degrees « 1 revolution. The circumference of a circle is divided into 360 equal parts, called degrees ; each degree into 60 minutes ; each minute into 60 seconds. The larger the circle, the greater the length of 1 degree. 1 degree of the earth's equator =- 60 knots = 69.16 miles. A quadrant =- J part of a circumference. VIII. Monet. United States Money. 10 mills = 1 cent (ct.). 10 dimes = 1 dollar ($). 10 cents = 1 dime. 10 dollars = 1 eagle. English Money. 4 farthings (far.) == 1 penny {d.). 20 shillings = 1 pound (£ or l), 12 pence >= 1 shilling (s.). 21 shillings ■- 1 guinea. 1 sovereign = 1 pound, 1 crown = 5 «., 1 florin = 2 «. Comparison of Units of Money. English Money : £ 1 = $ 4.8665 ; $ 1 = 4.1099 a. Canadian Money : 100 cents = 1 dollar. French Money : 100 centimes = J. franc (fr.) = $0,193. German Money : 100 pfennigs = 1 mark(M.) = $0,238. Austrian Money : 100 kreutzers = 1 florin (fl.) = $0,393. Russian Money : 100 kopecks = 1 rouble (rb.) = $0,636. Spanish Money : 100 centimes = 1 peseta = $0,193. Portuguese Money : 1000 reis = 1 milreis =$1,080. Brazilian Money : 1000 reis — 1 milreis = $0,646. Dutch Money : 1 florin « $0,402. Italian Money : 1 lira = $ 0.193. Mexican Money • 1 dollar -=$0,864. ChjJjan Money • 1 peso - $0,912. COMMON MEASURES. 83 IX. MiSOELLAirEOUS MEASUBEa 1. Capacity. The barrdf hogshead^ pipe^ and tun have no fixed values. The barrel varies from 28 gals, to 42 gals. • the hogshead, from 54 gals. to 63 gals. ; and the pipe, from 110 gals, to 140 gals. 40 ft of round timber, or 50 ft. of hewn timber — 1 ton, or load. 1 ton of a vessel's tonnage — 100 cu. ft. 1 ton of a vessel's cargo — 40 en. ft. A perch of masonry is usually reckoned at 25 cu. ft. The dimensions of common brick are 8x4x2 m The dimensions of Maine brick are 7i X 3| x 2f in. The dimensions of North River brick are 8 X 3 J X 2J in. The dimensions of Philadelphia brick are 8i x 4J x 2f in. The dimensions of Milwaukee brick are 8} X 4| X 2f in 2. Weight The weight of a bushel of grain is fixed by law in many of the States. The weights given below are those adopted in business : 1 bu. of wheat - 60 lbs. 1 bu. of potatoes — 60 lbs. 1 bu. of corn or rye - 66 lbs. 1 barrel of flour - 196 lbs. 1 bu. of corn or rye meal - 50 lbs. 1 barrel of beef or pork =» 200 lbs. 1 cask of lime = 240 lbs. 1 bu. of oats - 32 lbs. 1 quintal of fish — 100 lbs. 1 bu. of barley « 48 lbs. 1 stone of iron or lead =- 14 lbs. 1 bu. of timothy seed - 45 lbs. 1 pig of iron or lead — 300 Iba. 400 cu. ft. of well-settled English hay — 1 ton 500 cu. ft, of well-settled meadow hay =» 1 ton. 550 cu. ft. of clover hay ■- 1 ton S. Number. 12 units — 1 dozen (doz.). 12 dozen — 1 gross (gro.). 12 gross — 1 great gross. 20 units — 1 score. 4. Paper. 24 sheets — 1 quire. 20 quires — 1 ream. 2 reams — 1 bundle 5 buudW » \ \)^iX!^ 84 ARITHMETICAL EXERCISES, Beduce : 1. 20 rds. to feet. 11. 864 in. to yards. 2. 4 mi. to chains. 12. 31,680 ft. to miles. 8. 80 leagues to feet. 13. 1280 chains to miles. 4. 6 A, to square feet. 14. 1920 pts. to bushels. 6. 800 cds. to cubic feet. 16. 640 gi. to gallons. 6. 126 gals, to pints. 16. 60,000 pts. to gallons. 7. 1 wk. to seconds. 17. 266,000 oz. to tons. 8. 1 leap-year to hours. 18. 720 min. to hours. 9. 30® to seconds. 19. 1461 dys. to years. 10. £27 to pence. 20. 10,660 c?. to pounds. 21. Eeduce-3 mi. 230 rds. 3 yds. to feet. 22. Eeduce 29 A. 139 sq. rds. to square rods. 23. Eeduce 43 cu. yds. to cubic inches. 24. Eeduce 24 bu. 2 qts. to pinte. 25. Eeduce 5 gals. 1 pt. to gills. 26. Eeduce 119 oz. 17 dwt. to grains. 27. Eeduce 17 t. 640 lbs. to ounces. 28. Eeduce 1,000,000 in. to higher units. 29. Eeduce 14,080 A. to square miles. 30. Eeduce 261,360 sq. ft. to acres. 31. Eeduce 3780 cu. ft. to cubic yards. 32. Eeduce 7680 cu. ft. to cords. 33. Eeduce 17,280 gr. to Troy pounds. 34. Eeduce 55,3G0 oz. to higher units. 35. Eeduce 139,292 min. to higher units. 36. Eeduce 162,000'' to degrees. 37. Eeduce 1,950,067 far. to crowns. $8. What cost 6 t. of salt at 1^ cts. per lb. ? COMMON MEASURES. 85 89. Beduce 95,040 in. to miles. 40. Beduce 53,250 sq. yds. to acres. 41. Beduce 1,353,024 cu. in. to cubic yards. 42. Beduce 256 cu. yds. to cords. 43. Beduce 736 pts. to gallons. 44. Beduce 508 dry qts. to higher units. 45. Beduce 65,136 gr. to higher units Troy. 46. Beduce 1,000,000 oz. to tons, etc. 47. Beduce 119,000 gr. Troy to pounds avoirdupois. 48. Beduce 947,291 sec. to higher units. 49. Beduce 17 mi. 305 rds. 3} yds. to inches. 50. Beduce 33 A. 74 sq. rds. 18 sq. yds. 6 J sq. ft. to sq. feet. 51. Beduce 19 cu. yds. 22 cu. ft. to cubic inches. 52. Beduce 23 lbs. 9 oz. 17 dwt. 21 gr. Troy to grains. 53. Beduce 17 wks. 5 dys. 19 hrs. to minutes. 54. Beduce -j^ of a rod to the fraction of a mile. 55. Beduce 3f yds. to the fraction of a mile. 56* Beduce ^ of a sq. yd. to the fraction of an acre. 57. Beduce J of a cu. ft. to the fraction of a cubic yard. 58. Beduce -f of a gill to the fraction of a gallon. 59. Beduce J of a pint to the fraction of a bushel. 60. Beduce f of an oz. to the fraction of 2 pounds. 61. Beduce ^ of an hr. to the fraction of a week. 62. Beduce J of a sec. to the fraction of % day. 63. What part of an acre is 9000 sq. ft? 64. What part of a gill is 0.03 of a gallon ? 66. What part of 2 hrs. is 2^ min. ? 66. How many paces are there in 1 mi. ? 67, Beduce ^ of a pint to the fraction oi a,\i\x^^. 86 ARITHMETICAL EXERCISES. 68. Eeduce 84} mi. to inches. 69. Reduce 1^ mi. to feet. 70. Eeduce -f of a mile to rods, etc. 71. Reduce -^ of an acre to square feet. 72. Reduce 0.05 sq. mi. to acres. 78. Reduce -J- cu. yd. to cubic inches. 74. Reduce 0.15 cu. ft. to cubic inches. 75. Reduce -j^^ of a cord to cubic feet. 76. Reduce -j^g- of a bushel to pints. 77. Reduce ^^ of 9 bu. to quarts. 78. Reduce -J- of a gallon to quarts, etc. 79. Reduce -J- of a ton to lower units. 80. Reduce 0.8125 t. to pounds. 81. Reduce ■§■ lb. Troy to lower units. ' S^, Reduce \ of an hour to seconds. 83. -Reduce 0.58 of a year to days. 84. Reduce -J- of 10 ft. to the fraction of a rod. 85. Reduce f of a square yard to the fraction of a square rod. 86. Reduce -J- of a cord foot to the fraction of a cord. 87. Reduce J of a dry pint to the fraction of 2-J- qts. 88. Reduce -j^ of a gallon to the fraction of 3 pts, 89. Reduce 4.16 dr. to the decimal of a pound. 90. Reduce 61j- oz. to the fraction of a pound. 91. How many minutes and seconds are there in 0.00213 of a day ? 92. Find the number of quart boxes required for 5 bu. i pks. 2 qts. of strawberries. 93. Find the value of 40 bu. of beans, at 8 cts. per quart. COMMON MEASURES. 87 94. Reduce 2,914,367 in. to higher units. 95. Reduce 94,249 sq. yds. to acres. 96. Reduce 2,315,520 cu. in. to cubic yards. 97. Reduce 26,347,289 sec. to weeks, etc. 98. Reduce -j^ of a mile to rods, etc. 99. Reduce 56.24 rds. to feet. 100. Reduce 2^ A. to square feet. 101. Reduce 0.001 cu. ft. to cubic inches. 102. Reduce f of 42 gals, to quarts. 103. Reduce ^ of 3 lbs. to ounces. 104. Reduce -f^ of a week to lower units. 105. Reduce 0.713 of a day to hours, etc. 106. Reduce 0.25 of a mile to the fraction of 8800 yds. 107. Reduce ^ of a rood to the fraction of 2 A. 108. Reduce f of a pound to the fraction of a long hun- dredweight. 109. Reduce 2 ft. to the fraction of a rod. 110. Reduce 266 rds. 11 ft. to the fraction of a mile. 111. Reduce -J of 8| days to the fraction of a week, 112. Reduce 4 cd. ft. to the fraction of 4^ cords. 113. Reduce 3 pts. to the fraction of 4 bu. 2 pks. 114. Reduce 4^ gills to the decimal of a gallon, 115. Reduce 8 oz. to the fraction of a ton. 116. Reduce 5 oz. 17 dwt. 18 gr. to the fraction of a pound Troy. 117. Reduce 3 dys. 10 hrs. 30 min. to the fraction of a week. 118. Reduce 55 min. 37 sec. to the decimal of a day. 119. A manufacturer put up 7-|-- 1. of soda in half-pound packages. How many packages did he ijut uig ? 88 ARITHMETICAL EXERCISES. 120. In 1 mi. how many chains ? In 1 link how many inches ? 121 • The four sides of a field are found by measurement to be as follows: 2.2 chains, 6.35 chains, 7.76 chains, 6.94 chains. What is the distance around the field in feet ? 122. The captain found that the ship was still in 8 fath- oms of water. What is this distance in feet ? 123. The ship's rate is 4 knots per hour. Reduce this to miles. 124. Eeduce 160 leagues to miles. 126. We are told in the Bible that the height of the giant Goliath was ** six cubits and a span." What was his height in feet and inches ? 126. How many acres are there in a township ? 127. In 1155 dry quarts how many liquid quarts ? 128. In 10,652 liquid quarts how many dry quarts ? 129. Find the capacity in gallons of a tank containing 400 cubic feet. 130. How many bushels will the same tank hold ? 131. How many gallons will fill a bushel measure even full? 132. Eeduce 33,000 imperial bushels to U. S. bushels. 133. Reduce 1 lb. Troy to the fraction of a pound avoir- dupois. 134. Reduce 4320 lbs. avoirdupois to pounds Troy. 135. Reduce -f- of a pound avoirdupois to the fraction of a pound Troy. 136. In 8 lbs. avoirdupois how many drams apothecaries* weight ? 137. How many cubic feet capacity has a vessel of 300 1. ? 139. Reduce 16 sQor^ to units ; 33 gross to units. COUUON UEASUBES. 89 Add: 138. 140. 141. mi* rds. yds. It. IB. A. sq. rds. gals. qU. PM. 46 98 3 1 6 6 20 9 2 1 20 259 5 2 9 9 26 7 8 50 177 4 1 6 2 110 4 1 u 37 310 3 2 10 10 82 12 li 37 212 4 2 9 7 144 15 a u 142. Add : 3 ft. 6 in. ; 17 ft. 4J in. ; 4 ft. ; 3 ft. 3| in. ; 2 ft. 4 in. ; 7 ft. 11 in. ; 5i in. ; 1 ft. 21 in. ; 2 ft. 0} in. 143. Add : 6 bu. 1 pk. 7 qts. 1 pt ; 2 bu. 2 pks. 5 qts. i pt. ; 19 bu. 3 pks. qts. 1 pt. ; 14 bu. 2 pks. 4 qts. 1 J pts. ; 10 bu. 1 pk. 3 qts. 1 pt. ; 5 bu. 3 pks. 2 qts. 144. Add : 3 wks. 4 dys. 16 hrs. 26 min. 18 sec. ; 9 wks. 1 dy. 20 hrs. 44 min. 50 sec. ; 7 wks. 6 dys. 2 hrs. 5 min. 30 sec. ; 8 wks. 5 dys. 21 hrs. 59 min. 57 sec. 145. Add : 45° 6' 20" ; 30° 45' ; 21° 19' 40" ; 90° ; 6" 4' 40"; 7° 9'; 19° 7' 20". • 146. A stable-keeper bought hay during the winter, in lots weighing as follows : 2 t. 1240 lbs. ; 7 t. 600 lbs. ; 3 1. ; 4 t. 1800 lbs. ; 2 t. 200 lbs. ; 1 t. 820 lbs. How much hay did he buy altogether ? 147. How many grains are there in 3 nuggets of gold weighing respectively, 11 oz. 13 dwt. 17 grs. ; 15 oz. 14 dwt. 19 grs. ; and 17 oz. 9 dwt. 13 grs. ? 148. How many feet in -j^ of a mile + ^ of a rod + -j- of a yard ? 149. Add 1:5^ A., 5^ sq. rds., 15^ sq. yds., and express the result in square feet. 150. A painter used 2 gals. 3 qts. of oil on one house, and S\ gals, on another. How much did he use on both houses? 90 ARITHMETICAL EXERCISES. 151. Find the difference between 8 ft. and 3 ft. 8 in. 152. Find the difference between 2 A. and 200 sq. rds. 153. Find the difference between 4 cds. and 4 cd. ft. 154. Find the difference between 2 bu. and 5 qts. 1 pt. 155. Find the difference between 4^ cu. yds. and 1152 cu. in. 156. Find the difference between -J- of a bushel and \ of a peck. 157. Find the difference between 3^ gals, and 3 qts. 1 pt. 158. Find the difference between 8 long tons and 9 short tons. 159. Subtract 19 mi. 311 rds. 4 yds. 1 ft. 6 in. from 35^ miles. 160. From 1 mi. 1706 yds. 3 ft. 3 in. take 175 yds. 2 ft. 161. A gas company laid 18 mi. 144 rds. 9 ft. of pipe, and paid cash for 7 mi. 200 rds. 12 ft. How much remains to be paid for ? 162. From 2 A. take 112 sq. rds. 12 sq. yds. 6 sq. ft. 10 sq. in. 163. A field contains 6J acres. 2 A. 77 sq. rds. of the field is planted with corn, and the remainder with potatoes. How much is planted with potatoes ? 164. From a barrel containing 42 gals, of kerosene there were taken 14 gals. 3 qts. 1 pt. How much was left ? 165. From 4 lbs. 7 oz. 19 dwt. Troy take 2 lbs. 9 oz. 21 dwt. 166. From 35 wks. 3 dys. 15 hrs. 25 min. take 17 wks. 6 dys. 22 hrs. 39 min., and reduce the remainder to seconds. 167.' Take -J^ of a foot from -^^ of a yard. Give the answer in inches. 168. Take 12.5 rds. from 0.1625 of a mile. COMMON MEASUEES. 91 169. Multiply 18 ft. 7 in. by 9. 170. Multiply 4 sq. rds. 6 sq. ft. by 62. 171. Multiply 59 A. 105 sq. rds. by 27. 172. Multiply 696 lbs. 5 oz. by 2311. 173. Multiply 47 miles 150 rds. 3 yds. by 198. 174. Multiply 17 bu. 3 pks. 6 qts. by 8J. 175. Multiply 26 gals. 2 qts. 1 pt. by 12J. 176. Multiply 3 lbs. 5 oz. 6 dwt. 7 grs. by 45f . 177. If a man can mow 2 A. 20 sq. rds. of grass in a day, how many acres can he mow in 3 wks. ? 178. If a horse eat 2 bu. 3 pks. 3 qts. of oats in a week, how many bushels will he eat in 12 wks. ? 179. How much kerosene oil will a family use in one year, if they use 1 gal. 1 qt. per month from April 1, to October 1, and twice this amount per month during the remainder of the year ? 180. How many grains are there in 7 ingots of silver, each weighing 27 oz. 9 dwts. ? 181. Multiply 9 dys. 17 hrs. 35 min. 25 sec. by 28. 182. Find the weight of 27 bars of steel, each weighing 101 lbs. 8 oz. 183. Find the value of 11 A. 67t sq. rds. of land, at $850 per acrd. 184. A field is divided into 47 gardens, each containing 25 sq. rds. 16 sq. yds. What is the area of the field ? 185. A wealthy landowner wishes to give to 37 poor people of his parish small lots of land, each containing 50 sq. rds. 5 sq. yds. How much land will be required ? 186. Multiply $459 lbs. 11 oz. 15 dwt. 23 grs. by 77. 187. If a man take 750 steps of 2 ft. 8 in. each in 5 minutes, what is his rate of walking per \iO\xt*i 92 ARITHMETICAL EXERCISES. 188. Divide 18 mi. 143 rds. 1} yds. by 35. 189. Divide 39 A. 150 sq. rds. by 45, 190. Divide 84 cds. 100 cu. ft. by 16. 191. Divide 39 A. 73 sq. rds. by llf 192. Divide 373 oz. 8 dwt. 3 grs. by 35. 193. Divide 1 1. 1105 lbs. by 67}. 194. Divide 145 wks. 2 dys. 14 hrs. 55 min. by 19. 195. Divide 5616 wks. 2 dys. 23 hrs. 3 min. by 315. 196. How many bottles each holding 1} pts. can be filled out of a cask of wine containing 114 gals. ? 197. How long will 84 bu. of oats last 7 horses, if each korse eats f of a peck a day ? 198. How many barrels each holding 2 bu. 3 pks. will be required to hold 165 bu. of apples ? 199. How many bags each holding 2 bu. 1 pk. 3 qts. are required to hold 234 bu. 1 pk. 4 qts. of corn ? 200. How many panes of glass each containing 24 sq. in. are required for a house with 33 windows, each measuring 4 sq. yds. 201. How many times is 195 yds. 1 ft. 8 in. contained in 1 mi. ? 202. A mason laid 25 rds. 2} yds. of stone wall in 20 days. How much did he lay per day ? 203. How many books each If in. thick can be put on a shelf 2 ft. 5f in. long? 204. A field containing 5 A. 75 sq. rds. is divided into 25 equal garden lots. What is the area of each lot ? 205. How many tablespoons each weighing 2 oz. 17 dwt. 12 grs. can be made from 155 oz. 5 dwt. of silver ? 206. A fruit-dealer wishes to pack 585 lbs. of raisins in boxes each holding 7 lbs. 8 oz. How many boxes will he needF COMMON MEASURES. 93 Find the period in years from the following dates to Jan. 1, 1885 : 207. The discovery of America, 1492. 208. The Eeformation, 1517. 209. Landing of the Pilgrims, 1620. 210. Battle of Waterloo, 1816. 211. The time, of Abraham, 2000 B.C. 212. Founding of Kome,^754 B.C. 213. Battle of Marathon, 480 B.C. 214. Death of CsBsar, 44 B.C. At what age did the following men die ? 215. Luther, born Nov. 10, 1483 ; died Feb. 18, 1646. 216. Goethe, born Aug. 28, 1749 ; died March 22, 1832. 217. Newton, born Dec. 25, 1642 ; died March 20, 1727. 218. Washington, born Feb. 22, 1732 ; died Dec. 14, 1799. 219. Franklin, born Jan. 17, 1706 ; died April 17, 1790. 220. Shakespeare, b. April 23, 1564 ; d. April 23, 1616. 221. Daniel Webster, b. Jan. 18, 1782 ; d. Oct. 24, 1852. 222. H.W. Longfellow, b. Feb. 27, 1807; d. Mar. 24, 1882. Find the dates when the following men died : 223. Thomas Carlyle, born Dec. 4, 1795; age, 85 yrs. 2 mos. 1 dy. 224. Napoleon, b. Aug. 15, 1769; age, 51 yrs. 8 mos. 20 dys. 225. SirW.Scott,b. Aug.15,1771; age, 61 yrs. 1 mo. 6 dys. Find the dates when the following men were born : 226. Copernicus, d. Nov. 6, 1632 ; age, 70 yrs. 3 mos. 5 dys. 227. Galileo, d. Jan. 28, 1642 ; age, 77 yrs. 11 mos. 9 dys. 228. Byron, d. April 19, 1824 ; age, 56 yxs^^mQ^.^in $i.iv t> 94 ARITHMETICAL EXERCISES. How many days between : -229. Mar. 21, 1885 and Sept. 23, 1886? 230. Jan. 11, 1883 and Mar. 25, 1883? 231. Feb. 2, 1884 and May 22, 1884? 232. Feb. 2, 1885 and May 22, 1885 ? 233. Nov. 9, 1880 and Mar. 13, 1881 ? 234. Aug. 22, 1883 and July 21, 1885 ? ^235. If the summer vacatk)n begin June 27 and lasts 12 wks., on what date will school begin again ? -236. On April 4, a man gave his note for 3 mos. ; on what date does the note become due, 3 days of grace being included ? -237. On Monday a man set out on a journey. He was gone 100 dys. On what day of the week did he return ? -238. In what respect do the first day and the twenty- ninth day of the month agree ? - 239. Jan. 1, 1859, fell on Saturday. What day of the week was Jan. 1, 1860 ? Jan. 1, 1861 ? What was the first year after 1859 in which Jan. 1 again fell on Saturday ? 240. Jan. 1, 1876, occurred on Saturday. What day of the week was July 4, and what day was Christmas of the same year ? 241. If Aug. 8 is on Monday, what day of the week will Nov. 1 be ? 242. If a leap-year begin on Wednesday, what day of September will be the first Monday of that month ? 243. If in a leap-year July 9 is on Friday, on what day of the week did the year begin ? 244. How many hours from 5 P.M. June 18, to 9 a.m. Aug. 1 ? 245. How many minutes from 10.45 a.m. Monday, to 6.35 p.M, Fridsiy ? GfMM^K MEASURES 95 Note. The sun appears to move towards the west at the rate of 15° per hour, or 15-' per min., or 15^^ per sec. ; hence, Snn Time varies at the same rate, and the more easterly the place, the later the time. Standard Time is the sun time of some selected meridian. The meridian selected is 75* west of Greenwich, for Eastern standard time. 90* west of Greenwich, for Central standard time. 105* west of Greenwich, for Mountain standard time. 120* west of Greenwich, for Western standard time. 246. Find the diiFerence in time between Greenwich time and each of the standard times. 247. Find the difference between Eastern standard time and sun time at Boston (71° 4' W.), New York (74° 1' W.), and Washington (77° W.). 248. Find the difference between Central standard time and sun time at Cincinnati (84° 39' W.), Chicago (87° 38' W.), and St. Louis (90° 15' W.). Find the difference of longitude if the difference of sun time is : 249. 7 min. 48 sec. 251. 1 hr. 18 min, 12 sec. 260. 51 min. 25 sec. 252. 10 hr. 13 min. 19 sec. Find the longitude of a place whose sun time compared with Greenwich time is : -'253. 1 hr. 20 min. slow. 255. 46 min. 52 sec. slow. * 254. 2 hrs. 37 min. fast. 266. 3 hrs. 9 min. 32 sec. fast. Find the difference in sun time between : ,^57. Boston and Washington. 258. New York and Chicago. 259. Boston and London (0° 5' W.). 260. St. Louis and Rome (12° 27' E.). 96. ARITHMETICAL EXERCISES. 261. How many half-crowns are equivalent to 285 guineas ? 262. Add 23 guineas, 37 sovereigns, 55 crowns, 31 florins, 53 sixpences, and 79 pence. 263. A clerk saved from his yearly salary of 150 guineas the sum of £16 1 s. 3 d. What was his average daily expenditure ? 264. Subtract 57^ guineas from £89 12 s. 7^ d, 265. Subtract 119 half-crowns from 37 half-guineas. 266. Find the amount of a servant's wages for 135 dys. at 10^ d. per day. 267. A man takes furnished lodgings in London at 27 s. 6 d. per week. What rent will he have to pay for the months of April, May, and June ? 268. If a man*s income be 450 guineas, and his average daily outlay, 19 s. 7^ c?., how much can he save in 1 year? 269. A lady buys 12 yds. of silk at 3 5. 6 d, per yd. ; 8 yds. of flannel at 1 5. 8 d. per yd. ; 6 pairs of stockings at 1 5. 9 d. per pair ; and 3 pairs of gloves at 2 5. 6 d. per pair. If she gives a five-pound note in payment, how much change ought she to receive ? 270. How many dollars are required to pay a debt oi £153 19 s. 2 c?., counting a dollar worth 4 s. 2 c?. ? 271. Find the equivalent in English money of $20,000. 272. What is the value in XJ. S. money of 3 pipes of sherry wine, each containing 130 gals., if they are invoiced at the Custom House at 10 pesetas per gallon ? 273. A man changed $1000 to English money, paying $4.84 per pound. After spending £ 72 17s. 3rf., he changed the remainder to francs, paying 10 d. per franc. After spending 1146 fr. he changed the remainder to marks, pay- f'ng 24 fr. for 19 marks. How many marks did he obtain? COMMON MEASUBES. 97 274. How long will it take a man to walk 1 mi. 240 rds. 120 yds. at the rate of 3J mi. per hour? 276. In a walking-match a man walked 109^ mL in 24 hrs. What was his average rate per hour ? 276. If an express train travels 45 mi. an hour, how many feet does it pass over in 1 sec. ? 277. A train travels the distance between two places in 4 hrs. 35 min. at the rate of 16f mi. per hour. How long would a train going at the rate of 19:|^ mi. per hour take to travel the same distance ? 278. If a man steps 28 in. each step, and takes 117 steps per minute, how long will he be in walking 26 mi. ? 279. If the telegraph posts are placed 80 yds. apart, and one is observed to pass the window every 5 sec, how many miles per hour is the train travelling ? 280. If a man walk 23 mi. in 6 hrs. 20 min., what is his rate per hour ? 281. A vessel sailed 11,067 mi. between 6 a.m. May 13, and 6 p.m. July 11. What was her average rate per hour? 282. A man wishing to find his rate of walking, observes that he takes 750 steps of 2 ft. 8 in. each in 5 min. What is his rate of walking per hour ? 283. A carriage wheel 10 ft. 9 in. in circumference makes 12 revolutions in 10 sec. At what rate per hour is the carriage travelling ? 284. The distance between two hills is 9 mi. A cannon was fired on one hill, and persons on the other hill observed that the interval between seeing the flash and hearing the report was 42J- sec. How far did the sound travel in 1 sec. ? 286. In what time would a train travelling 31 mi. an hour pass from the earth to the moon, a diatance oi ^^1 .^'^^y.'I 98 arithmetical exercises. Miscellaneous Exercises. (Including also the subjects of the preceding chapters.) 286. How many quires of paper are there in 64 bales? 287. How many sheets of paper are there in 80 reams? 288. How many reams of paper in 19,200 sheets? 289. How many half-pint bottles can a druggist fill from a demijohn containing 5 gals, of cologne- water ? 290. How many short tons in 1000 long tons of coal ? 291. How many minutes in the first 3 months of 1888? in the first 3 months of 1889 ? 292. I bought I of an acre of land for $1500, and sold it in lots at 10 cts. per square foot. Find my profit. 293. How many quart boxes will 6 bu. 1 pk. 3 qts. of grapes fill ? 294. How many gill bottles can be filled with 4 gals, of rose-water ? 295. If a man spend 7 hrs. each day in sleep, how many days will this be in 1 yr. ? 296. Add ^ of a month, -J^ of a week, -J-^- of a day, and ^ of an hour. 297. What is the cost of building a railroad 27 mi. long, at $12.50 per yard? — -- . ^ 298. How many quart boxes-can be filled from a pile! of cherries containing 6 bu. 2 pks. 5 qts. ? ] 299. How many pint bottles can be filled from a pipe of wine holding 120 gals. ? 300. If you buy 3 pts. of milk a day, how many gallons wi}} you buj in one common year ? COMMON MEASUKES. 99 301. The length of the civil year is 365 dys. 5 hrs. 48 min. 49.7 gee. Express the length in days and the decimal of a day. 302. The mean interval between a new moon and the next following is 29.530588715 dys. Express this interval in days, hours, minutes, and seconds. 303. A farmer raised 322 bu. 3 pks. of corn from 9 A. of land. What was the yield per acre ? 304. A lamp which burns 3 hrs. each evening, burns 1 gal. of kerosene oil in 4 wks. How much does it burn per hour? 305. A man had a barrel of cider containing 42 gals. He sold 6 gals, to one neighbor, 6 qts. to another, and 6 pts. to a third. What is the i:emainder worth, at 5 cents per ^uart ? 306. Farmer Ross raised one year 560 bu. of potatoes. He sold 300 bu. at $0.80 per bushel, and peddled the remainder at $0.30 per peck. How much did he receive for his potatoes ? 307. From a field containing 27 A. 95 sq. rds. 26 sq. yds. I sold 11 A. 148 sq. rds. 20 sq. yds. How much was left? 308. Subtract 29-j^ rds. from ^ of a mile. Give the answer in yards. 309. j^ubtract fj of a day from -^ of the month of April. 310. A fruit-dealer sold 3 bu. 3 pks. of apples on Mon- day ; 4 bu. 2 pks. 5 qts. on Tuesday ; 7 bu. on Wednesday ; 1 bu. 1 qt. on Thursday ; 5 bu. 3 pks. 6 qts. on Friday ; and 8 bu. 1 pk. 7 qts. on Saturday. How many apples did he 8ell during the week ? 100 AEITHMETICAL EXERCISES. 311. A manufacturer puts up 4000 doz. of four-ounce packages of yeast-powder every week. How many pounds does he put up ? 312. A stationer buys paper ^ at $2.80 per ream, and retails it at 18 cts. per quire. How many reams must lie sell in order to make a profit of $ 1000 ? 313. How many steps averaging 2 ft. 6 in. each must I take in walking a distance of 11 mi. ? 314. How many times will a pendulum vibrate in a week, if it vibrate 5 times in 6 sec. ? 316. A milkman sells 93 qts. of milk per day. How many gallons will he sell during the three summer months? 316. If a man steps 3 ft. at a time, and takes 2 steps each second, how far will he walk in 4 hrs. ? 317. A coal-dealer bought a cargo of 400 long tons of coal at $5.10 per ton, and retailed it at $5.75 per short ton. What was his profit ? 318. From a piece of land containing IJ A. there were sold 4 lots, each containing 42 sq. rds. 116 sq. ft. What is the remainder worth, at 20 cts. per square foot ? 319. A spice-merchant put up 8 t. of ground mustard in cans, each holding 4 oz. The mustard cost him $350 per ton ; the cans, half a cent each ; and the labor of can- ning, $0.80 per hundred cans. What will be the profit, if he sells the mustard at 10 cts. per can ? 320. I wish to print 6000 copies of a pamphlet of 72 pages, on paper weighing 40 lbs. per ream and costing 8 cts. per pound. Each sheet of the paper makes 32 pages of the pamphlet. How much will the paper for the pam- phlet cost ? COMMON MEASURES. 101 321. On July 1, Mr. Sawyer paid to the city his annual water-tax of $24. On Nov. 8, he moved to another city. How much money should the city return to him ? 322. What is the circumference of a wheel which makes 16,920 revolutions in going 17 mi. 200 rds. ? 323. Divide 84 wks. 3 dys. 16 hrs. 35 min. by 3 wks. 4 dys. 17 hrs. 25 min. 324. How many parcels each weighing 2 lbs. 12 oz. can be made up from 1848 lbs. ? 326. Divide 203 lbs. 9 oz. 1 dwt. 12 grs. by 36. 326. How many trees can be planted on 5i A. of ground, 35 sq. yds. being allowed to each tree ? 327. How many vibrations will a pendulum make dur- ing the month of December, at the rate of 65 per minute ? 328. If a field of 7 A. produce 392 bu. of wheat, how many bushels may be expected from a similar field contain- ing 9 A. 140 sq. rds. ? 329. A gold snuff-box weighs 7 oz. 17 dwt. 12 grs. What is its value, at the rate of $20.80 per ounce? 330. A gentleman hires furnished rooms at $6.60 per week. How much will he have to pay for the months of April, May, and June ? 331. If 7 horses eat 21 bu. of oats in 16 dys., how long will 99 bu. 3 pks. last them? 332. The four sides of a field measure respectively, 125 yds. 2 ft., 114 yds. 1 ft. 6 in., 80 yds. 2 ft. 3 in., and 137 yds. 1 ft. 9 in. What will it cost to surround the field with wire fence at 36 cts. per yard ? 333. How many pounds avoirdupois are equivalent to 55 lbs. Troy ? 102 ARITHMETICAL EXEECISES. 334. A composition consisting of half a dram of sulphate of iron, 10 grs. of subcarbonate of potash, a dram of myrrh, and half a dram of aloes is to be divided into 30 pills. "What will be the weight of each pill ? 336. A cask of wine containing 52i gals, was bottled off into an equal number of quart, pint, and half-pint bot- tles. How many dozen of each kind were there ? 336. At what rate per hour does a man walk who goes 26 mi. 1100 yds. in 7 hrs. and 6 min. ? 337. A milkman charges for his milk 7 cts. per quart from Nov. 1 to April 1, and 6 cts per quart for the rest ot the year. If a family use 1 qt. daily from Nov. 1 to July 1, and 3 pts. daily for the rest ol the year, find the amount of their milk bill for the year. 388. If A can mow 275 sq. yds. per hour, and B 330, in what time will both together mow a field of 2 A. 160 sq. rds. ? 339. My gas-bill for the last 4 mos. of the year was $33.60, and the meter showed a consumption of 16,760 cu. ft. during that time. What was the rate of charge per 1000 cu. ft. ? 340. How much land in Boston, at $2.25 per square foot, will $400,000 buy? 341. What must be paid for 6 bu. 2 pks. 6 qts. of timothy seed at $ 2.24 per bushel ? 342. How many times is 3 wks. 19 h. 25 min. 15 sec. contained in 133 wks. 6 dys. 19 h. 5 min. 45 sec. ? 343. Take 0.09375 of an acre from 33 sq. rds. 344. Take |^ of 7 A. 120 sq. rds. from -j^ of 12 A 60 sq. rds. COMMON MEASURES. 103 346. Take ff of a day from -J^ of a week. 346. Take -J^ of a week from -^ of the month of April. 347. Mr. White's store is 2 mi. 45 rds. 2 yds. from his house. If he walks from his house to his store and back daily (Sundays excepted), how far will he have walked in 1 yr. on this road ? 348. What will 23,280 lbs. of wheat cost at 80 cents a bushel ? 349. A milliner in the busy seasons can earn $3.50 a day. If the busy seasons are 12 wks. in the spring and 12 wks. in the fall, how much can she earn during them? 360. Sold 28 bu. of rye at $ 1.10 per bushel, and 57 bu. of oats at 60 cents per bushel. How much did I receive for the rye ? for the oats ? for both together ? 351. Make out a bill for the following goods : 240 bbls. of sugar, at $17.50 ; 800 lbs. of raisins, at $0.16 ; 167 bbls. of flour, at $7.25; 95 Webster's Dictionaries, at $6.85; 3,200 bbls. of flour, at $4.45 ; 375 silver watches, at $ 14.75 ; 980 yds. of carpeting, at $0.95 ; 69 office chairs, at $3.15. 362. Farmer Allen sold to Rice & Co. 3 loads of hay weighing respectively 1850 lbs., 1455 lbs., and 1920 lbs., at $16.80 per ton ; and 281 lbs. of pork at $8.25 per cwt. He received in exchange 40 yds. of sheeting at $0.09, 8^ yds. of cloth at $3.50, and the balance in money. How much money did he receive ? 363. A reservoir which holds 800 gals, of water receives 75f gals, per hour from one pipe, 86-J gals, per hour from another pipe, and loses 64|- gals, per hour by a third pipe. If the reservoir be empty, and all three pipes are opened, in what time will the reservoir be filled*} 104 ARITHMETICAL EXERCISES. 364. How many cords of wood will be required to make 7 t. of charcoal, if 4^ t. of wood make 1 1. of charcoal, and 1 cd. of wood weighs 3500 lbs. ? 365. A farm consists of 7 fields measuring as follows : 9 A. 67 sq. rds. ; 13 A. 35 sq. rds. ; 11 A. 99 sq. rds. ; 7 A. 55 sq. rds. ; 19 A. 25 sq. rds. ; 8 A. 135 sq. rds. ; 12 A. 80 sq. rds. Required the area of the farm. 366. A line of railroad is 43-^ mi. long. 19 mi. 455 yds. have already been constructed. How much remains to be constructed ? 367. A regiment marching 3 J mi. an hour makes 110 steps in a minute. What is the length of the step ? 358. A burns kerosene oil, costing 20 cents per gallon, and B burns gas, costing $2 per thousand cubic feet. A's lamp consumes f of a gill of oil per hour, and B*s burner consumes 6 cu. ft. of gas per hour. If both use light on the average 3 hours daily, from Oct. 1 to May 1, how much less will A's oil cost than B's gas ? 369. The distance between two wickets was marked out for 22 yds. ; but the yard measure was -^ of an inch too short. What was the actual distance ? 360. How many yards of carpet ^ of a yard wide will cover a floor 27| ft. by 19 ft. ? 361. For carpeting a room 10| yds. long and 7-J^ yds. broad $56.32 are paid. At 54 cents per yard, what is the width of the carpet used ? 362. A farmer planted 2 A. 16 sq. rds. of land with potatoes. The yield amounted to 150 bu. per acre. He kept f of the potatoes for his own use, and exchanged the rest for meal at the rate of 2|- bu. of potatoes for one bag of meal. How many bags of meal did he get ? COMMON MEASURES. 105 363. Find the expense of carpeting a room 15f ft. long and 13^ ft. broad, with carpet f of a yard wide, at 54 cents per yard. 364. Find the cost of varnishing the floor of a room 14 ft. 14 in. broad and 15 ft. 6 in. long, at 6 cents per square yard. 366. A lady has 20 lbs. of red currents for making jelly. 7 lbs. of currents yield 5 lbs. of juice, and the weight of the sugar required is ^ of the weight of the juice. In boil- ing down the loss in weight is \. How much sugar is required, and how much jelly will be obtained? 366. What weight of water will a rectangular cistern contain, the length being 4 ft., the breadth 2 J ft., and the depth 3J ft ; a cubic foot of water weighing 1000 oz. ? 367. A block of stone 4 ft. long, 2J ft. broad, and IJ ft. thick, weighs 27 cwfc. of 112 lbs. each. Find the weight of 100 cu. in. of the stone. 368. A milliner with $100 purchased 6 yds. of velvet at $4:^ per yard, 10 yds. of ottoman ribbon at $0.46 per dollar per yard, 12 yds. of satin ribbon at f of a dollar per yard, 8 yds. of black lace at -J of a dollar per yard, 24 yds. of white lace at -J of a dollar per yard, 3 doz. felt hats at f of a dollar each, 2 doz. plumes at f of a dollar each, and 10 bunches of flowers at ^ of a dollar per bunch. How much money remained ? 369. Samuel picked 7 qts. of berries on Monday, 9 qts. on Tuesday, and 6 qts. on Wednesday. He sold what he picked on Monday and Tuesday for 12 cents per quart, but received only 10|- cents per quart for those picked on Wednesday. He put $ 1.00 in the savings bank, and bought a hat for $ 1 J. How many handkerchiefs, at 10 cents each, pould he get is^rith the remainder? 106 ARITHMETICAL EXERCISES. 370. From a rye-field containing 3^ A. a farmer ob- tained 52 bu. of rye, and 2 t. 9 cwt. of straw. He sold tbe rye at $1.05 per bushel, and the straw at $13 per ton. How much money per acre did the field yield him ? 371. A man walks 18 mi. 2 fur. 26 rds. 3f yds. in 5^ hrs. In what time will he walk 1^ mi. ? 372. A farmer exchanged corn, at $ 0.85 per bushel, and rye, at $1.40 per bushel, for 12 t. of hay, at $18.50 per ton delivered. If he gives 150 bu. of corn, how many bushels of rye are required to square the account ? 373. A farmer exchanged 6 cds. of wood, at $7.25 per cord, for 3 bbls. of flour, at $5.75 per barrel, and the rest of the pay in sugar, at 6f cents per pound. How many pounds of sugar should he receive ? 374. What is the freight bill for carrying 87,550 lbs. of beef from St. Louis to New York, at $0.56 per hundred- weight? 376. In Trenton, N. J., there are 23 pottery establish- ments with an aggregate of 110 kilns, and an annual pro- duction of $4,000,000 worth of goods. What is the- average value produced by each pottery ? by each kiln ? 376. At a printing house, male compositors get 35 cents per 1000 ems, and female compositors, 25 cents. If a male compositor can set 6000 ems in a day, how many ems must a female compositor set in order to earn the same amount of money ? 377. What is the value of a chest of tea containing 79 lbs. 10 oz., at 62^ cents per pound ? 378. Add together 6 sq. yds. 7 sq. ft. 56f sq. in., 17 sq. yds. 4 sq. ft. 91|- sq. in., 5 sq. yds. 3 sq. ft. 100|- sq. in., and subtract 20 sq. yds. 7 sq. ft. 140f sq. in. from the sum. COMMON MEASURES. 107 379. Reduce 7 hrs. 15 min. to the decimal of a day ? When it is 7 a.m. sun time at Paris (2** 20' E.), what is the time : 380. At Petersburg (30** 19' E.)? 381. At Calcutta (88** 26' E.) ? 382. At New York (74** W.) ? 383. At San Francisco (122** 14' W.) ? 384. How many yards of flannel, at 54 cents per yard, are equal in value to 12 pairs of blankets, $ 7.56 per pair ? 385. Reduce 56 days to the decimal of a year. 386. Two railway trains start at 7 a.m. at opposite ends of a line 640 mi. long. Their average rate is 32 mi. an hour. At what hour will they meet ? 387. For transporting a pile of coal from one place to another, 18 laborers were employed with wheelbarrows holding on the average 220 lbs. of coal. After they had made 10 trips, the pile was reduced one-half in size. What was the weight of the pile ? 388. How many days and hours are there from March 8, 10 a.m., to Nov. 13, 11 p.m. ? 389. How many days and hours are there from 2 a.m., Feb. 3, 1887, to 6 p.m., Dec. 23, 1889? 390. A bicyclist travels 50 miles in 3 hrs. 6 min. 40 sec. What was his rate in feet per second ? 391. I own 4 out of 75 shares in a business. What will be my share of a profit of $ 19,837.56 ? 392. How many times does a wheel whose circumference is 18^ ft. turn in going 2^j mi, ? 108 ARITHMETICAL EXERCISES. 393. Extract from a farmer's note-book, January, 1885 : Dally Rations. No. of Animals Jan. 1, Animals, Oats, qta, 12 Meal, qta. Hay, Iba, Straw, Iba, Roota, Iba, Notes, Horses, Oxen, Cows, Sheep, 4 2 16 8 14 3 12 10 10 2 30 20 10 7 9 11 62 Jan. 4, sold S cows. Jan. 9, sold 1 oow. Jan. IS, sold 1 horse. Jan. IS, sold 41 sheep. Jan. 16, bought 8 oxen. Jan. 16, bought 36 sheep. Hence, find the total consumption of each article of food for the month. 394. If a postman walk 3f mi. every morning, and 2^ mi. every evening, how far will he walk between Jan. 1, 1888, and the end of the following June, supposing no delivery of letters on Sundays ? 396. A bequest of $251.28 is left to 7 men and 10 women, so that each man is to have twice the share of each woman. How must it be divided ? 396. A farmer hires two farms, of 53 A. and 27 A. respectively. He pays $8.40 an acre for the one, and $6.80 an acre for the other. After paying $499.20 in money, how much wheat at $ 1.35 per bushel must he give to make up the remainder of his rent ? 397. The leading- wheels of a locomotive are 5 yds. 2 ft. 2 in. in circumference ; the driving-wheels, 8 yds. 1 ft. 9 in. How often will the former turn while the latter turn 618 times ? and what distance will have been run ? 398. Find the G.C.M. of 116,039, 122,067, and 137,137. 399. A cargo steamer leaves port at the rate of 8^ mi. per hour at 3 a.m. on Monday. At midnight, Monday night, a despatch boat starts in pursuit at the rate of 15 mi. an hour. When will they be in sight of one another, sup- posing them to be visible 6 mi. off? COMMON MEASURES. 109 400. I am asked to supply a ton of fusible metal consist- ing of 8 parts by weight of bismuth, 5 lead, and 3 tin. The only bismuth' I happen to have in stock is in an alloy consisting of 9 parts of bismuth, 4 lead, and 3 tin. How much of my alloy must I take, and how much lead and tin must I add to make up the order ? 401. Two wheels in gear have, respectively, 10 teeth and 64 teeth. How many times will the smaller revolve while the larger revolves 575 times? 402. A, B, C are three places on a river, A and C being equally distant from B. A boat can go from A to B and back in 5-^ hrs., and from A to in 7 hrs. How long would it take to go from C to A ? 403. The new English ordinance maps are made on the scale of 25 in. to the mile. The map of a certain parish is 5 sq. ft. in area. Find the number of acres in the parish. 404. At a collection after a sermon the boxes were found to contain 4 five-dollar bills, 9 one-dollar bills, 22 half- dollars, 34 quarters, 73 dimes, 96 half-dimes, and 118 nickels. What was the sum collected ? 406. A fire is maintained in a stove 14 hrs. daily, from Nov. 1 to May 1. The price of coal is $7.50 per ton, and the stove consumes on the average 2^ lbs. of coal per hour. Find the total cost of maintaining the fire. 406. Reduce 10 min. to the decimal of a day. 407. Mr. B engages a seamstress to make him one dozen of shirts. She pays 12|- cents per yard for the cloth, and 60 cents apiece for the bosoms, and charges him 15 cents apiece for thread and buttons, and 50 cents apiece for the making. What is the amount of her bill, alloN^ii^^^\'^^^. of cloth to each shirt ? 110 ARITHMETICAL EXERCISES. 408. If a man saves $ 77.40 out of a yearly income of $ 1260, how much does he spend per day ? 409. A dealer in notions paid $ 7.20' for 12 bunches of feathers, each bunch containing 12 doz. of feathers. How many feathers should he sell for 5 cents in order that his profit may amount to $3.60? 410. Mr. Glaisher, when in a balloon 4 mi. from the earth, heard a railway train directly below him. How many seconds was the sound in reaching him if it travelled at the rate of 1100 ft. per second ? 411. How many days are there from Dec. 17, 1887, to Oct. 3, 1888, both dates included ? Express the result as the fraction of a year. 412. Divide the product of 17.161 and 0.098 by the product of 1.31 and 64.33. 413. Find to the nearest second the time occupied by light in passing to the planet Neptune from the sun, the velocity of light being 186,000 mi. per second, and the dis- tance 2746 millions of miles. 414. How many times must I walk round a garden 80 ft. long and 36 ft. wide in order to walk 3 mi. ? 416. Sound travels 1120 ft. per second. What is the distance of a thunder-cloud when the thunder is heard 17-| sec. after the lightning is seen ? 416. Europe contains 3,375,860 sq. mi., and Australia contains 4,255,000. How much larger is Australia than Europe ? Find the population of each, if Europe has 90 inhabitants to the square mile, and Australia 3 inhabitants to every 4 sq. mi. 417. A man sold -^ of his farm, and then -J of the remainder; he then had 44 A. left. How many acres were there in his farm ? COMMON MEASURES. Ill 418. A market-woman bought eggs at 18 cents per dozen, and sold them at the rate of 6 eggs for 8 cents. After the day's sales were finished she found that she had made just 48 cents on the eggs. How many eggs had she sold? 419. Divide 288 lbs. between A and B so that if A give B 4^ of his share, they may have equal weights. 420. Which is the faster rate, 42 mi. per hour or 20 yds. per second ? By how many yards per minute is one rate faster than the other ? 421. How much will it cost to carpet a room 21 ft. long and 18 ft. wide, with carpeting f of a yard wide, the strips running across the room, at $1.75 per yard, if there is no waste in matching the pattern ? 422. A room is 16 ft. long, 14 ft. wide, and 10 ft. high. It has 3 windows 6 ft. by 3 J ft., 2 doors 7 ft. by 3 ft., and the baseboard is 9 in. wide. Find the cost of plastering the room at 15 cents per square yard. 423. A milkman takes 2 qts. of milk from a can con- taining 2 gals, of milk, and fills the can up with water. Seeing, however, that his supply of milk is still likely to run short, he pours out 2 qts. more from the can and fills up with water. How many quarts of milk are left in the can? 424. A tank contains 3027 gals, of water. To empty it three cocks are opened, which allow to flow out per minute, the first 4-J- qts., the second 3 J- qts., and the third 2| qts. In how many minutes will the tank be empty ? 425. The great bell of Moscow weighs 202 long tons. If bell-metal consists of 77 parts copper and 23 parts tin, how many tons of copper and of tin are t\ieT^ m \)DL^\i^'\ 112 ARITHMETICAL EXERCISES. 426. If a walk 4 ft. wide is made round a park 300 ft, square within the enclosure, how many square yards will it contain ? 427. How many bushels of grain will a bin hold that is 15 ft. long, 6J ft. wide, and 3f ft. deep ? 428. A man who had 332 gals. 2 qts. 1 pt. of wine sold 239 gals. 3 qts. 1 pt., at 25 cents per pint, and then bottled the rest in bottles each holding 1 pt. 3 gi. How many pints did he sell ? How much did he receive for what he sold ? How many bottles did he fill ? 429. How many pickets 3 in. wide, placed 3 in. apart, will be required to fence a lot 99 ft. by 231 ft., and what will they cost, at $3.25 per 0. ? 430. How many yards of carpeting f of a yard wide will be required for a floor 18 ft. long, 16 ft. 4 in. wide, if the strips run lengthwise of the room, and there is a waste of -J- of a yard in each strip in matching the pattern ? « 431. An apothecary bought 15 lbs. of opium, at $10.24 per pound avoirdupois, and sold the same in pills of 1 gr. each, at the rate of 25 cents for 10 pills. How much did he gain? 432. A grocer buys 30 hhds. of molasses, containing each 122 gals., at 54 cents per gallon, and sells them at 70 cents per gallon. What profit does he make, allowing a waste of 6 gals, for each hogshead ? 433. A gentleman's income amounts to $4000. He pays $ 800 for rent ; his average daily outlay for food and servants is *$ 3.20; the cost of light for the year is $21; and of heat, $116 ; and he pays out during the year $550 for clothing and for the education of his children ; he also puts $800 in the savings bank. How much of his salary is left for incidental expenses? COMMON MEASURES. 113 434. The length of the sidereal year is 365.2564 dys. Express the decimal fraction in hours, minutes, and seconds. 435. A bookseller bought 912 copies of a dictionary, at the rate of $45 per hundred. He sold 400 of them in lots of 10 each, at $ 6 per lot. How much apiece must he ask for the remainder to make $50 by the transaction? 436. A grocer has two hogsheads of molasses : one con- tains 100 gals., but the quantity in the other is unknown. He has paid for the molasses 60 cents per gallon, and he sells it all at 75 cents per gallon thereby gaining $27, How many gallons did the second hogshead contain ? 437. To pay an election bet, Mr. Mullen had to sell peanuts on Boston Common until the profit amounted to $50. If he can sell 2 bu. an hour, and the profit is 4 cents per quart, how long will it take him to pay the bet, and how many quarts of peanuts must he sell ? 438. Find the expense of erecting 7 mi. 1300 yds. of telegraph wire at $ 120 per mile ; also the cost of the same length of wire at $8 per hundredweight (100 lbs.), reckon- ing 1000 yds. to the ton. 439. Reduce to their lowest terms the fractions iVsV^ , iVaVa * ^^^ ^^^^ subtract the less from the greater. 440. The Flying-Dutchman Express runs from London to Exeter, a distance of 193^ mi. in 4 J hrs., making one stop of 10 min., two of 5 min. each, and one of 3 min., on the way. What is its average speed when in motion ? 441. The Scotch Express runs from London to Edin- burgh, a distance of 393^ mi. in 9 hrs. making one stop of 80 min., three of 5 min. each, and one of 3 min. on the way. "What is its average speed when in motion ? 114 ARITHMETICAL EXERCISES. 442. A runs a mile in 5y\ min. ; B, in 5^ min. Which is the faster runner? By how many seconds would he win in a mile race ? 443. If $8853.66 are divided equally among 909 persons, how much will each person receive ? 444. For repairing a road, a town employs 6 men who work each 10 hrs. a day, and together repair 15 yds. in one hour. The road is 3J mi. long. How many days will the men be employed ; and what will the work cost, if each man receives 25 cents per hour ? 446. Reduce 5 hrs. to the decimal of o, day. 446. A grocer owes a silversmith for 3 doz. of table- spoons, at $10.92 per dozen, and 4 doz. of teaspoons, at $9.06 per dozen. How much tea at 92 cents a pound will cancel the debt? 447. How many dollars, worth 4 s. 2 c?. each, will pay abillof£1117s. 6c^.? 448. Divide 0.07504 by 23.45, and 0.00044408 by 112, and add your results. 449. After drawing off 132 gals, of water from a cistern, it was found to be just -J- full. How many gallons will the cistern hold ? 450. If a roll of paper a mile long will just cover 1210 sq. yds., how wide is the paper? What will the roll weigh, if 6J yds. weigh 7-J- oz. ? 451. A contractor estimates that he can complete a piece of work in 51 dys. by employing 28 men. At the end of 34 dys. he wishes to engage additional men enough to finish the work in 14 more days. How many men must lie engage ? COMMON MEASURES. 115 452. If 50 yds. of silk worth $1.08 per yard are ex- changed for 30 yds. of cloth, at what price per yard is the cloth reckoned ? 453. The lunar month is 29.53 dys. Express this value in days, hours, minutes, and seconds. 454. A laborer is in the habit of spending 10 cents daily for beer, and 20 cents a week for tobacco. If he gives up the habit, how many yards of carpeting at 90 cents per yard could he purchase with the money saved in one year? 455. A can do a piece of work in 6 dys., and B can do it in 7 dys. If they work together for 2 dys., and A then leaves, how long will it take B to finish the work ? 456. If 35 yds. are equal to 32 meters, and 3 meters of silk cost 84 frs., and 1 fr. is equal to 20 cents, what will 5 yds. of silk cost ? 457. Express tj^ of a common year in days, hours, etc., and subtract the result from a week. 458. A boy has a certain sum of money, of which he spends f, and then J of the remainder, and he has $1.22 left. How much had he at first ? 469. Reduce to their lowest terms the fractions 3^VA» "5^^^, and then subtract the less from the greater. 460. A clothier bought 175 yds. of cloth at $2.82 per yard, and retailed it at $3.24 per yard. What did he gain on the whole ? 461. A man bought a piano for $600, a writing-desk for $140, and an easy-chair for $30, and paid for them in ten-dollar gold pieces. What was the whole sum paid? How many ten-dollar pieces were paid for each article, and how many all together ? 116 ARITHMETICAL EXERCISES. 462. A farmer buys 25 sheep for $180, and 17 more for $125. What will he gain by selling the whole at $7.87^ each? 463. If a boat 63 ft. long travel ^ of its length each stroke, how many strokes will be required in rowing a course of |-J- of a mile ? 464. Multiply 2 mi. 3 fur. 117 yds. by 67f 465. A watch is set right at 9.15 A.M., and it gains 3^ min. every hour. At what o'clock will it have gained exactly f of an hour, and what time will it then indicate ? 466. How many miles will be travelled between 11.40 A.M. and 4 p.m., at an average rate of 27-J- mi. per hour for 2 hrs. 25 min., and of 43^ mi. per hour for the remainder of the time ? 467. A man bought 35 sheep at $19.20 a head. He sold 7 sheep at $ 25.20 a head. At what price per head must he sell the others in order to gain $ 140 on the whole ? 468. Divide $36 among 5 persons so that the shares of two of them shall each be $2.40 less than the shares of each of the others. 469. Reduce -j^ of 2^ yds. to the fraction of a rod. 470. If I can walk 350 yds. in 2 min. 40 sec, how long will it take me to walk 560 yds. ? And how far can I walk in 3 min. 44 sec. ? 471. Simplify 7 - 2^1 + '3^ - 5f + 3^2,^ + If - If . 472. From a field of rye containing 4 A. 64 sq. rds. a farmer obtains 84 bu. of rye worth 90 cents per bushel, and 3 t. 18 cwt. of straw worth $ 10.50 per ton. What is the gross income per acre from the field ? 473. A box containing 9 doz. pairs of kid gloves was offered at $ 97.20. What was the price per pair ? COMMON MEASURES. 117 474. A man bought at the same rate per acre two fields, one containing 28 A. 40 sq. rds., the other 34 A. 62|^ sq. rds. The larger field cost $456 more than the other. What was the cost of each field ? 475. The rails of a railroad weigh 70 lbs. per yard, and cost $42 per ton. Find the cost of the rails needed to build a double-tracked road 64 miles long. 476. A bushel of wheat weighs 60 lbs., and 100 lbs. of wheat yield 74J lbs. of farina. When wheat is worth 90 cents per bushel, what is the value of farina per hundred- weight, disregarding the cost of making it? 477. A gentleman spends on the average $10.44 daily. At the end of the year he has saved $1680. What is his yearly income ? 478. I use 4 lamps, each burning -J^ of a pint of oil per hour, and keep them burning for 4 hrs. each evening. On the evening of Oct. 13 I began to supply them with oil from a 40-gallon cask full of oil. On what date will the cask be empty ? 479. A cistern holding 200 gals, is filled by 2 pipes. One pipe supplies 0.15 of a gallon per second, the other If qts. per second. If the first is turned on for 10 min. and afterwards both run together, in what time will the cistern be filled ? 480. A barometer, in four successive days, rose 0.135, 0.044, 0.095, and 0.573 in. respectively. It then fell 0.021 and 0.417 in. in the two next days. If the first reading was 29.024 in., find the last reading. 481. Bronze consists of 4^ parts of copper to 1 part of tin ; how much copper must be added to 656^ lbs. of tin to make bronze ? 118 ARITHMETICAL EXERCISES. 482. Simplify 4X3^X5^^. 483. The total length of the lines of railway open in the United Kingdom in 1872 and in 1882, with total traffic receipts and working expenses, were as follows : Total Length. Total Receipts. Total Expenses. 1872, 15,814 mi. £51,304,114 £26,293,304 1882, 18,457 mi. £ 66,537,128 £ 36,170,436 Find for each year to the nearest penny the net receipts per mile. 484. If the scale of a map is 25 in. to the mile, how many sq. ft. will there be in the map of a town containing 4800 A. ? 485. A, B, and C agree to do a piece of work for $12.60. A does ^ of it, and then goes away ; B does ^ of what A leaves ; and then C finishes the work. What sum of money should each man receive ? 486. Find the value in days, hours, etc., of 2.723 dys. + 4.659 hrs. + 21.234 min. + 7.36 sec. 487. A man starts at 9 a.m. on a journey of 21 miles, walking 3^ mi. per hour. At 11.48 a.m. he quickens his pace by -J- mi. per hour. At what o'clock will he arrive at the end of his journey, and how much sooner than if he had kept on at his original rate ? 488. By what number must you multiply 49 in order to diminish it by 35 ? 489. What fraction of 21 cu. yds. 11 cu. ft. 1215 cu. in. are 3 cu. yds. 1 cu. ft. 1161 cu. in. ? 490. The mean daily temperatures registered during a certain week in January were, 7®, 3.6°, —9®, 6°, —-3°, 0°, 8°; £nd the average temperature for the week. COMMON MEASURES. 119 491. A boy can swim in still water 1 yd. per second, and a stream flows at the rate of 15 yds. per minute. How far can the boy swim down the stream in 10 min. ? How long will it take him to swim 180 yds. up the stream ? 492. The longitude of Pekin is 116° 29' E. of Green- wich, and of Chicago 87° 40' W. of Greenwich. What is the mean solar time at Chicago when it is midnight at Pekin? 493. Air weighs ^hf ^ niuch as water, and a cubic foot of water weighs 62i lbs. very nearly. How many cubic feet of air will weigh 1 lb. ? 494. A crew can row 12 mi. an hour in still water. How long will they be in rowing 3i mi. against a stream whose rate is 2 mi. an hour? How far could they row down the stream in 23 min. ? 495. An imperial gallon of water weighs 10 lbs., and a cubic foot of water weighs 1000 oz. ; how many imperial gallons are there in a cistern containing 64 cu. ft. ? 496. I have three lamps. The first burns -J as much as the second, and the third burns 9 pts. of oil while the -sec- ond burns 10 pts. If the third burns a pint of oil in 6 hrs., in what time will the first burn a pint of oil ? 497. The moon revolves around the earth in 27 dys. 7 hrs. 48 min. Express this interval as a decimal number with the day for the unit. 498. A man who has bought 342.45 A. of pasture land, at $18.25 per acre, wishes to sell it so as to realize a profit of $500. He divides the laud into nine equal lots, and sells seven of them at $19.40 per acre. What price per acre must he ask for the other two loUl 120 ARITHMETICAL EXERCISES. 499. Find the total product of each principal crop pro- duced in Massachusetts in 1880, from the following data: Average yield per Acre. 65,980 33.5 bushels. Number of Acres. 20. 17.5 31. 126. 1.08 tons. (( ti It Indian corn. Buckwheat, 5,212 Eye, 24,600 Oats, 23,139 Potatoes, 41,620 Hay, 799,714 500. A clock which loses 35 min. daily, is set exactly right at noon. What is the correct time when this clock indicates 10.30 p.m. of the same day ? 501. Simplify ^-^/jW) _2^,f^. 502. Simplify 3| X 5| - 2^1^^ X 1^ - 4^ X 3^ + 1054^. 503. If 1 lb. of dry oak wood has -J^ ^^ ^^^ heating power of 1 lb. of coal, and 1 cd. of oak wood weighs 3610 lbs., and costs $10.50, what must be the price of coal per ton to make it just as cheap to burn the one as the other? 504. In an estate of 3779 A. 16 sq. rds., the roads occupy 66 A. 48 sq. rds. What fraction of the estate is occupied by the roads? 505. If 1 yd. = 0.9144 meters, how many meters are there in 1-J- mi. ? 506. Light travels 186,000 mi. per second. What is the distance from the earth to the sun, if light takes 8.1583 min. to travel the distance ? 507. Starting at 10.10 a.m. I find I have walked 6^ mi. by 11.45 A.M. ; I then walk at a slower rate Bi mi. further by 1.55 P.M. What was my average rate in miles per hour a^ £r8t? During the last 81 mi.? For the whole journey ? COMMON MEASUEES. 121 508. What is the value of 127 mi. 224 rds. of telegraph wire, at $35.28 per mile? 509. Simplify M^-^.lOf. 510. Four bells toll at intervals of 3, 4, 5, and 8 sec, respectively, commencing at the same instant; at what intervals will they toll simultaneously ? 511. Simplify 2^ x 3^ - 3^ X 4^- -^ 2^ X 5 J + 1098^^. 512. If the range of a gun is 9500 yds., what is it in kilometers ? (One kilometer = 1094 yds.) 613. From a heap of shot weighing 3 J- lbs. 560 shot are taken, and the heap is then found to weigh 2i lbs. Find the weight of a single shot, and the number originally in the heap. 514. Reduce 3 wks. 4 dys. 20 hrs. 6 min. to the decimal of 60 dys. 515. A can do a piece of work in 3 dys. ; B can do twice as much in 5 dys. ; and C three times as much in 7 dys. How long will it take them, working together, to do five times the original work ? 516. A vessel holds 4^ qts. How many times can it be filled from a tank holding 94}-| gals., and how much water will remain ? 517. Simplify ^~i^/i + ^). ^~23| 518. Reduce 3 yds. 2 ft. 9 in. to the decimal of 5 mi. 519. After drawing 5 gals, from a cask, and then half of what was left, the remainder, sold at 6 cents a pint, pro- duced $3.36. What did the cask hold ^\i^ii i'^'l 122 ARITHMETICAL EXERCISES. 520. A can walk 4 J mi. per hour ; and B* can walk 110 yds. per min. Which is the faster walker, and in what time would he overtake the other, if the latter have 2 min. the start ? 521. At what times between 4 and 5 o'clock are the hands of a clock at right angles? together? opposite? 522. It is 3.13 P.M. mean sun time at a place A when it is 11.44 A.M. at a place B. Find the difference in longi- tude between A and B. 523. Multiply 2 dys. 15 hrs. 35 min. 14 sec. by 3-j^. 524. The length of a journey is 82 mi. If I go i of it by rail, at 41 mi. per hour; -^ by coach, at 7 mi. per hour; and walk the rest of the way, at 3f mi. per hour, how long will it take me to make the journey ? 525. If a knot is -gij- of a degree, and a mile is 0.01477 of a degree, find the value of a knot (to four decimal places) in terms of a mile. 526. What number contains 1832 as often as 6.9 con- tains 0.023 ? 527. If the telegraph poles by the side of a railway are placed at intervals of 70 yds., at what rate in miles per hour is a train travelling, which passes three of these intervals in 11 sec. ? 528. By what fraction must you divide 62 in order to increase it by 12|- ? 629. Simplify 3f of ^^^^"15^ - 1 A " 1^- 530. A very good soil is one f of which is clay, ^ is sand, and the remainder is lime. How many pounds of each substance are there in 70 lbs. of this soil ? COMMON MEASURES. 123 531. If f and then \oi& piece of cloth are sold, and 3^ yds. remain, what was the whole length of the piece ? 532. The amount of juice in the sugar-beet is ^ of its weight, but the amount that can be extracted is only ^. How many pounds of sugar-beets are required to furnish 1000 lbs. of juice, and how much juice will be thrown away with the pulp? 533. There is a barn 40 ft. long, and each side of the roof is 20 ft. wide. It is shingled with shingles 18 in. long, and averaging 4 in. wide. The shingles lie -^ to the weather. How many bunches of a quarter-thousand each will be required to cover the roof? 534. A man engaged to work a year for $360 and a suit of clothes. At the end of 8 mos. he quit work on account of sickness, and received for his wages the suit of clothes and $220. Find the value of the suit of clothes. 536. If it is worth $ 1 to saw a cord of wood consisting of sticks 4 ft. long into pieces 1-^ ft. in length, how much is it worth to saw a cord consisting of sticks 8 ft. long into pieces of the same length ? 536. A boat, whose rate in still water is 14 mi. per hour, is 10 hrs. longer in going up a river a certain distance than in coming down the same distance. Find this dis- tance, knowing that the current of the river is 2J mi. an hour. 537. The longitude of Boston is 71* 4' W. What is the time by the sun at Boston when it is 3.35 a.m., June 9, in London (long. 0° 5' W.) ? 538. The captain of a steamer, sailing from London to New York, found on taking an observation, that the sun crossed his meridian at 1 hr. 42 min. 50 sec. p.m. by Green- wich time. Find his longitude. Olum rKi!-^ V CHAPTER V. PERCENTAGE. What per cent of a number is : 1. 0.05? 0.10? 0.46? 0.06J? 0.8? 2. 0.6? 0.165? 0.875? 0.2875? 0.16? 3. 1.20? 2.50? 3.625? 4.015? 6.375? 4. ^? i? I? I? I? I? I? II? 5. i? i? H? A? iftr? irV? i!^? 6. 1^? A? ^? A? 3^? 1^5^? iV^? What decimal fraction of a number is : 7. 10%? 60%? 701% ? 92J%? 87^%? 8. 20%? 20.6%? 83.17%? 144%? 256%? 9. 35i%? 4|.%? 216.76%? 1.18%? 12.5%? What common fraction of a number is : 10. 5%? 15%? 6i%? 33i%? 60%? 11. 46%? 12J%? 16|%? 66|%? 70%? 12. |%? 6^3^%? 114^%? 222J%? 93J%? Find: 13. 18% of $1297. 14. 11% of $1000. 15. 5% of $742.10. 16. 47|% of $7893. 17. 87|% of $1624.50. 18. 2i% of $7135.80. 19. 8f% of $777.50. 20. 12^% of $994.70. PERCENTAGE. 125 21. What per cent of 200 is 4 ? 22. What per cent of 480 is 12 ? 23. What per cent of 16,400 is 2624 ? 24. What per cent of 270 is 90 ? 25. What per cent of 90 is 270 ? 26. What per cent of 8217 is 1643.4 ? 27. What per cent of 4530 is 6040 ? 28. What per cent of 10,400 is 650 ? 29. A merchant imports 2740 boxes of oranges, and finds upon receiving them that 548 boxes are decayed. What per cent of the whole number was decayed ? 30. A gentleman purchases a farm for $ 7490, and agrees to pay 10% down, 17% at the end of the first year, 27% at the end of the second year, and the remainder at the end of the third year. Find the amount of each payment. 31. A brick kiln contained 29,800 bricks, and, after burn- ing, it was found that only 24,734 were in good condition. What per cent had been spoiled in burning ? 32. What is the difference between 4^% of $740 and 2^% of $1680? 33. A house worth $4000 rents for $360 a year. What per cent of its value does it rent for ? 34. If 24 bu. of corn are raised from 1 pk. of corn, what per cent is the increase ? 35. For the fiscal year 1885, the revenue of the United States was $181,471,939, and the expense of collecting it was $6,494,847. What per cent (to two decimal places) was the latter sum of the former ? 126 ARITHMETICAL EXERCISES. 36. 87 is 20% of what number ? 37. 40 is 6J% of what number ? 38. 620 is 33^% of what number ? 39. 24832.08 is 36% of what number ? 40. 4140.16 is 8|% of what number ? 41. 2f is 3% of what number ? 42. :J is 12^% of what number ? 43. 0.08 is 16|% of what number ? 44. 630 is 140% of what number ? 45. 190 is 250% of what number ? 46. The population of Arizona increased between 1870 and 1880 from 9658 to 40,440. Find (to two decimal places) the increase per cent. 47. The population of a city increased 30,000 in ten years, a gain of 24%. What was the population at the beginning and the end of the period ? 48. A clerk spent 50% of his salary for board, 20% for clothes, and 8% for amusements, and saved $330. What was his salary ? 49. A man owning 30% of a mine gave 25% of his share to his son, who sold what he received for $12,000. What was the value of the mine ? 60. A farmer raised 20% more corn this year than last, and 25% more last year than the year before, when he raised 160 bu. How many bushels did he raise this year ? 61. In a barrel of alcohol containing 36 gals, the water is 20% of the spirit. How many gallons of each? 62. If milk yields 18% of cream, and cream yields 24% of butter, and a quart of milk weighs 1 lb., how many quarts of milk will jield 470 lbs. of butter ? PERCENTAGE. 127 53. 145 is 26% more than what number? 64. 91 is 40% more than what number ? 65. 39 is 40% less than what number ? 56. 297 is 12^% more than what number ? 57. 110 is 66|% less than what number ? 58. 1240 is 55% more than what number? 59. 260 is 33^% less than what number? 60. 901 is 6J% more than what number ? 61. What number increased by 27% becomes 5.08? 62. What number diminished by 16|% becomes 60 ? 63. What fraction increased by 37-^% becomes 1 ? 64. What fraction diminished by 60% becomes -^? 65. If I am offered 8% for the use of money for one year, what sum must I lend in order to receive $972 at the end of the year ? 66. Iron expands 0.64% of its length when heated from the freezing-point of water to the boiling-point. If an iron bar surrounded by boiling water is 10 ft. long, find its length (to the nearest inch) when placed on ice. 67. A man sold a house for $6800, which was 15% less than what the house cost him. What did the house cost him? 68. Add together 25% of $763.22, 16% of $847.16, and 6i% of $1234.17. 69. The cattle of a ranch have been increased 600% since the ranch was established. They now number 1400. What was the original number ? 70. If the population of a city has increased 35% during the last ten years, and is now 113,400, what was the i^oi^ur lation ten years ago ? 128 ARITHMETICAL EXERCISES. What must be tlie selling price of a thing : 71. Costing $4 in order to gain 26% ? 72. Costing $12 in order to lose 12J%? 73. Costing $3.50 in order to lose 18% ? 74. Costing $226 in order to gain 200% ? What per cent is gained or lost if a thing : 75. Cost $6 and is sold for $5 ? 76. Cost $0.62i and is sold for $0.50? 77. Cost $ 1360 and is sold for $ 1428 ? 78. Cost $1700 and is sold so as to gain $204? 79. A man bought a horse for $250. What price must he ask for him in order to gain 40% ? 80. If I buy flour at $5.25 per barrel, and sell it at $6.25, what is the gain per cent? 81. If 80 cds. of wood are bought at $4.50 per cord, and sold so as to gain 33^%, what amount of money is gained ? 82. What per cent is made by buying coal by the long ton and selling it by the short ton, at the same price? 83. How many pounds of sugar costing 5 cents per pound must be sold for a dollar, in order to gain 25% ? 84. If I buy cloth at $2.75 per yard, and sell it at $3.10, what is the gain per cent ? 85. If 125 overcoats cost $2600, for what must they be sold apiece in order to gain 7i % ? 86. A grocer bought 120 bbls. of apples, each containing 2 bu. 1 pk., at $1.50 per barrel, and paid $14.40 to have them brought to his store. If the loss from shrinkage and decay amounts to 20%, what is the lowest price per peck at which he can sell them in order to be sure of clearing 10^ on his outlay? PERCENTAGE. 129 What is the cost of a thing if: 87. 20% is gained by selling it for $60? 88. 20% is lost by selling it for $60? 89. 5^^% is gained, and the sum gained is $38.12J? • 90. 2i% is lost, and the sum lost is $20.25? 91. 160% is gained, and the sum gained is $36,000? 92. 150% is gained, and the selling price is $36,000? 93. By selling milk at 6 cents per quart, a milkman gains 50%. What did the milk cost him? 94. A grocer lost 15% by selling a 40-lb. tub of butter for $ 17. What did the butter cost him per pound ? 95. A man sold a house for $2360, which was 10% less than cost. What did the house cost him ? 96. A merchant gained 17% by selling a quantity of velvet for $3789.40. What did he pay for the velvet? 97. If I buy cloth at $2 per yard, and silk at $2.80 per yard, and sell the cloth at $2.50 per yard, at what price must I sell the silk to make the profit on one the same as on the other ? 98. A gunsmith gained 20% by selling revolvers at $8.75 each. What was the sum gained on 30 revolvers? 99. I sold a horse for $425, thereby losing 15%. For what ought I to have sold him to gain 20% ? 100. If 15% is gained by selling 80 sheep for $1104, at what price apiece should they have been sold in order to make 25% ? 101. A merchant lost 10% by selling flour at $4.50 per barrel. If he had sold it at $5.75 per barrel, what would have been the gain per cent ? 102. What must I ask for a watch costing $30, in order to take off 10% for cash, and yet make a ^xcAX, oi ^^o"^. 130 ARITHMETICAL EXERCISES. 103. A commission merchant sold 625 bu. of potatoes at 80 cents per bushel, and received 4^% commission. What was his commission ? ^104. What is the rate of commission when $36 are paid for selling $ 1600 worth of goods ? 105. An agent sells 718 bbls. of flour, at $7.13 per barrel. What is his commission, at 4J% ? 106. A real-estate broker sold a house on 3% commis- sion, and sent to the owner as net proceeds $ 2425. For what sum was the house sold ? 107. A book-agent sells books on 20% commission until his commission amounts to $500. What sum ought he to remit to the owner of the books ? 108. A Boston merchant sent $10,000 to Chicago to be expended for wheat, the agent to receive 2% commission. What sum was expended for the wheat? 109. An agent in New Orleans received $5125 with which to buy molasses, after deducting 2^% ^^ ^^® sum expended. What is the agent's commission ? 110. A lawyer collected 60% of a debt of $1600, and charged 5% on the sum collected. What did the creditor receive ? 111. An agent sold 220 bu. of oats at 75 cents a bushel, and his commission amounted to $5.28. What rate of commission was charged? 112. A broker sold for a farmer 14,400 lbs. of beef, at 10-J- cents per pound, and 850 bu. of corn at 72 cents per bushel. He charged 3% commission for selling, and paid $ 40.28 for freight. How much land, at 10 cents per square foot, can the broker buy with the net proceeds, after deducting a commission of 1% for buying? PERCENTAGE. 131 113. What will it cost to insure a house valued at $4500, the rate of premium being i%? 114. Find the premium to be paid for insuring a store worth $6000 for f of its value, the rate being f %. 115. What is the rate of insurance, if $225 is paid for an insurance policy for $18,000? 116. A man paid $ 345.30 for insuring a cargo of sugar at li%. For what amount was the sugar insured? 117. A merchant shipped a cargo of flour worth $72,750 to Liverpool. For what must he insure it at 3% to cover the value of the flour and the premium ? 118. A stock of goods worth $24,000 was insured for i of its value at 1J%. If the whole stock is burned, what will be the loss to the owner, including the premium paid for insurance ? 119. What sum must be insured at 2J% on property worth $15,000, so that in case the property is destroyed the owner will sufier no loss ? 120. A vessel worth $33,000 is insured at 5f % for such a sum that, in case it becomes a total wreck, the owners recover both the worth of the vessel and the insurance pre- mium. For what sum is it insured ? 121. If a mill worth $7800, and insured at the rate of li% for f of its value, is half destroyed by fire, what is the exact loss to the owner ? 122. What annual premium at If % must be paid on a life insurance of $5000? 123. At the rate of $16 upon $1000, what annual pre- mium must be paid on a life insurance of $ 4800 ? 124. If the annual premium paid for a life insurance at 1J% is $135, what is the sum insured? 132 ARITHMETICAL EXERCISES. The censas of 1880 gives the financial condition, for that year, of every city in the United States having a population exceeding 7500. The following table, compiled from the census reports, exhibits the condition as regards taxation of fifteen cities. Of these, the first twelve are taken in pairs from certain States, and the two cities of each pair have respectively the highest and the lowest tax rates of all the cities of the State in which they are located. Narne, Popvlation. Vahmtion. Tax Levied. Portsmouth, N.H. Dover, N.H. . . 9,690 11,687 42,551 11,666 8,184 13,063 50,137 12,093 7,847 8,787 22,408 22,254 362,839 332,313 503,185 $6,553,079 7,080,178 46,255,340 5,136,529 548,491 6,802,077 18,687,955 5,173,520 699,450 1,857,717 4,361,090 13,000,000 613,322,691 244,043,181 117,970,035 ? 135,565 107,318 Hartford, Ct. . . . Danbury, Ct. . . , Shamokin, Pa. . Norristown, Pa. . . Toledo, Ohio . . . Steubenville, Ohio . La Salle, 111. . . , Elgin, 111 Des Moines, Iowa . Dubuque, Iowa . Boston, Mass. . , Baltimore, Md. . . Chicago, 111. . . . 4 1,288,661 63,495 29,871 80,375 685,129 85,880 49,322 39,859 225,894 260,951 7,666,534 2,977,580 5,112,375 From the figures above given find (i.) the valuation per capita (to the nearest dollar) ; (ii.) the tax per capita (to the nearest cent) ; (iii.) the tax rate per $ 100 (to the near- est cent) for : 130. Norristown. 125. Portsmouth. 126. Dover. 127. Hartford. 128. Danbury. 129. Shamokin. 131. Toledo. 132. Steubenville. 133. La Salle. 134. Elgin. 135. Des Moines. 136. Dubuque. 137. Boston. 138. Baltimore. 139. Chicago. PEBCENTAQE. 133 Note. In the foUowing examples, the tariff rates named are those imposed by the Tariff Act of 1883. 140. What is the duty on 800 doz. bottles of Hoff s Malt Extract, the invoice value being $ 1.80 per dozen, and the tariff rate being 50% ad valorem? 141. A merchant tailor imported woollen cloths as fol- lows: 340 lbs. invoiced at $1.25 per pound; 716 lbs. invoiced at $1.10 per pound; and 836 lbs. invoiced at $1.05 per pound. How much duty did he have to pay, the rate being 35 cents per pound, and 40% ad valorem ? 142. What duty must be paid on an oil painting valued at $3200, the rate being 30% ? 143. Find the duty on 3600 pint-bottles of cologne water, invoiced at $3 per gallon, the tariff being $2 per gallon, and 50% ad valorem. 144. A tobacconist imported 20,000 cigars, net weight 240 lbs., paying for them $3.75 per hundred, and for freight, etc., $12.50. The tariff on cigars is $2.50 per lb. and 25% ad valorem. What profit would be made by retailing the cigars at the rate of 8 for $ 1 ? 146. Find the duty on 4000 yds. of Brussels carpeting at $1.10 per yard, and 2400 yds. of Wilton carpeting at $1.85 per yard, the tariff being 30% ad valorem, and in addition, 30 cents per yard on the former, and 45 cents per yard on the latter. 146. What amount of duty must be paid on 800 doz. quart-bottles of sherry wine, the tariff being $1.60 per dozen, and in addition 3 cents on every bottle ? 147 A commission house received an invoice of 1000 silk umbrellas valued at $2.25 each, 600 clocks valued at $16 each, and 800 watches valued at $40 each. Find the duty, the rates being 50% on the umbrellas, 30% on the clocks, and 25% on the watches. 134 ARITHMETICAL EXERCISES. Find the simple interest of: 148. $1 for 11 yrs. 7 mos., at 6%. 149. $1 for 12 yrs. 5 mos., at 6%. 150. $279.40 for 3 yrs. 2 mos., at 6%. 151. $189.70 for 6 yrs. 7 mos., at 6%. 152. $1463 for 3 yrs. 11 mos., at 6%. 153. $1 for66dys., at 6%. 154. $1 for 8 mos. 12 dys., at 6%. 155. $1 for 2 yrs. 2 mos. 19 dys., at 6%. 166. $917.30 for 7 mos. 17 dys., at 6%. 167. $842.50 for 3 mos. 13 dys., at 6%. 158. $573.83 for 2 yrs. 11 mos. 10 dys., at 159. $709.63 for 4 yrs. 7 mos. 16 dys., at 160. $68.70 for 3 yrs. 4 mos. 27 dys., at 161. $742.63 for 3 yrs. 28 dys., at 6%. 162. $6250 for 1 yr., at 5%. 163. $21,850 for 3 yrs., at 4i%. 164. $21,750 for 1 yr. 7 mos., at 4}%. 166. $945 for 2 yrs. 5 mos. 8 dys., at 5%. 166. $1800 for 3 yrs. 5 mos. 8 dys., at 5%. 167. $715.30 for 3 yrs. 7 mos. 10 dys., at 8%. 168. $1234.56 for 4 yrs. 4 mos. 25 dys., at 7%, 169. $576 for 3 yrs. 5 mos. 7 dys., at 10%. Find the amount of: 170. $1200for 93dys., at8%. 171. $200 for 7 yrs. 4 mos. 11 dys., at 6%. 172. $743.63 for 9 yrs. 3 mos. 9 dys., at 6%. 173. $7766.55 for 100 dys., at 5%. 174. $500 for 8 yrs. 8 mos. 8 dys., at 16%. PERCENTAGE. 135 Find the simple interest of : 175. $300 from April 1 to Sept. 18, at 6%. 176. $600 from May 5 to Dec. 17, at 7%. 177. $ 758.50 from Jan. 5 to July 1, at 9%. 178. $2500 from Nov. 15, 1888, to Mar. 1, 1889, at 5%. 179. $638.40 from June 7 to Oct. 31, at 6|%. 180. $750 from Aug. 8, 1887, to Mar. 20, 1889, at 7%. 181. $3650 from April 5, 1888, to Aug. 15, 1890, at 7|%. 182. $780 from May 9 to Dec. 11, at 8%. 183. $1830 from Aug. 16, 1887, to June 19, 1888, at 7%. Find the amount of : 184. $175 from Sept. 26, 1888, to Mar. 10, 1889, at 8%. 185. $613 from Oct. 20, 1888, to May 22, 1889, at 5%. 186. $684.84 from Feb. 1, 1888, to Mar. 10, 1889, at 7%. 187. $3605 from Aug. 8, 1888, to Mar. 11, 1889, at 6^%. 188. $2017 from Jan. 18 to Mar. 20, at 6i%. 189. $620 from Mar. 1 to Aug. 26, at 7%. 190. $6200 from Sept. 3, 1886, to Jan. 9, 1887, at 6%. 191. $254.72 from Dec. 20, 1885, to July 11, 1887, at 9%. Find the rate per cent, if: i 192. The interest on $24,840 for 1 yr. is $869.40. 193. The interest on $14,500 for 1 mo. is $84.56. 194. The interest on $680 for 7 mos. is $35.70. 195. The interest on $24 for 2 yrs. 5 mos. is $3.19. 196. The amount of $700 for 5 yrs. is $1200. 197. The amount of $750 for 4 yrs. is $900. 198. A sum of money doubles itself in 16 yrs. 8 mos. 199. A sum of money quadruples itself in 3 yrs. 136 ARITHMETICAL EXERCISES. Find the time in which : 200. The interest on $2130 will be $436.65, at 6%. 201. The interest on $676 will be $108, at 8%. 202. $2000 will amount to $2600, at 4%. 203. A sum of money will double itself, at 4J%. 204. The interest at 4^% will equal f of the principaL 206. A sum of money will quadruple itself, at 23%. 206. $270 will give $87 interest, at 7%. 207. $273 will give $100 interest, at 9%. 208. $640 will amount to $1000, at 5%. Find the principal that will : 209. Produce $572 interest annually, at 4^^%. 210. Produce $830 interest annually, at 4§%. 211. Produce $325 interest annually, at 5|^%. 212. Produce $32.10 interest in 5 mos., at 4%. 213. Produce $150.10 interest in 3 mos. 2 dys., at 8J%. 214. Produce $873.30 interest in 3 yrs. 5 mos., at 6%. 215. Produce $161.25 interest in 3 yrs. 9 mos., at 216. Produce $100 per month, at 7%. 217. Produce $500 quarterly, at 5%. 218. Amount to' $9050 in 1 yr., at 5%. 219. Amount to $840 in 3 yrs., at 4%. 220. Amount to $1500 in 3 yrs. 4 mos., at 6%. 221. Amount to $100 in 6 mos., at 20%. 222. Amount to $3500 in 5 yrs., at 8%. 223. Amount to $4810 in 4 yrs. 6 mos., at ^%. 224. Amount to $2551.50 in 13 mos., at 5%. 225. Amount to $2000 in 20 yrs., at 8%. 226. Amount to $1111.11 in 11 yrs., at 11%. PERCENTAGE. 137 227. Which will yield the greater income, to loan $13,500 at 6^% per annum, or to buy a store with the money and rent it for $850 per annum ? 228. Is it better to loan $17,450 at 6%, or to buy a store with the money and rent it for $ 1200 ? 229. A man bought, Mar. 12, goods to the value of $325, and, having no ready money, gave his note payable Nov. 12 of the same year, with interest at 6%. How much money did he have to pay ? 230. How much money is required to yield $2900 in- terest annually, if ■§■ of the money is invested at 5% and the remainder at 4|^% ? 231. April 1 a man put $500 in a savings-bank, and July 15 following he put in $360 more. Jan. 1 he received as interest $ 18.90. What was the rate per cent ? 232. A note for $620, dated Oct. 18, 1886, payable on demand, with interest at 6%, bears the following indorse- ments : Nov. 25, 1886, $47.50; Dec. 28, 1886, $108.93; Feb. 11, 1887, $216.18; June 6, 1887, $60.10; Sept. 2, 1887, $183.25. What is due Nov. 10, 1887 ? 233. A note for $1217.30, dated June 2, 1887, payable on demand, with interest at 6%, bears the following in- dorsements: July 17, 1887, $207.80; Oct. 6, 1887, $209.60 ; Dec. 11, 1887, $320.90; Mar. 29, 1888, $421.83. How much is due Oct. 7, 1888? 234. A note for $1200, dated June 17, 1887, drawing interest at 6%, bears the following indorsements : Feb. 15, 1888, $125; Nov. 30, 1888, $75; Sept. 19, 1889, $20; Jan. 1, 1890, $45 ; July 9, 1890, $500. What was due on this JiPte Jan. 1, 189J ? 138 AEITHMETICAL EXERCISES. Find the compound interest of: 235. $80 compounded annually for 3 yrs, at 6%. 236. $150 compounded annually for 6 yrs., at 7%. 237. $200 compounded semi-annually for 2 yrs., at 8%. 238. $1800 for 5 yrs., at 6% per annum. 239. $700 for 3J yrs., at 14% per annum, compounded semi-annually. Find the amount at compound interest of: 240. $100 for 8^ yrs., at 5% per annum. 241. $4500 for 10 yrs., at 5% per annum. 242. $3500 for 12 yrs., at 4J-% per annum. 243. $875 for 11 yrs., at 6% per annum. 244. $1 for 45 yrs., at 6% per annum. 245. $78.20 for 7 yrs., at 12% per annum, interest pay- able every 3 mos. 246. $860 for 3 yrs., at 8% per annum, interest payable semi-annually. 247. What sum of money will amount to $6000 in 10 yrs., at 4% per annum, compound interest? 248. What sum of money will amount to $7439.87 in 7 yrs., at 4% per annum, compound interest? 249. At what rate per cent, compound interest, com- pounded annually, will $4000 increase in 10 yrs. to $6000? 250. At what rate per cent, compound interest, will a sum of money triple itself in 25 yrs. ? 251. For what period must $5000 be placed at 4%, compound interest, in order that the capital and interest together may amount to $ 9000 ? 252. In what period of time will a sum of money plsjcedl at 5% compound interest double itself? PERCENTAGE. 139 Find the day of maturity, and the proceeds of the fol- lowing notes : 253. A note dated Aug. 31, 1886, payable in 4 mos., face value $2045.82, discounted Sept. 2, at 7%. 254. A note dated Sept. 3, 1886, payable in 5 mos., face value $15,000, discounted Sept. 3, at 6|%. 255. A note dated Sept. 3, 1887, payable in 3 mos., face value $2000, discounted Sept. 3, at 7%. 256. A note dated Sept. 3, payable in 45 dys., face value $600, discounted Sept. 3, at 6%. 257. A note dated July 3, payable in 2 mos., face value $4821.23, discounted Aug. 3, at 5%. 258. A note dated Mar. 5, payable in 6 mos., face value $1392.30, discounted Aug. 13, at 5^%. 259. A uote dated Mar. 8, payable in 6 mos., face value $10,500, discounted Mar. 8, at 4^%. 260. A note dated Mar. 14, payable in 4 mos., face value $5000, discounted Mar. 14, at 7%. 261. A note dated Oct. 8, payable in 60 dys., face value $4263, discounted Oct. 8, at 6|%. 262. A note dated Jan. 11, payable in 3 mos., face value $520.25, discounted Jan. 21, at 7%. 263. A note dated May 10, payable in 4 mos., face value $6425.80, discounted May 17, at 10%. 264. A note dated Feb. 4, 1886, payable in 40 dys., face value $125, discounted Feb. 5, at 7^%. 265. A note dated July 3, payable in 2 mos., face value $340.82, discounted July 6, at 6%. 266. A note dated Oct. 1, 1886, payable in 4 mos., face value $25,000, discounted Oct. 1, at 5|%. 140 ARITHMETICAL EXERCISES. Find the date of maturity and proceeds of the following : 267. A note dated Sept. 25, payable in 47 dys., face value $6000, discounted the same day at 6^%. 268. A note dated Mar. 6, payable in 3 mos., face value $3000, discounted April 10, at 4|%. 269. A note dated Nov. 10, payable in 45 dys., face value $7010.10, discounted Nov. 12, at 6%. 270. A note dated June 20, payable in 3 mos., face value $576.74, discounted June 25, at 6|%. 271. Find the face value of a note for 4 mos., in order that the proceeds may be $5000 when discounted at 6%. 272. Find the face value of a note for 60 dys., in order that the proceeds may be $1000 when discounted at 4^%. 273. Find the face value of a note for 30 dys., in order that the proceeds may be $3000 when discounted at 5%. 274. Find the face value of a note for 3 mos., in order that the proceeds may be $600 when discounted at 5^%. 275. Find the face value of a note for 45 dys., in order that the proceeds may be $7864.17 when discounted at 4%. 276. Find the face value of a note for 4 mos., in order that the proceeds may be $5893.41 when discounted at 6%. 277. On Mar. 4 a man obtained $10,000 from a bank by giving his note for the same amount payable on demand. He redeemed the note Mar. 14. What sum did the bank receive for the note, the rate of interest being 6% ? 278. A bank holds a note dated Nov. 4, payable on de- mand, face value $20,000. What sum is required to redeem this note if paid Nov. 15, the rate of interest being 5% ? 279. When the rate of discount is 6%, find the proceeds of a note for $930, payable Aug. 1, and discounted at a bank April 1, PERCENTAGE. 141 Find the present worth of : 280. $962 due in lyr., at 4%. 281. $500 due in 1 yr., at 5%. 282. $650 due in 1 yr., at 5%. 283. $2180 due in 1 yr., at 5%. 284. $1700 due in 2 yrs., at 6%. 285. $650 due in 5 mos., at 5%. 286. $1726 due in 14 mos., at 6%. 287. $925 due in 3 mos., at 5%. 288. $1710 due in 90 dys., at 6%. 289. $2202 due in 5 yrs. 9 mos., at 6%. 290. $1003.50 due in 8 mos., at 6%. 291. $716 due in 7 mos., at 7%. 292. $1342.50 due in 125 dys., at 6|%. 293. $4360 due in 1 yr. 5 mos., at 6%. 294. $1647 due in 11 mos., at 6%. 295. $2000 due in 3 yrs. 7 mos., at 6%. 296. $970.63 due in 11 mos., at 8%. 297. What sum of money paid Mar. 16 will cancel a note for $1125 due Aug. 20, if money is worth 7% ? 298. A legacy of $2400 was left to me in May, to be paid on the next Christmas day. What is its value in cash on May 3, if money is worth 5% ? 299. What sum discounted for 6 mos., at 4-^-% per annum, will yield a cash value of $900? 300. Find the difference between the bank discount and the true discount of a note for $1600, payable in 10 mos., at 6%. 301. Find the true discount on $3224, at 7%, one-half payable in 6 mos.f and th^ remainder ixv \^ xag^. 142 ARITHMETICAL EXERCISES. 302. Find the net amount of a bill of $1200, 10% off being allowed for cash. 303. Find the net amount of a bill of $1550, 5% off being allowed for cash. 304. Find the net amount of a bill of $88, discounts being 20 and 10. Hint. This means that a discount of 20% is allowed, and then a discount of 10% on the remainder. 305. Find the net amount of a bill of $209.25, discounts being 50 and 10. 306. Find the net amount of a bill of $3, discounts being 25 and 10. 307. Find the net amount of a bill of $150, discounts being 30 and 10. 308. Find the net amount of a bill of $2.70, discounts being 50 and 10. 309. Find the net cash amount of a bill of $800, dis- counts being 75 and 5, and an additional discount of 2^% for cash. 310. Find the net cash amount of a bill of $272, dis- counts being 50 and 10, and an additional discount of 5% for cash. 311. Find the net cash amount of a bill of $1440, dis- counts being 55 and 10, and an additional discount of 5% for cash. 312. Find the net cash amount of a bill of $1125, dis- counts being 50, 10, 10, 10 ; or, as it is commonly expressed, 50 and 3 tens. PERCENTAGE. 143 313. Find the cost of 40 shares of railroad stock, at 92. 314. Find the cost of 120 shares of bank stock, at 137f . 315. A man owns 40 United States 4% bonds of $1000 each. What are they worth in cash when the market quo- tation for them is 87 J? 316. How many shares (par value $100) of Union Pacific can be bought with $ 1625, the market value being $65? 317. "When Atchison sells at 92, and pays 6% per annum, what will be the cost of 60 shares, and what income will be derived from them ? 318. Bought 27 shares of a 4% stock, at 80, brokerage $0.25 per share. What did the stock cost me, and what income did it yield ? 319. The trustees of an academy invested $70,000 in Old Colony Railroad stock when it was selling 40% above par. If the stock pays 8%, how much of the annual divi- dend will be left after paying the expenses of the academy, amounting to $3300? 320. Will $3336 yield a larger income if invested in an 8% stock at 139, or if loaned at 6% simple interest, and what is the difference of income in the two cases ? 321. A man sold 150 sheep, at $22 each, and invested the proceeds in a 6% stock, at 110. What income did he derive from the investment ? 322. A man bought 265 shares of a 3% stock when it was 50^, and sold it at 65^. Find his profit per cent and his total profit. 323. I buy 500 shares of Western Union, at 78^. What must be the market value of the stock, that I may gain 10% on my money by selling, brokerage being -1% on each transaction ? 144 ARITHMETICAL EXERCISES. Which will yield the larger income (the sums invested being supposed the same in both cases) : 324. A 3% stock at 71, or a 4|% stock at 102? 325. A 3% stock at 73, or a 4^% stock at 104? 326. A 6% stock at 120, or an 8% stock at 160? 327. A 6% stock at 110, or an 8% stock at 144? 328. A 6% stock at 93, or a 10% stock at 172? 329. A 4% stock at 75, or a 9% stock at 167? 330. When a 4% stock is quoted at 90, what should be the price of a 5% stock, that it may yield the same income? 331. What must be the price of 4|% bonds of $1000 each, to yield an income equal to that of 5% bonds which sell at par? 332. A railroad costing, all told, ten millions yielded a net income of $750,000. What annual dividend will a man receive who owns 250 shares of the stock ? 333. What sum of money must a man invest in a 9% stock, selling at 207, brokerage 25 cents per share, in order that the annual income derived from it may be $360, and what rate per cent does he receive on his investment? 334. If an 8% stock is worth 152, what rate of interest will a purchaser receive on his money ? 335. What sum must be invested in 3% bonds at 85, that the income may be $1200, brokerage at \% included? 336. What amount of bank stock does a man hold if his quarterly dividend at 7% per annum is $294? 337. What must be the price of an 8% stock, that a buyer may receive 6% on his investment? 338. What sum invested in Government 6s, at 126J- will yield an annual income of $1800? . - 339. What income do Government 4s yield at 124? PERCENTAGE. 146 340. Find the cost of a sight draft on Chicago, for $3500, at 1% premium. 341. Find the cost of a draft on Atlanta, payable 60 dys. after sight, for $4000, with exchange at l-J-% premium, and interest at 6%. 342. Find the cost of a draft on San Francisco, for $1500, payable in 90 dys., with exchange at -J-^ discount, and interest at 6%. 343. The par of exchange between the United States and Great Britain is $4.8665 for the pound sterling. What will a sight draft on London for £800 cost, if exchange is l\% premium ? 344. Find the cost of a draft in Boston on New Orleans, at 30 dys., for $2500, exchange being at ^% premium, and bank discount being at 6%. 345. Find the cost of sending a bill of 10,000 marks to Hamburg, by first sending a bill of the required amount to Paris, exchange in New York on Paris being 5.15 francs per dollar, and in Paris on Hamburg 1.24 francs per mark. 346. What must be paid in New York for a draft on Minneapolis, for $2400, payable 90 dys. after sight, at a premium of If %, reckoning bank discount at 7% ? 347. Find the face of a draft which cost $4053.09, ex- change being at a premium of l|-%. 348. A banker in New York remits $12,000 to London, as follows : first, to Paris, at 5.32 francs per dollar ; from Paris to Hamburg, at 1.8 francs per mark ; from Hamburg to London, at 14 marks per £1 sterling. How many pounds sterling does he gain by this method over direct exchange at $4.87 for £1 sterling? 349. Find the cost of a sterling bill on London for £897 28,, when sterling exchange is at $4.8&|. 146 arithmetical exercises. Miscellaneous. (Including also the subjects treated in the preceding chapters.) 350. What per cent is 17 of 85? 25 of 1000? 3.5 of 50? 351. If sold at an advance of 33-J^% , what will be received for a dozen and a half pencils which cost a cent and a half each? 352. In 1882 the total immigration into the United States amounted to the unusually large aggregate of 788,992. Of these, 76,342 were Irish. What per cent (to two decimal places) is this of the whole number for that year? 353. A cheese weighing 42 lbs. was sold for $9.08. What was the price per pound? If the profit to the seller was 2 cents per pound, what is the per cent profit ? 354. The quotient of an example in division is 379, the divisor 257, and the remainder 73. What is the dividend ? 355. Five dozen eggs are packed equally in three baskets, and the contents of each basket are equally distributed among five poor persons. How many eggs does each per- son receive ? 356. Find the cost of 19-J- yds. of cloth, if when sold for 36 cents a yard there is a loss of 22%. 357. Find 10% of that number which divided by 437 will give 129 for a quotient and leave 78 for a remainder. 358. In 1880, out of 227,542 emigrants from the United Kingdom, 111,845 were English, and 22,056 were Scotch. How many were Irish ? What per cent of the whole num- ber were the English, Scotch, and Irish, respectively ? I PERCENTAGE. 147 359. The circumferences of the large and small wheels of a bicycle are 176 and 48 inches, respectively. How many more turns will the latter make than the former in going 16 mi. ? 360. If by selling a house for $2650 a man gain 6% on the cost, what would be the gain or loss per cent if the house had been sold for only $2300 ? 361. The population of Texas was 818,579 in 1870, and 1,591,749 in 1880. Find (i.) the numerical increase, (ii.) the per cent of increase. 362. The population of the State of New York in 1870 was 4,382,759, and in 1880 it was 5,082,871. Find the increase per cent. 363. Find the amount of $50, at compound interest, for 18 mos. at 16^^, interest compounded once in six months. 364. ' In what time will $ 700 be increased 0.15 of itself, at 2-^-% per annum? 365. Find the interest on $125 for 2J- yrs. at 4%. 366. Find the interest on $3000 for 6 mos. 24 dys. at 7J% per annum. 367. Compute from the following data, supplied by the census of 1880, the per cent of illiterate population in the States mentioned, for persons ten years of age and upward : Number Whole Number. unable to read Massachusetts, 1,432,183 75,635 New York, 3,981,428 166,625 Ohio, 2,399,367 86,754 Iowa, 1,181,641 28,117 South Carolina 667,456 321,780 Louisiana, 649,070 297,312 148 ARITHMETICAL EXERCISES. 368. The population of Kansas between 1870 and 1880 increased from 364,399 to 996,096. What was the amount of increase, and what was the per cent of increase ? 369. During 1881 there were in the United Kingdom 1,135,672 births, and 654,199 deaths. During the same year 243,002 emigrants left the Kingdom, and 77,105 im- migrants entered it. What was the change in the total population for the year, and what per cent of the emigrants were the immigrants ? 370. A man owns a paper-mill valued at $12,000. For one year his expenses are, for repairs $50, for insurance $45, for taxes 1J% on f of the valuation. What rent must he receive to gain 6fo on the value of the mill and pay the other outlays ? 371. Find the time in which $1000 will gain $200 at 8% per annum. , 372. At -J- of 1% what sum can be insured for $80? 373. Three Germans own a silver mine in Nevada. Hans Heuser owns 41|% of it; Karl Krantz, 33^% ; and Fritz Stenck, 25%. If the mine is sold for $4300, what sum does each receive ? 374. A boy sells two books for $1 each, and thus gains 25% on one and loses 25% on the other. Find the cost of the books, and the total gain or loss. 375. If the interest on a note, at 7^% for 1 yr., be $174.36, what would it be at 8|% ? 376. Find the gain or loss per cent in buying lemons at 66 cents per hundred and selling them at eight for 2J cents. 377. In what time will money double itself at 1J% a month simple interest ? PEECENTAGE. 149 378. What is the rate when the insurance of $18,000 costs $36, exclusive of the policy ? 379. A boy bought 20 peaches at 2 cents each, and sold them at the rate of 2 for 7 cents. What was his total gain and his gain per cent ? 380. At what rate of simple interest will money double itself in 3 yrs. ? 7 yrs. ? 9 yrs. ? 11 yrs. ? 16 yrs. ? 20 yrs. ? 381. What will be gained by selling, at 24^% premium, six $100 United States bonds, bought at par ? 382. At 3%, what principal will yield $1^.64 in 1 yr. ? 383. What per cent of 625 is 28J? 300 is 25% of what number ? 384. At what rate will $ 750 amount to $ 783.75 in 1 yr. ? 385. Sugar-cane yields 0.9 of its weight of juice, and 100 lbs. of juice contain 17 lbs. of sugar. Half the sugar is usually lost in the process of manufacture. What weight of sugar-cane is required to make 300 lbs. of sugar ? 386. On the following bill, find the amount due in 6 mos. after its date, interest reckoned at 7^% : 50 pieces of silk, 30^ yds. each, at $2.50 ; 22 coats, at $40 ; 15 pieces of flannel, 110 yds. each, at $0.32 ; 20 pieces of diagonal, 95 yds. each, at $ 0.38 ; 60 pieces of linen, 12 yds. each, at $0.50. 387. A man invests his net profit for 1 yr. in b^% min- ing stock, at 105, and another man with his surplus income buys 4^% bank stock, at 81 J. Which is the better invest- ment ? Write a clear explanation of the technical terms used in the example. 388. In 4 mos., at 2% a month, what principal will amount to $5265? 150 ARITHMETICAL EXERCISES. 389. In 1 wk. a newsboy sold 360 papers, which were 90% of his whole stock. How many papers had he left ? 390. "When 3% bonds are 10% below par, how much money must be invested in them to secure an income of $2000 ? • 391. The number of persons engaged in the four chief classes of occupations in the United States in 1870 and in 1880 were as follows : 1870. 1880. Agriculture, 6,922,471 7,670,493 Professional ^d personal service, 2,684,793 4,074,288 Trade and transportation, 1,191,238 1,810,256 Manufactures and mining, 2,707,421 3,837,112 Find (i.) the increase in number, (ii.) the per cent of increase, for each class of occupations for the decade. 392. At 10% per annum, what interest will a merchant receive on $9000 for 10 dys. ? 393. The cost price of a book is 57 cents, the expense of sale is 6%, and the profit is 24%. What is the retail price ? 394. Find from the following data of 1883 the dividend each road could have declared had it been free from debt : Name, Capital Stock. Net Earnings. Eastern, $4,997,600 $1,273,676 Boston & Maine, 6,921,274 845,183 Boston & Lowell, 3,792,000 615,171 Fitchburg, 4,950,000 637,088 Boston & Albany, 20,000,000 1,945,053 Boston & Providence, 4,000,000 335, 14C Old Colony, 10,248,620 1,228,441 New York & New England, 20,000,000 405,12£ 395. Find the bank discount on a note of $1600 foi 8 mos. PERCENTAGE. 151 396. A merchant received $1998.80 from his lawyer, who retained 5% on the debt for collecting. What amount was collected ? 397. After losing a battle, a general found that he had but 66|% of the men under his command fit for action ; 11^% had been wounded, and the remainder, 2000 men, had been killed or were missing. How many had he before the battle ? 398. Compute the value of the silk goods consumed in the United States for the fiscal year ending June 30, 1883, from the following data : Invoiced value of imported goods : Dress and piece goods, $16,964,733 Hosiery, 820,088 Other manufactures, 18,979,455 Value of our own manufactures, 39,464,541 To the invoiced value of the imported goods the tariff of 50% must be added, and also 25% for estimated under- valuation. 399. Three men have agreed to drain a swamp. Tte first can do 8^%, the second 6|%, the third 5%, of the work in 1 day. In what time can it be accomplished when the three work together ? 400. George Heath bought forty $100 railroad bonds at 90, and sold them immediately for 95. He invested the money in oats at 50 cents per bushel, paying 3% insurance, $300 freight and storage, and losing 2% in handling ; and he then sold at an advance of 15 cents per bushel. How much did he gain or lose ? What per cent ? 401. What is the rate of interest when $800 gains $32 in 8 mos, ? 152 ARITHMETICAL EXERCISES. 402. Find the present worth, and the discount of $1245.50, due 3-J- yrs. hence, when money is worth 5%. 403. What amount must be assessed for building a bridge which is to cost $10,000, when 6% of the sum levied will not be collected, and 5% of the sum collected must be allowed for collection ? 404. A town paid $9 for insuring the school furniture, books, etc., of a public school, the insurance being effected on "I the value of the property, at the rate of f %. What was the estimated cost of the articles insured ? 405. A builder having a six-month note for $2400 dated May 2, 1885, has it discounted at a bank on the 1st of June at 5%. At $4 per thousand, how many thousands of shin- gles can he buy with the proceeds ? 406. Find the discount and the present worth of $ 750 due in 6 mos., when money is worth 5%. 407. A merchant fails, owing $31,620, and has property to the amount of $6324 above the necessary expenses for sej;tling his affairs. How much money will the family dressmaker receive, whose bill is $50? 408. A gentleman took for a debt of $4624 a farm con- taining 150 A. He repaired the buildings, and . let the farm at the rate of $1.50 per acre, thus realizing 4^% on his money. What was the cost of the repairs ? 409. An iron-merchant purchased 550 long tons of iron at the importer's price, $30 per ton. He paid for cartage and freight $1200, and sold the iron at $36 per ton of 2000 lbs. What was his gain per cent ? 410. The net income of an estate, after deducting 4^% for collection, and 4% on the remainder for other expenses, is $437. What is the gross rental? I PERCENTAGE. 153 411. A wheat-grower in Minnesota had three six-month notes discounted at 5%, 6%, and 7%, respectively. Each note yielded $ 500 proceeds. What was the face of each ? 412. The net income for a certain half-year of a railway company, whose capital is $29,480,000, shows an increase of $92,125 over that of the corresponding half of the pre- vious year, when a dividend at the rate oi 5i^o p^r annum was declared. What will be the rate of dividend for this half-year ? 413. By selling a cotton crop for $777, a planter lost 7^%. For what should he have sold it to gain 12J^% ? 414. Three notes were discounted at a bank for 3 mos., 4 mos., and 6 mos., respectively, at 69J;. The proceeds were $1200, $800, and $600. What was the sum of the notes? 415. How much cotton can be bought for $4379.125, allowing 2^% commission for buying ? 416. What must be the face of a note, that when dis- counted for 10 mos., H,t b^o, the avails may be $2000? 417. For what price must cloth be sold to gain 12%, when 15% is lost if it is sold at $2.50 per yard ? 418. A grocer sold 180 boxes of lemons, at a loss of $36, which was 10% of their cost. What did he pay for them per box? 419. A certain railroad has 20% of its capital owned in Ohio, 25% of it in New York, 30% of it in Illinois, 5% of it in Maine, and the remainder, $240,000, in Michigan. Which State holds the largest amount of stock, and in what two States are equal amounts held ? 420. A horse was sold for $132.50, at a gain of 6%. Had $115 been the price received, what would have been the loss per ceni ? 154 AEITHMETICAL EXERCISES. 421. A speculator bought 250 hhds. of New Orleans molasses, and sold them for $10,645|^, at a gain of 16-J%. What was the cost price per hogshead ? 422. Find the discount and the present worth of $2400 at 6%, -^ due in 3 mos., -J^ in 6 mos., and the remainder in 9 mos. 423. A man bought 180 tomato-plants for 2 for a cent, and 180 for 3 for a cent, and sold them all at the rate of 5 for 2 cents. What was the gain or loss per cent ? 424. From a dividend of 17%, what income will be received from 56 shares (par value $ 100) in a Lowell calico- mill ? 425. What was paid for $8000 Virginia 6s bought with- out a broker, at 10% discount? 426. In the year 1248 the Jews were not allowed to charge the Oxford students a higher rate of interest than 2 d. for the use of £1 for a week. How much is this per cent per annum ? 427. I of 128 is 5% of what number ? 428. 0.75 of 64 is 2% of what number? 429. Six times 25 is 6% of what number? 430. Six-hundredths of 25 is 6 times what number? 431. 6% of 25 is .06 of what number? 432. Which stock yields the greater return, a 6-J-% stock at 161-J-, or a 5% stock at 123^? 433. Required the face of a bank note due in 90 dys., whose proceeds shall be $3000, discount being reckoned at 6%. 434. For six $500 United States bonds $3262.50 were paid. At what premium were they sold ? PERCENTAGE. 155 » 435. A ranchman bought 768 head of cattle, an addition of 25% to the stock already owned by him. What was the number of his herd after the purchase? 436. At what rate per cent will $22,200 invested in bank stock at par yield a semiannual return of $999? 437. A sugar-planter obtained $3000 at a bank by having his note for 30 dys. discounted at 6%. Required the face of the note. 438. On a note for $1000 dated Jan. 1, 1875, there were four indorsements: Mar. 10, 1876, $40; Aug. 1, 1876, $271.18; Dec. 12, 1876, $40; May 5, 1877, $400. What was still due July 8, 1878? 439. When money is worth 4^% per annum, what is the present worth Aug. 1, of $100 due Nov. 1 ? 440. By selling tea at 56 cents per pound a grocer makes a profit equal to -f of bis outlay. What profit per cent will he make by selling the same tea at 60 cents per pound ? 441. A six-penny piece is what per cent of 14 half- crowns ? 442. A gentleman had a note for $ 1200 payable in 90 dys., discounted at a bank at 7%. He offered his eon -J- the discount if he would reckon the difference between the true and the bank discount. The boy found the correct answer to the question. How much more than the required difference did he receive ? 443. On the 1st of May, 1879, Jacob Jackson gave to his grocer a note to the amount of $315.74 on interest at 6%. The three following payments have been made on this note: Dec. 10, 1879, $20.60; Nov. 10, 1880, $80.50; July 1, 1881, $90. What was due Sept. 30, 1881 ? 156 ARITHMETICAL EXERCISES. 444. What is tte duty at 40 ^J^ on 150 bales of cotton weighing 375 lbs. each, invoiced at 15 cents per pound, tare 10% ? 445. On the note given below what remains due April 1, 1882? $2600. St. Louis, Sept. 4, 1880. On demand I promise to pay Caleb Metcalf, for value received, twenty-six hundred dollars, with interest at seven per cent. Indorsement, July 12, 1881, $1200. Seth Jones, 446. Find the day of maturity, the time to run, the dis- count, and the proceeds of the following note : $ 325. Boston, Nov. 3, 1884. For value received I promise to pay three hundred and twenty-five dollars, six months after date, with interest at six per cent. Discounted at 7%, Jan. 3, 1885. Charles Gale. 447. What principal will give $63 interest in 2 yrs. 3 mos., at 8% ? 448. A railroad company employs 336 men daily on a certain part of its line ; this is 8% of the whole number of laborers. What is the entire force on the road ? 449. A veteran in the civil war received from the gov- ernment pension money amounting to $1251. On Jan. 1, 1884, he lent the money to his brother, who paid Jan. 1, 1885, $400 ; Nov. 1, 1885, $40 ; Jan. 1, 1886, $600. With interest at 6% what will be due May 1, 1886? 450. A young man invested his first earnings in a 6% $100 bond, at a price which paid him 5% on his money. What was the market value of the bond ? PERCENTAGE. 157 451. What must a merchant pay for a 6% investment, that it may bring him 9% annually? 452. Theophilus Jenkins sent to a broker in Cincinnati $6166 for the purchase of salt pork. How many barrels, at $24 each, can be bought, the broker's commission being 5% for buying ? 453. Carl Heuser bought $ 1499.68 worth of Kentucky 7s at 105. What was his rate of income, and his actual income ? 454. A settler in Arizona sold his farm for -J of its value. What was the loss per cent ? 455. $500. Georgetown, Jan. 1, 1876, For value received I promise to pay Seth Wilton, or order, five hundred dollars, on demand, with interest at 6%. John Hurry. Indorsements: April 1, 1876, $12; Aug. 1, 1876, $2; Dec. 1, 1876, $3; Feb. 1, 1877, $30; July 1, 1877, $40. What is still due June 1, 1880? 456. If I wish to pay a coal-dealer a debt of $961.35 by giving him a note for 60 dys., which he can have dis- counted at a bank at 8^, what must be the face of the note? 457. A lumberman in California has two wood-lots of Sequoia trees. From one he cuts yearly 112 tons of timber : this amount is 40% more than the quantity he cuts from the other. How much timber does he cut from the other lot? 458. A man bought a farm on the 8th of May, 1881, for $7600, and gave his note bearing 6% interest from the time of the purchase, secured by a mortgage on the farm. Having made the payments given below, what balance had he to pay on taking up the mortgage Dec. 30, 1882? Indorsements: Dec. 1, 1881, $240; Mar. 6, 1882, $1000; Nov. 19, 1882, $150. 158 ARITHMETICAL EXERCISES. 459. The owner of a ranch in Colorado has 800 sheep in two pastures. In one pasture there are 480 ; what per cent of his entire flock is there in the other ? 460. A merchant sold IQ^-^ hhds. of molasses at $33^ each, and received in payment a note due in 5 mos. 15 dys. What sum will be received for the note if discounted at a bank immediately, at 7% ? 461. A young lady received by bequest from her grand- father, Jan. 1, 1881, $1000. She invested it on compound interest at 7%, interest payable semiannually. What did the bequest amount to Jan. 1, 1884? What was the com- pound interest ? 462. If hemp be bought at the rate of $17 per bale of 196 lbs., and sold at the rate of 20 lbs. for $2, what will be the gain per cent ? 463. $1040.32. Speingfield, Mass., Dec. 1, 1885. Sixty days after date I promise to pay to George Gordon, or order, one thousand forty and -j^ dollars, for value received. Discounted at 6%, Feb. 1. William Brewster. It is required to find the day of maturity, the time to run, the discount, and the proceeds of the foregoing note. 464. When a tax of $31,500 is assessed on property valued at $630,000,000, what is the rate per $1000? 465. In what time will $800 at 6% gain $40 interest? 466. A man insured his life for $39,000, the annual premium being $4.91 on each $100 insured. What was the yearly payment required of him ? 467. What will be the proceeds of a bank note, for 90 dys., for $1250 at 7% ? > PERCENTAGE. 159 468. When 11 yrs. old, a boy received from his grand- father $ 15,000. What will be his age when this sum, placed at simple interest at 10%, shall amount to $30,000? 469. What will be the increase of income if $ 1250 of 3% stock at 96 be exchanged for railroad bonds at 75, paying an annual dividend of 2J% ? 470. Henry Ives sold to John Carr two Alderney cows, at a loss of 12^%. J. Carr sold them to George Sumner for $504, and gained 12J% on the price he paid. What did the cows cost Henry Ives ? 471. In settling an account, a carpenter took a note estimated to be worth only 50% of its face. He collected 13% more of the face of the note than the estimated value, and thereby gained $56. What sum was collected ? 472. A carpenter buys 11,625 ft. of hemlock plank at $30 per M., and pays the bill with his note at 15 dys. The lumberman holds the note 3 dys., and then has it dis- counted at a bank, at 7%. How much money does he realize ? m 473. Find the proceeds and the discount of a note for $900, due in 6 mos., discounted at 8%. 474. What per cent of a number is 50% of 50% ? 475. A grocer bought sugar at \ discount from $9 per hundredweight. What per cent did he make by selling it at $9 per hundredweight ? 476. What capital must be invested in bank stock at par in order to obtain $160 when an 8% dividend is declared? 477. A farmer sold for 60 cents per bushel corn which in its cultivation cost him 36 cents. What was the gain per cent and the actual gain on 90 bu. ? 160 ARITHMETICAL EXERCISES. 478. At 10}% premium, what amount of bonds can be bought for $10,497.60, without brokerage ? 479. A nurseryman marked his trees at 80% above cost, and then sold them at 76%, and 6% discount. What was the loss per cent ? 480. What is the cost of a sight draft for $1000, the rate of exchange being 1}% premium ? 481. Hqw many yards of silk 1^ yds; wide are needed to line a portiere which contains 20 yds. of silk 1} yds. wide? 482. A woman bought lemons at 30 cents per dozen, and sold them at the rate of 3 for 6 cents. What per cent did she lose ? 483. What alteration in income will occur if $1000 of 6% stock be sold at 76, and the proceeds be invested in 7% stock at 110? 484. When exchange is $4.86}, what is the face of a bill on Dublin for $29,190? 485. Find the cost of a bill on Amsterdam for 5262 florins, worth 40 cents each, at 1% premium. 486. The value of the capital invested in silk manufac- tures in New Jersey, in the year 1883, was $8,968,000, the amount paid for labor was $6,692,189, and the value of the product was $22,183,346. What per cent of the capi- tal is the gross product ? What per cent of the product is the amount paid for labor ? 487. Find the proceeds and the discount, at 7%, of a bank note due in 3 mos. ; face of the note $2000. 488. What sum will be raised by taxation in a town where the taxable property amounts to $4,200,000, and the rate is 1^ mills on a dollar, 8% being uncoUectable, and 3% being paid for collecting? PEECENTAGE. 161 489. £ 409. BosTOK, Dec. 4, 1886. Thirty days after sight of this first of exchange (second and third of the same tenor and date unpaid) pay to the order of Hiram Humphrey four hundred and nine pounds sterling, value received, and charge the same to Baring Brothers, London. Adams, Anthony & Co. Find the cost of the preceding draft, thirty-day bills being quoted at $4.89. 490. Find the maturity, the time to run, the discount, and the proceeds of the note which follows : $944. New York, Jan. 15, 1887. Ten months from date I promise to pay George Johns or order nine hundred and forty-four dollars, value received. Discounted, at 7%, Jan. 15. - James Gage. 491. A grocer received $24 for the sale of sugar in one day. Of this sum 12% was gain. What was his gain per cent, and what the actual gain, on a sale amounting to $275? 492. A lady in Baltimore wishes to buy a draft on Paris for 5140 francs, when exchgyige is 5.14 francs to a dollar. What must she pay for it ? 493. The assignee of a bankrupt broker found his assets to be real estate worth $3750; cash, $750; furniture, $650; horse and carriage, $200; interest in a flour-mill valued at $400. His aunt held a mortgage of $2250 on the real estate ; he owed $3000 to his sister ; $3825 to his father; and $2540 to his brother. The assignee had 5% on the assets, and other expenses amount to $350. In set- tling the estate, what sum will the brother receive ? 494. What will be the net proceeds on the sale of goods which brought $13,242.50, after a commission of 2J% has been deducted? 162 XEITHMETICAL EXEEOISES. 495. Find the cost in New York of a draft for £1500, payable to Longman, London, exchange being at $4.86^. 496. A collection of natural history specimens, for which the owner paid $7360, is insured for its full value, at 4-J-%. What would be the actual loss in money to the owner from its entire destruction by fire ? 497. Orrin Heath, of Cincinnati, received $1230.38 for the purchase of pork, after deducting his commission of 2f %. What sum did he invest? 498. George Levitt owes $500 in Omaha. He pays the debt through an agent who is to receive for his services the difference between the $500 and the face of a draft, pay- able 30 dys. after sight, which the $500 will buy at -J- of 1 ^0 premium. What sum did the agent receive ? 499. Which is more profitable, a 6% stock at 85, or a 7% stock at 95? How much more income would be received by investing $16,150 in the more profitable stock ? 500. A Chicago library bought books of Rivingtons to the amount of £251 6 s. What will be the cost of a draft on London to settle the bill, sterling exchange being quoted at $4.85? 501. A milliner sold her business for $182, and lost 9%. Had she sold it for $214, what would have been the gain per cent? 502. A bankrupt whose liabilities are $43,000 has property to the amount of $16,500. What will be paid on a claim of $1300? 503. A merchant bought $5000 worth of stock at 120, and sold it at 84. Without any allowance for interest or brokerage what was his loss, and what per cent of his investment did he lose ? PERCENTAGE. 163 604. A farmer living in Dakota sent 12 t. of maple sugar to a Chicago merchant, who paid 50 cents per hundred- weight for storage, $3 for cartage, and reserved 2^% for commission. He remitted to the farmer $6727. Find the selling price of the sugar per pound. 505. A Boston apple- woman bought a certain number of apples at 3 for a cent, and an equal number for 2 for a cent. She then mixed them and sold them at 5 for 2 cents. What was the gain or loss per cent ? 506. A merchant sold a 3% stock at 99, and gained 10% on his investment. He realized $15,345. What did the stock cost him ? What income did it yield ? 507. An avenue ^ of a mile long is lined with shade trees standing 60 ft. apart, (i.) How many trees are there ? (ii.) Had they stood 33^% farther apart, how many trees would there have been ? 508. Find the net proceeds of a consignment sold for $6700, on which there are charges of $470 freight, $500 insurance, and S\% commission. 509. A gentleman pays $285 premium for insuring his house and furniture at 2f %. What is the value of each, the furniture being worth J the sum at which the house is valued ? 510. A real estate agent received $137.50 for effecting the sale of a house, the rate of commission being 2J-%. For what sum was the property sold ? 511. What sum must be invested in a stock, paying ^1^%, and worth 106J in market, that a college professor- ship may be endowed with a salary of $2044 ? 512. Find the principal that will gain $200 in 4 yrs. 6 mos., at 3%. 164 ARITHMETICAL EXERCISES. 513. Fritz Rheinhart sent 3745 bbls. of flour from St. Paul to New York City to be sold by an agent on 3J% commission. The flour brought $10-J- per barrel. Find the agent's commission? 514. Henry Hancock pays $3000 to a St. Louis flour- merchant, by a draft on Boston. What will be the face of the draft, Boston exchange being at -I- of 1% premium in St. Louis? 515. Which is the better investment, 4|^ stock at 95, or 5^^ stock at 104? What investment must be made in the better stock to secure a yearly income of $613.60, after paying an income tax of If % ? 516. Brown Brothers pay a bill for $3000 in Denver, Col., with a sight draft on New York. What will the draft be worth in Denver at -j^ of 1 % premium ? 517. Find the value in New York, at a discount of -^^ot of a sight drafb on Memphis for $ 3650. 518. An Alabama cotton-planter sent 284 bales of cotton, weighing 450 lbs. each, to his agent in Manchester, Eng- land. The agent sold it Vld. per pound. He paid Ic?. per pound freight, £4 3 s. for storage, and charged 2^% commission. What did the planter realize, with exchange on the net proceeds at $4.92J- to the pound? 519. Elihu Enright collects 556 bills of $3.80 each for an agricultural society. His commission is 4^^. How much must he pay over ? 520. A ship, worth $17,500, is insured at 3^% o^ \ of its value; and the cargo, valued at $37,500, is insured on I of its value, at 2|%. Find the premium to be paid for the insurance of both ship and cargo. PERCENTAGE. 165 621. An estate valued at $3000 is taxed $50. What tax must be paid on a house worth $1727.50 when the tax rate is half as much again ? 522. A merchant agreeing to receive $500 on a bad debt, found that he had been paid 62^% of his actual claim What was the original amount of the debt ? 523. What must be paid in United States money for a bill on Liverpool for £1100, the rate of exchange being $4.80? 524. Find the face in English money of a draft on Glas- gow, that can be bought for $7297.50, exchange at $4.86J-. 525. How much money in Birmingham will remit $600 to Chicago, when 48^ c?. make $1 ? 526. When exchange on Paris is quoted at 5.15-J- francs for $1, for what sum in francs must a bill be drawn to send $ 1000 for merchandise ? 527. A dairyman sold the butter made from one week's milk for $38.25 at a loss of 8%, while his neighbor, by sending his butter to New York, received $57 net for the same quantity. What was the neighbor's gain per cent ? 528. Find the sum of money which put at interest for 9 mos., at 4% per annum, will amount to $193,125. 529. James Stone bought an 8% stock at 120, and his brother bought a 5% stock at 75. Which investment yielded the better income ? 530. Joseph Skinner, when 40 yrs. old, insured his life for $ 10,000 ; he died at 70. Without allowing interest on the payments, how much did they exceed the amount received from the insurance company? Eate, $46 per $1000. 166 ARITHMETICAL EXERCISES. 531. Two brothers invest each the same sum in the 3 and 3-J- per cents, and receive an income of equal amount. The 3 per cents are at 75 ; at what price are the 3^ per cents ? 532. Find the cost of 6% bonds that they may bring 6|^% income. 533. What income will be received from $14,350, in- vested in 6% bonds at 2J% premium? 534. What is the value of a $3064.90 draft on Chicago bought at f % discount? 535. Jared Moller sent coal to New York which was sold for $2850 ; for freight and cartage $485 was paid, and $2272.37 was remitted from the sale. Find the amount of the agent's commission. 536. What investment in United States 4% bonds at 102|^, will yield a quarterly income of $250? 537. A butcher adds 20% profit to the price of his meat. What is the cost price of a pair of chickens which he sells for $2.04 ? 538. Silas Dresser transferred $1000 of 3% bonds at 96 to 5% stock at 108. What difference of income was caused by the exchange ? 539. A factor received $48.35 for selling goods whose net proceeds amounted to $ 1709.99. What sum was paid for the goods ? 540. Find the tax rate per $1000 in a city where $2,000,000 is raised on property valued at $260,000,000. 541. By selling sugar at $12 per barrel, a grocer lost 25%. At what price per barrel should the sugar have been sold to gain 25% ? 542. What sum must be invested in 10% bonds selling at 104, to secure an annual income ctf $ 1600 ? PERCENTAGE. 167* 543. David Secord bought 120 shares of mining stock at 97, and, after receiving a dividend of 2^%, sold the shares at par. What was the actual gain, and the gain per cent ? 544. What principal at 6%, from Sept. 13, 1880, to Aug. 15, 1883, will amount to $11,532.57? 545. King & Co. of Chicago pay a New Orleans debt for $5000, by a sight draft on Chicago. What sum will settle the account, Chicago exchange being at ^% premium in New Orleans? 546. In Massachusetts a certain fertilizer is made of 75 parts bone dust, 10 phosphate of lime, and 15 light loam ; in Connecticut of 77 parts bone dust, 9 phosphate of lime, and 14 light loam. If ^ of a ton of each be mixed, what weight of bone dust, phosphate of lime, and light loam will there be in the compound ? 547. A cargo of 8000 bu. of corn, worth 60 cents per bushel, is insured at f of 1^% oii f of its value. If the cargo is lost, what will be the loss to the owner of the corn ? 548. A New York wholesale grocer sells tea to a coun- try merchant at a profit of 60% ; the merchant is unsuc- cessful in business and pays only 37^ cents on a dollar. What is the grocer's gain or loss per cent on the sale ? 549. What was the total levy of a tax, whose net pro- ceeds were $300,000, 4^% having proved uncollectible, and 3^% commission being paid for collection ? 550. Find the duty at 15% on 350 bags of cinnamon, each bag containing 115 lbs. valued at 15 cents per pound. 551. A young lady received from her father's estate $20,000, so invested as to pay 3 %. She sold this invest- ment at 94J-, and bought bank stock at 225, paying 8J% interest. What was the change in her income ? *168 ARITHMETICAL EXERCISES. 552. A merchant marked a piece of silk at $1.50 per yard; this price was an advance of 25% on the cost. He sold at 15% discount on the price asked. What was his gain per cent ? 553. Lorenzo James buys 86 A. 80 sq. rds of land at $80 per acre. With the proceeds of a note for $8561.50 payable in 90 dys., discounted at 6%, he pays for the land and invests the remainder in horses at $ 150.88 each. How many horses does he buy ? 554. A grocer wishing to make cash purchases, borrows $840.25 from a bank. For what sum did he give his note payable in 5 mos. 21 dys., at 6% ? 555. A merchant had 3 six-month notes discounted at 5, 6, and 7% respectively. The proceeds of each were $800. What was the face of each ? 556. Find the cost per yard of cloth which was sold at the rate of 28 yds. for $61.25, at a gain of 25%. 657. A farmer sold some sheep at $5.25 each, thereby losing 12^%. For what price should they have been sold to gain the same per cent ? 558. John Barlow bought 200 shares of railroad stock at 8^% premium, with brokerage at J%, and other expenses $4.75. What was the cost of the investment? 559. Find the premium on six $1000 United States 6s, at 17^% above par. 660. Find the cost of a draft for $240 payable 80 dys. after sight, interest at 6%, exchange 8% premium. 561. Find the value of 90 shares of Housatonic Railroad stock, at 4% premium. 562. What will be received for $28,000 of Kentucky State bonds at 92, without allowance for brokerage ? PERCENTAGE. 169 663. Isaac Hopkins imported 25 bbls. of linseed oil, each containing 31^ gals., invoiced at 54 cents per gallon. Allowing 29^ for leakage, what duty did he pay at 24% ad valorem ? 664. What is the present worth of $8323.15 due in 3 mos., when money brings f % per month? 666. An insurance agent agrees to insure a store worth $12,000 for a sum sufficient to cover its value and the pre- mium. Find the sum, the rate being 1% ? 666. At 12% ad valorem, what duty must be paid on 50 hhds. of West India molasses, each hogshead containing 63 gals., invoiced at 36 cents per gallon, with an allowance of ^ % for leakage ? 667. A broker received $6630 by selling $500 United States bonds, at 10^% premium. How many bonds did he sell? 668. A man owning 70% of a silver mine in Nevada sold 40% of his share for $7000. What was the value of his share, and the value of the whole mine ? 669. Find the difference in rate of income between a 6% stock at 105, and a 6% stock at 75. 670. Thomas O'Neill bought 20 shares of 6% railroad stock at 107f, brokerage J%. Required his yearly income from the stock. 671. Find the sum paid by Henry Brown who sent two pupils 118 dys. each to a district school supported by a "rate-bill," under the conditions given. Teacher's wages $400, fuel and other expenses $151.14; the public money received was $ 196, and the whole number of days' attend- ance WAS 3946, 170 ARITHMETICAL EXERCISES. 672. When 5% bonds are bought at 83^, what is the rate of interest on the money invested ? 573. Owen Glendower bought a 5% stock at such a rate as to secure 7% annually. What did he pay for it? 674. The proprietor of a hotel lost by leakage 10 gals. 3^ qts. from a cask of molasses containing 72 gals. Ke- quired his loss per cent. 576. How much will a Chicago broker invest out of $7872 for an Albany grain merchant, if he charges 2^% commission for buying ? 576. For necessities of the first year in business, Ralph Seton borrowed of his sister $400 on the 4th of July, 1884. At 6% interest what amount was due June 1, 1885, the following payments having been made: Aug. 10, 1884, $72; Nov. 1, 1884, $45; Jan. 1, 1885, $200; Mar. 4, 1885, $50? 677. A ship was insured for $20,000, and its cargo for $ 10,000, at the rate of 30 cents on $ 100. What was the whole cost of insurance, $2 being paid for the policy? 678. The principal of a school bought an organ valued at $ 1000 on 3 mos. credit ; after that period interest was to accrue at 7%. The purchase was made Jan. 1, 1882; he paid $400 Jan. 1, 1883. What was due April 1, 1883 ? 679. A bankrupt owing his creditors $16,682.50 paid them $3336.50. What per cent of their claims did they lose? 580. A store and its contents, insured for three-fourths of their united value, were burned. The owner lost $1200. What was his loss per cent, and what was the united value of the store and its contents ? FEBCENTAGE. 171 681. Find the face of a draft that can be bought for f 2000, exchange being at a discount of }%. 682. What will be the face of a draft, payable 30 dys. after sight, that can be bought for $3000, exchange being i% premium, and interest 6% ? 683. James Appleton gained $180 by selling 24 shares of mining stock which was bought at par. What was the selling price ? 684. What amount will be invested in a mortgage for $4391 by an agent charging ^% commission? 686. A grocer, having sold crude naphtha at a profit of 75%, collected but \ of his bill from his purchaser who failed immediately after the conclusion of the ^ale. What was the grocer's gain or loss per cent ? 686. How many shares of Michigan Central Railroad stock at 80 can be bought for $4427.50, brokerage }% ? 687. 300 is 100 per cent more than what number ? 300 is 90% less than what number? 688. James Stirling received $1700 on a claim of $2500 against a bankrupt estate. What per cent was paid? With liabilities amounting to $190,000, what were the assets ? 689. What investment in California 8% bonds at 95 will yield a semiannual income of $1500? 690. Find the interest M 6% on $2800 for the month of July, reckoning 365 dys. to a year. 691. A gentleman gave 20% of a tract of land to his daughter, 10% to his son, and the remainder to his wife. What was the wife's share, the tract containing 363 A. 126 sq. rds. ? 172 ARITHMETICAL EXERCISES. 592. Find the principal which, placed on interest for 3 yrs. at 10%, will amount to |2970.50. 693. A butcher received from a bankrupt customer $154.16, which was 40% of the amount due. What was the amount due ? 594. A wholesale druggist marked his goods at 90% above cost, but to a friend beginning business he sold them at 40% and 5% discount. What per cent profit did he make? 595. How many $100 bonds at 5% premium can be bought for $8400? 696. Find the cost in New York of 270 t. of Russia rail- road iron, invoiced at $50 per ton, on which there was a duty of 24%. 597. A grocer bought 40 bu. of potatoes at 75 cents per bushel, and 160 bu. at 65 cents per bushel. What price per bushel must he ask for the whole lot in order to clear 20% by the transaction? 598. The cost of constructing a railway is $10,000,000, of which 40% is borrowed at 6% , and the remainder is held in shares. What must be the average weekly receipts in order to pay 5% dividend per annum, the working expenses being 65% of the gross receipts ? 599. The customs revenue of the United States for the fiscal year ending July 1, 1885, was $181,471,939. The expenses of collecting it amounted to $6,494,847. What per cent was the expense of collection of the whole amount? 600. The proprietors of a certain boot and shoe factory say that 100 persons in their factory now make by machin- ery as many shoes as 500 persons formerly made working by hand processes. What per cent of the manual labor is displaced by the use of machinery ? PEECENTAGE. 173 601. A man and a boy can heel 300 pairs of shoes per day by the use of machinery. It required formerly 5 men per day to do this amount of work by hand. Reckoning the boy's labor as equivalent to half that of a man, what percentage of the former amount of labor has the use of machinery displaced in this case ? 602. A certain furniture manufactory is now able by the use of improved machinery to make the same amount of goods as before with the labor of 77 men, whereas the number formerly einployed was 110. What per cent sav- ing in the cost of labor has the improved machinery effected for the owners of the manufactory ? 603. By a hand-loom a weaver used to weave 70 picks of a certain kind of cotton per minute. A good power- loom will now weave 180 picks of the same kind per min- ute, and a good weaver can tend 4 looms. What per cent of labor for this purpose is rendered unnecessary by the use of power-looms ? 604. A first-class workman can make 800 2-lb. tin cans per day by hand process. By the use of machinery he can make 2400. What decrease per cent in the manual labor required is here effected by the introduction of machinery ? How many hands would be required to turn out 96,000 cans per week (i) by hand process, (ii) with the aid of machinery ? 605. At a coal mine in the Hocking Valley, Ohio, it is estimated that mining machines, employing 160 men, pro- duce as much coal as 500 men would produce, working by hand for the same number of hours. What per cent of labor have the machines displaced ? 606. Will 25 negroes or 18 white men do a certain piece of work the quicker, supposing the whites 40% quicker workers than the negroes? 174 ARITHMETICAL EXERCISES. 607. The amount of wheat in hundredweights, imported into Great Britain and Ireland from the United States and from India for the years 1883 and 1884, was as follows ; Date. From the United States, From India. 1883, 36,128,761 14,193,763 1884, 22,641,050 21,001,412 Express in percentage form (i) tho falling off for the United States, (ii) the increase for India. 608. The quantities of wheat and of corn exported from the United States for 1880 and for 1885 were as follows : Year. Wheat. Com. 1880, 153,252,795 bu. 98,169,877 bu. 1885, 84,653,714 " 51,834,416 " Find the decrease per cent in the exportation of each of these products in 1885 as compared with 1880. 609. The values of the exports from the United States for the years 1884 and 1885, collected under the three heads of agriculture, manufactures, and mining, etc., were as follows : Year. Agriculture. Manufactures. IHning, etc. 1884, $536,315,318 $111,330,242 $77,319,293 1885, 530,172,966 117,259,810 79,250,170 Express these values as percentages of the whole exports for each year. 610. The amount of specie in the United States treasury on Sept. 30, 1878, and on Sept. 30, 1885 was as follows : Other silver coin Gold coin and Date. Silver dollars. and bullion. hvUion. 1878, $12,155,205 $15,777,937 $136,036,302 1885, 165,483,721 27,558,016 251,251,114 Compute for each year the per cent which the silver and- the gold, respectively, form of the whole amount. PERCENTAGE. 175 611. What per cent must be added to the numerator of •J-|f to make the fraction equal to ^ ? 612. A man having $250 paid 6% of it to another man having $300. How much per cent is the latter sum in- creased? 613. Simplify ,Vof 16^-1. 5^-4^ ^of 12f+l • l + -fofl2| 614. A man owning 10 shares of 3% stock sells it at $74 per share. With part of the proceeds he buys enough h^o stock at 105 to yield the same income that he received before. How much money has he remaining ? 615. Two fields together have an area of 2 A. One of the fields contains 60 sq. rds. more than the other. What is the value of each field at $80 per acre ? 616. Simplify ^ of ^--h—h X (4| _ 2} + ^\ 617. The value in round numbers of the merchandise imported into the United States for the fiscal year 1882 from Great Britain, France, Germany, and Cuba was as follows : Great Britain, $ 196,000,000 ; France, $89,000,000 ; Germany, $56,000,000; Cuba, $70,000,000. What per cent of the imports from Great Britain were the imports from each of the other countries ? 618. By selling goods at $1173.92 a merchant gained 15%. What was his gain, and what did the goods cost him? 619. If to 336 lbs. of sugar 14 lbs. of sand were added, what would be the percentage of sand to the sugar and to the whole mixture ? 620. A is 45 yrs. old. B is older than A by 12% of A's age. Find B's age, and express the difference of their ages as a percentage of B's age. 176 ARITHMETICAL EXERCISES. 621. If a long ton (2240 lbs.) of ore produce 27 oz. Troy of pure silver, what is that per cent ? How much ore must be raised to produce $30,240 worth of silver, when silver is worth $1.12 per oz. ? 622. A man bought some cranberries for $30, and sold J of them at a loss of 10%. For how much should he sell the remainder to gain on the whole 20% ? 623. Four reapers, working together, reap 50 A. of rye in 23 dys. They are paid at the rate of $4.50 per acre, but they employ during the whole period 2 binders to aid them, paying each of them $ 1 per day. If the first reaper was absent 3 dys., and the second reaper 1 dy., what sum of money should each reaper receive for the job ? 624. A wine merchant paid $ 182.07 for a pipe of wine containing 102 gals. He put the wine in bottles such that 3 bottles hold just 2 qts. of wine. The bottle? cost him $3.50 per hundred, and the corks 52 cents per hundred. For what price must he sell the wine in order to make a profit of 20 cents per bottle, and what will be his profit per cent? 625. The hop acreage in England amounts to about 70,000 A. What is the difference between the value of a good crop of 10 cwt. to the acre at $25 per hundred- weight, and a blighted crop of 2 cwt. to the acre at $50 per hundredweight ? 626. Find the change in income due to transferring $27,216 ^% stock at 83^ to 5|% stock at 94|, a broker- age of ^% being charged on each transaction. 627. If $19,200 in 3.% United States bonds at lOOf are transferred to a 4% railway stock at 110J-, the iBxpense of the charge being $74.59, what alteration in the income is the result? PEBCENTAGE. 17? 628. Dry chestnut wood weighs 2320 lbs. per cord. 4 lbs. of the wood will yield 1 lb. of charcoal, and 20 lbs. of the charcoal make 1 bu. If the wood is worth $6 per cord, and 67 cents per cord is allowed for making the char- coal, what is the value of a basket of charcoal holding 2 bu. ? 629. Find (to two decimal places) the population to the square mile in each of the following states : Massachusetts, New York, Ohio, Texas. (For data, see page 4.) S30. Of an electric cable -J-J- rests on the bottom of the sea, -^ hangs in the water, and 234f yds. are employed on land. What is the length of the cable ? 631. If it cost $3. 87 J to carry 15} cwt. 60 mi., how far ought 31 cwt. be carried for the same money ? 632. Two ships leave a harbor at the same time for the same port, distant 1200 miles ; the faster vessel averages 10 miles an hour, and arrives at the port a day and a half before the other. What will the latter vessel average an hour? 633. Find the present worth of $1000 due in 315 dys. at 4%. 634. Find the interest on $2938.25 at 3}% for 200 dys. 636. A farmer was offered 60 cents a bushel for 400 bu. of potatoes. He declined the offer, and soon after they fell 20% in value. What did he lose by keeping them? 636. A man sold a horse for $384, and thereby lost 4%. For what should he have sold him to gain 15% ? 637. A grocer bought 20 chests of tea, each containing 42 lbs., for $18 a chest, and sold the tea for 60 cents per pound. What was his total gain, and what was his gain per cent? 178 AEITHMETIOAL EXERCISES. 638. If a salesman lose 16% by selling shoes at $2.55 a pair, what must he ask for them in order to make 15% ? 639. Simplify 2f of 4P^=44-^tt+ ^ 640. If the ore of a mine yield 250 lbs. of metal for every 4 tons of ore, what is that per cent ? 641. How much metal should 15 tons of ore yield to make the return 125^^ ? 642. A man sells $9600 stock at 94|-, and on the price of the stock rising to 95^ he sells $4800 more; afterwards, when the price had risen to 96, he buys back $ 14,400 stock. What did he gain or lose by the transaction ? 643. A certain piece of work can be done in 5 hrs. by a man, in 8 hrs. by a woman, and in 12 hrs. by a child. In what time can they do it working together ? 644. A lamp burns half a cent's worth of oil per hour. What was the expense of using the lamp from Oct. 1, 1884, to Mar. 10, 1885, 4 hrs. and 40 min. each evening ? 645. Simplify -iiiiH^l^iiili-xi+i. 646. In an examination, the maximum mark for which was 1000, A got 680 marks, and B got 10 J % more than A. What was B's mark, and what percentage were As marks of B's marks? 647. A regiment consisted of 800 men. If 3% are killed, 15% wounded, and 27% on the sick-list, how many are still fit for duty ? 648. A can do a piece of work in 25 dys., B in 20, C m 86. A and B work together for 4 dys., and then B and for 6 dys. How much of the work remains to be done ? PERCENTAGE. 179 649. Find the difference between the greatest and the least of the following fractions : f , ^, ^, ff . 651. Which are the cheaper, eggs at 7 for 24 cents, or at 43 cents a dozen? How much would be gained by buying 672 eggs at the lower rate, and selling them at the higher rate ? What would be the gain per cent by buying them at the lower rate, and selling them at 4 cents each ? 652. How much lead must 1400 lbs. of lead ore yield to make the return 15% of the ore? 653. There are three cities. A, B, C. The rainfall at A is 25% greater than that at B, and that at B 14iJ^% greater than that at C, which is 21 in. Find that at A and B. 654. If 5 cu. ft. of air consist of 4 cu. ft. of nitrogen, and 1 cu. ft. of oxygen, express the percentage of oxygen to air, and of oxygen to nitrogen, in a cubic foot of air. 666. A skating rink is illuminated by 54 gas jets which are turned on at 5.15 p.m., and put out at 11 p.m. The price of gas is $2.25 per thousand cubic feet, and each jet consumes 12 cu. ft. per hour. What is the cost of illumi- nating the rink for the month of January, if the month be- gins on Friday, and the rink is open every evening except Sunday ? 666. A man has an orchard covering 5i A., and each acre contains 36 apple-trees. One season the average yield per tree was 14 bu. of apples. These were made into cider, 8 bu. of apples yielding 1 bbl. of cider holding 36 gals. The man sold the cider for 11 cents per gallon, after reserv- ing 4 bbls. for his own use. How much did he receive for the cider? 180 ARITHMETICAL EXERCISES. 657. A lead mine yields 1 lb. 1 oz. of lead to 85 lbs. of ore. What is that per cent ? 658. If 17 qts. of wine costing $1.40 per quart are mixed with 30 qts. of wine costing 95 cents per quart, and the mixture is sold at $1.50 per quart, what profit is real- ized? 659. For sewing water-proof hats, girls in Boston now (1884) receive $ 1 for 6 doz. If a girl can sew 8 hats in an hour, how much can she earn in a day of 10 hrs. ? In a year of 304 working days ? How much would she earn in a year at the old rate, which was 30 cents a dozen? 660. A good cutter in a Parisian butcher-shop can earn 8 frs. a day, and in Paris the butcher-shops are closed only one day in the year, Good Friday. How much can the cutter earn in 1 yr. ? Take 1 fr. = $0,193. 661. If the charge for carting 1 t. of stone 1 mi. is 75 cents, what will it cost to carry 360 1. a distance of 800 yds. ? 662. A bookseller buys 68 copies of a book at $3.25 each, and sells them at $3.75 each. What does he make, if for each dozen copies purchased by him one copy is thrown in free of cost ? 663. If 100 lbs. of green coffee yield 91 i lbs. of burnt coffee, and the burnt coffee is worth $37.50 per 100 lbs., what is the value of the green coffee per 100 lbs. ? 664. 1 bu. = 2150.42 cu. in. 1 gal. = 231 cu. in. How many gallons are there in 1 bu. ? 665. The consumption of coal in Great Britain rose in a certain year from 92 millions to 97i millions of tons. State this increase as a percentage to two decimal places, and find what the consumption would be in the next year, at the same rate of increase. PERCENTAGE. 181 666. If a journey take 3} hrs., travelling 35 mi. per hour, how much must the rate be increased to save 42 min. ? What per cent must the rate be increased ? 667. The population of a town was 87,640 at one census, and 100,000 at the next census. Express the per cent of increase to three decimal places. 668. A horse is bought for $343, and sold for $371. What is the gain per cent ? At what price should it have been sold to gain 12% ? 669. A man bought a lot of 3 A. 135 sq. rds. at $880 per acre, and spent $7617.50 in erecting a house and out- buildings. He then let the premises for $715 a year. What rate per cent did he get on his investment ? 670. If m 15 min. a vessel receives by one pipe 22 gals. 3 qts. of water, and loses by another pipe 3 J- gals., how much water will the vessel contain at the end of an hour and a half ? 671. Simplify 3.28167 + 0.0004193 + 3.8961028 + 0.8218. 672. Find the simple interest on $81,176 for 120 dys. at4i%. 673. What is the simple interest on $2962.50 from Dec. 30, 1887, to Mar. 12, 1888, at 4% ? 674. The marks for perfect answers to the questions on an examination paper being 6, 6, 10, 10, 6, 10, 10, 8, and a boy having obtained the marks 4, 5, 7, 9, 3, 10, 0, 6, respectively, find what per cent of the mark for the whole examination he has obtained. 675. What sum of money, at 5% simple interest, will produce in 2 yrs. the same amount of interest as $2160 at 4% in 3 yrs. ? 182 ARITHMETICAL EXERCISES. 676. By selling out 3% bonds at 102f, and investing the proceeds in a railway stock at 137, a man finds that he can double his income. What is the annual dividend of the railway stock ? 677. What sum of money, lent at 4% per annum simple interest, will produce in 3 yrs. the same amount of interest as $2592 lent at 5% will produce in 2 yrs. ? 678. A gas factory uses a coal which yields 10,500 cu. ft. of gas per ton. The loss in purifying and by leakage is ^^. The factory has to supply 100,000 cu. ft. of gas daily. The cost of the coal is $4.90 per ton. How many tons of coal are consumed each day ? How much per 1000 cu. ft. must be the price of the gas, in order that the gross daily profit may be $ 100 ? 679. A teamster carries 4 loads of gravel daily from a gravel pit to a railroad line 2f mi. from the pit, and each load contains 2J- cu. yds. of gravel. He is paid at ihe rate of 35 cents for carrying 1 cu. yd. one mile. How much will he receive for carrying 500 loads, and how many days will it take him to carry them ? 2f + 2|of^-ii 680. Simplify H ^ 681. The sum of $2500 is to be raised by a tax in a cer- tain town. The assessed valuation is $850,000, and there are 300 polls, each taxed $1.25. Find the rate per $100, and the tax of a man who is assessed $4480 and pays 2 polls. 682. A city hall, in a city whose assessed valuation is $4,000,000, was built at a cost of $57,000. The money was raised by direct taxation, and the expense of collection was 5%. What was the rate per $100, and what sum did a man pay whose property was valued at $50,000? PERCENTAGE. 183 683. The distance between two stations, A and B, was measured with a 10-ft. pole, and found to be 3430 ft. The pole was afterwards found to be long by 9|- in. What is the true distance from A to B ? 684. On Mar. 4, 1885, the assets of the United States treasury amounted to $210,663,621.15, and the liabilities to $201,899,031.04. On Nov. 1, 1885, the assets were $259,437,431.25, and the liabilities $192,619,138.87. How much surplus balance was in the treasury Nov. 1, and what was the increase between the two dates? 685. In 1884, the quantity of sugar produced in the United States was 287,712,230 lbs., while the quantity imported was 2,756,416,896 lbs. The quantity exported that year was 85,532,916 lbs. How much sugar remained for consumption, and what per cent of the amount con- sumed was produced in the United States ? 686. For the fiscal year ending June 30, 1885, the value of the sugar and molasses imported into the United States was estimated at $73,517,063. The duty collected thereon amounted to $52,184,744. Find (to the nearest unit) the average ad valorem rate of duty on these two articles. 687. For the fiscal year ending June 30, 1885, the value of the dutiable merchandise imported into the United States was (in round numbers) $387,000,000, and the value of the merchandise imported free of duty was $193,000,000. The amount of duty collected was $178,000,000. Find (to the nearest unit) the average ad valorem rate of duty, (i.) on the dutiable merchandise ; (ii.) on all the merchandise. 688. A county jail is to be built at a cost of $16,800. The money is to be raised by a tax assessed on property valued at $1,400,000. What rate will cover the cost of the jail, and the collector's commission of 4% ? 184 ARITHMETICAL EXERCISES. « 689. A lady received $1517.40, the amount due on a note which had been on interest at 8% for 1 yr. 6 mos. 18 dys. What was the face of the note ? 690. On an invoice of body Brussels from London, the duty was $174. What was the rate, the cost of the carpet being $2175? 691. Find the difference between the true discount and the interest of $600 for 2 yrs. 6 mos., at 8%. 692. For supplying a town with water a tax of $34,500 is assessed. There are 100 polls taxed $1.50 each; the real estate of the town amounts to $1,700,000, the personal property to $500,000. What is the rate of taxation ? 693. Find the rate per cent when $2700 worth of New Jersey Central Kailroad stock pays $ 248 dividend. 694. A Pennsylvania Petroleum Co., assessed the stock- holders 15%. What was paid by a director who owned 70 shares ? 695. To secure an annual income of $2100, how much must be invested in South Carolina 6s at 80 ? 696. A Florida land agent received $636 for invest- ment. With commission at 6%, how many $50 lots can he buy for this sum ? 697. The proprietor of a clothing store in Boston sent a note of $5000 to a lawyer in New York, with directions to secure upon it what he could from the maker of the note, who had gone into bankruptcy. The lawyer secured 62^% of the note, and charged 5% commission. What suin did the merchant receive ? 698. At 10% discount how many $1000 Northern Pacific Railroad bonds can be purchased for $21,600? PEECENTAQE. 185 699. A commission merchant paid over to a grocer $366.72, the net proceeds of a months sale of peaches. Find the gross receipts and the quantity of peaches sold, rate of commission being 4^%, and the price of the peaches being 60 cents per peck. 700. For how much must a 3-mos. note, without interest be made, that when discounted at 9% it may yield $1000? 701. A stockholder in a gas company paid $42.25, his share of a 3;^% assessment for extra expenses. How many shares did he own ? 702. A commission merchant purchases coal with the residue from $441, when 5% commission has been deducted. How many tons at $ 7 can he buy ? 703. How much below par is a stock when 65 shares of it can be bought for $ 5200 ? 704. What amount must be invested in Virginia 6s at 90, to realize an income of $ 3600 annually ? 706. A gentleman wishes to secure to his wife an income of $1680. To realize this sum what amount must be in- vested in 6% stocks 5% below par? 706. A bank with a capital of $240,000, in 6 mos. has accumulated $14,770 net, and after declaring a semiannual dividend of 5%, reserves the remainder for surplus. What is the surplus and the dividend on 25 shares ? 707. Find the yearly income from $4214 invested in five per cents, bought at 98. 708. A sheep farmer in Texas sold his wool for 26 cents per pound, and thus realized 8^% over expenses. Had he sold the wool at 22 cents, what would have been the loss per cent? 186 ABITHMETIOAL EXERCISES. 709. A young farmer having received $3420 from his grandfather's estate, invested the money in a 6% stock purchased at 95. What yearly income was received ? 710. With brokerage J%, how much stock at 104f can be bought for $5260? 711. A Colorado land agent charged $67,825 for the purchase of 257 A. of land at 4^% commission. What was the price per acre ? 712. To secure an annual income of $3720, what sum must be invested in five per cents at 98J with brokerage 713. The owner of pine forests in Georgia shipped from Savannah to New .York a quantity of turpentine worth $ 1.75 per gallon, to the amount of $ 224. By leakage 8 gals, were lost. For what price per gallon must the remainder be sold that there may be an advance of 25% on the cost? 714. What per cent of unlawful gain will be made when 14 oz. are sold for 1 lb. ? 715. What draft may be purchased for $487.20 when exchange- is at 1^% premium? 716. Find the cost of a draft on Albany for $800, pay- able at sight, with exchange at a premium of f %. 717. In a town whose real estate is valued at $246,500, and the personal property at $88,500, and in which there are 506 polls paying 75 cents each, the sum of $2054.50 is to be raised by taxation. Find the tax of B. J. Ingersol, owning property, real and personal, to the amount of $3000, and paying for 2 polls. 718. A Maryland peach dealer invested $2397.50, the net proceeds of one summer, in five per cents at 87%, brokerage J-%. What yearly income will he receive? PERCENTAGE. 187 719. A library and library building were insured on -J of their united value for $302. Find the value of the books and the building, the policy costing $2, and the rate being 75 cents on $100? 720. At an agricultural store, a reaper which cost $40, was sold for a sum that gave the maker 128% profit, and also h^o comn^ssion to the agent. What was the selling price? 721. A druggist bought quinine at 10% discount from net price, and sold it at $18 per pound, which was 25% more than he paid. Find the net price. 722. A New Orleans merchant sent to his agent in Chicago $2000. What was the cost of the draft, exchange being 3% premium? 723. Find the face of a draft that can be bought for $158.40, exchange being at 1% discount. 724. A lumber-dealer, by the wreck of a vessel, lost \ of a cargo of 84,780 t. of white oak. What per cent must be advanced on the cost price, that he may lose nothing ? 725. A lady in Illinois inherited 45% of a lead mine, and from it received an income of $7200. Her brother owned 36% of the same mine. What was the brother's income and the value of the mine, the earnings being 16% of the cost of the mine ? 726. An upholsterer bought 70 bales of curled hair at $36 per bale, but found 10 bales so injured that he sold them at 16% discount. At what price per bale must the rest be sold to secure an advance of 20% on the purchase? 727. A lawyer charging If % for making safe invest- ments, receives from one of his clients $27,684.14 for the purchase of Pacific Kailroad stock. What amount of stock will he send to his client ? 188 ARITHMETICAL EXERCISES. 728. A lady had property insured to the amount of $2000 in a mutual insurance company. Upon renewal she received a dividend of $12.50. The premium was $25. What per cent of the premium was the dividend ? What was the rate of insurance ? 729. Samuel Eliot had a farm of 218 A. yielding a rent of $1362.50. He sold the land for $1^ per acre, and through a broker invested the proceeds in New York six per cents at 108}%, with brokerage \%. What was the change in the yearly income ? 730. The charges of an agent who purchases grain are 3% commission, and 1^% additional for guaranteeing prompt delivery. How much money must be sent to him in order that, after deducting his fees, $9000 may be left with which to buy grain ? 731. What amount of duty must be paid on plain china ware valued at $2540, on which the rate is 55% ad valorem, and 500 boxes of window glass, each containing 50 lbs., on . which the rate is 2J cents per pound ? 732. For renting a house and securing payment, the charge of an agent amounted to $56,275, of which sum $23.75 were costs, and the remainder the commission of 5% on the rent paid. Kequired the rent. 733. Jones, Jenkins & Co. import from Liverpool 80 pieces of pongee silk 40 yds. each, valued at 3 s. per yard, duty 50% ; 1000 yds. hair-cloth at 4s. per yard, duty 50% ; 500 yds. cretonne at 2J-s. per yard, duty 35% ; and Irish linen worth £30, duty 40%. Find the whole amount of duty, allowing $4.86 to the pound sterling. 734. How much 5% stock at 120 must be bought to yield an income of $720, and what will it cost? PERCENTAGE. 189 735. Isaac Ives sent to New Orleans 160 bbls. of lime to be sold at $6.25 per barrel, by an agent, on a 3% com- mission for selling. The agent paid $5.75 for cartage, and deducting 1^% for investing, bought 50 bbls. of sugar with the proceeds. What was the cost per barrel of the sugar ? 736. A florist insured his greenhouses and stock, to- gether valued at $8000, for f of their value, at 29& ; they were injured by fire to the amount of $6000. Find the florist's loss, including his premium, and the loss of the insurance company. 737. A New Orleans merchant paid $61.44 for duties at 24% ad valorem, and $20.48 for other charges on 16 pieces of linen containing 32 yds. each, imported from Dub- lin. What was the invoice value per yard, and the cost per yard, after the payment of duties and other charges ? 738. A merchant paid $46.25 for insuring the cargo of a ship at f % on -f- of its value. What was the entire value of the cargo ? 739. A note for $151.74, under date of Nov. 1, 1878, had four indorsements ; viz., April 5, 1879, $20 ; May 20, 1881, $6.20; Sept. 4, 1881, $11.84; Jan. 1, 1882, $80. What balance was due Oct. 7, 1882 ? 740. If $20,500 be invested in 6% stock at 102J, what will be the yearly income? What would be the yearly receipts, were an equal sum invested in 5% stock at par? 741. A Patterson silk manufacturer sent to his agent in Canton to buy 2500 lbs. of raw silk at $17 a pound. With an allowance oi Z^o for the agent's commission, and $315 for other charges, what must be the face of the draft for- warded to Canton ? 742. At 7y^% what time will be necessary for $1500 to gain $228.12^? 190 ARITHMETICAL EXERCISES. 743. The agent for a St. Louis wholesale grocery receives 6% on the sums received from his sales, and 4% additional at the end of the year on the net profits. His sales for the year were $30,456.50, and the net profits $10,642.35. What was his commission ? 744. A lady invested for her daughter $512.50 at com- pound interest at 8%, when the young lady was 17 yrs. 5 mos. 9 dys. old. What amount will be due at the com- pletion of the daughter's twenty-first year ? 745. A judge of probate has the care of an orphan's property valued at $4890. Will a better income be secured by investing this money in a ^i% stock at 81:J, with brokerage at -J- %, or in real estate paying 7% ? 746. A coal dealer, through an agent charging 3% com- mission, sent to Scranton for 5000 1. of coal. At $4.25 per ton, and with $157.50 for freight, what will be the gross outlay for the coal ? 747. Find the rate at which $ 75 will amount to $ 144.80, from June 6, 1870, to May 12, 1881. 748. A farmer sold some land, whose value had been injured by the erection of a dam over a stream, at a loss of $1200, which was 10% of the cost price. What sum did the farmer pay for his land ? 749. A father having received ^^ of an estate, transferred J of the legacy to his son, whose tax on the property, at the rate of 2^%, amounted to $5.50. Find the value of the whole estate. 750. Clark & Crane, wholesale grocers, sent to San Gabriel, Cal., for 3500 lbs. of grapes, invoiced at 8 J cents per pound, and 2J% on the invoiced price to the commis- sion merchant. Find the B\im -gaid by the grocer. PEECENTAGE. 191 751. A cargo of cotton was insured for $40, the rate being -J- of 1 % . What was the value of the cotton ? 752. Seth Mapes of Boston sent $10,246.50 to his agent in Chicago for the purchase of 1800 bbls. of flour, the agent's commission being 3^%. What price per barrel was paid for the flour ? 753. A government clerk bought a small house in Georgetown for $1728, giving his note and a mortgage on the house. The note was dated Jan. 1, 1884, at 6%. What was due Dec. 11, 1884, the following payments hav- ing been made ? Mar. 1, 1884, $300 ; May 16, 1884, $160; Sept. 1, 1884, $270; Dec. 1, 1884, $135. 754. A commission merchant, for selling wool at 32 cents per pound, is paid a commission of 2|%, amounting to $235.40. How many pounds were sold ? 755. A miller insures 2400 bbls. of flour worth $8 a barrel at their full value, at \%. Only 900 bbls. are saved from a destructive fire. What will be the actual loss of the company ? What premium will the merchant pay, and how much will he receive from the company ? 756. $1600. Boston, May 17, 1874. For value received, on demand, I promise to pay George Slow sixteen hundred dollars with interest. * ^ T Indorsements: Feb. 20, 1877, $228.64; Aug. 8, 1877, $70; May 16, 1878, $850.86; Oct. 4, 1878, $24. What was due Sept. 1, 1880? 757. What is the diiFerence between the true discount and the interest on $1600 for 90 dys. at 7% ? Between the bank discount and the true discount ? 758. At 122^, how much stock can be bought for $19,293.75? 192 ARITHMETICAL EXERCISES. 759. A note dated May 3, payable Nov. 3, and dis- counted at 6%, yielded $730. What was the face of the note? 760. A teacher 30 yrs. old insures his life for $ 15,000. What annual premium will he pay at the rate of $23,023 on $1000? 761. When $17,500 are the net earnings of a company with $240,000 capital, what rate of dividend will be de- clared, with a reservation of $1500 for contingencies? 762. If a 7-3^% stock be bought at 8f % discount, what rate of income will it pay ? 763. What annual income will accrue from a 6% stock bought at 94f, brokerage being \%, sum invested $28,500? 764. A Quincy merchant paid his agent in New York $16.30 for selling wheat at $1.63 per bushel on a commis- sion of 2J-%. How many bushels were sold ? 765. What is received for 116 shares of stock at 110, \% being paid for brokerage, and $3.78 for telegrams? 766. When bank stock pays a dividend of 5%, how many shares will furnish an income of $750? 767. Jeremiah Peirce imported 100 gross of Florence oil, valued at $1.20 per dozen. If 2^% were allowed for breakage, what duty was paid at 12% ? 768. A captain paid $83.50 for the insurance of f of a fishing schooner at 2-^%, the cost of the policy, $1, being included. What was the whole value of the schooner ? 769. George Peirce having invested $15,000 at par in Georgia 7s, sells at 15% discount. What will he receive if he pay ^% for brokerage, and $2.78 for other expenses? PERCENTAGE. 198 770. What is the rate when $ 1250 dividend is paid on $ 100 shares of Boston and Albany Railroad stock ? 771. Which investment will secure the better income, bank stock paying 10%, at 234 J, or railroad bonds paying 3%, at 921? 772. $1240. Syracuse, N.Y., Nov. 1, 1882. On demand I promise to pay Simon Phelps, or order, twelve hundred and forty dollars, with interest, for value received. Henry Shores. Indorsements: Received Oct. 6, 1883, $122.14; Mar. 4, 1884, $178.06; Dec. 11, 1884, $215.54; July 20, 1885, $401. Find amount due Oct. 15, 1885. 773. A bankrupts assets are $675. By a special arrangement with his creditors, he pays 75% on half his debts, and 60% on the other half. What is the amount of his debts ? 774. Stephen Fitch sold a house and lot, with the pro- ceeds of which he bought 12 Illinois State bonds of $500 each, at 12% premium, brokerage f%. What were his receipts from the sale ? 775. A country merchant bought three pieces of carpet, 190 yds. in all, for $880. Thirty yards were unsalable, and he disposed of the rest at 15% advance on first cost per yard. Did he gain or lose, and how much ? 776. Robert Cheney sold (without a broker) $50,000 of railroad bonds at 93|%, and invested such a sum in United States 6s, at 109 J, as was necessary to yield an annual income of $1920. How much money remained for the purchase of a house ? 777. At what price must 6% stock be bought, to yield 7^% on the investment ? 194 ARITHMETICAL EXERCISES. 778. $1975.60. liTKir, Jan. 11, 1883. For value received, on demand two months after date, I promise to pay Alice Dunn nineteen hundred seventy-five dollars fifty cents, with interest after two months at G^J?. George Geith. Indorsements : May 1, 1883, $600 ; June 5, 1883, $800 ; Sept. 25, 1883, $300. What is due Dec. 13, 1883? 779. George Thomas invested in four per cents, bought at such a price that he realized 3% income. What did he pay for them ? 780. A collector, receiving |-% commission, was paid $56.25 for collecting taxes. What sum did he put into the town treasury ? 781. A butcher bought 160 lbs. of meat for $9.60, and sold f of it at 8 cents per pound. At what price per pound must the remainder be sold to gain 56J% on the whole cost? 782. How much stock at 90 must be sold to pay for a legacy of $9000, on which is due a tax of 10% ? 783. Find the balance due Feb. 3, 1884, on the account which follows : Eli Sheldon, ^^ ^^^^^ q^^^_ ^^ For lumber, labor, and board, $600, with interest at 6% after Jan. 1, 1877. Five payments had been made ; viz., Feb. 16, 1877, $100; April 16, 1877, $150 ; Dec. 24, 1879, $12.50; May 3, 1880, $7.50; Nov. 3, 1882, $200. 784. An agent, after deducting a commission of 5%, sent $2625.135 to his employer. What was the amount of the sales ? 785. How much stock at 5% premium will pay for $6000 worth of stock at 8^% premium ? I I>ERCENTAGE. 195 786. An Ohio grain-merchant received $3694.95 to invest in corn, on a commission of S^%. How many bushels, at 75 cents per bushel, were bought ? 787. Find the value of a 6% stock paying 5^% interest on the amount invested. 788. A sugar planter from Louisiana invested the net proceeds of a year's crop in a certain railroad stock, pay- ing 4% semiannually. With the stock at 116^, broker- age being -|-%, what will be the yearly rate per cent of income, if 4% semiannually be considered the same as 8% per annum ? 789. A dishonest dealer wishes to lower the price of his best quality of syrup. What per cent of water must be mixed with 45 gals, of syrup, at $1.65, to reduce the price to $1.35? 790. An owner of fancy cows finds his wholesale cus- tomers unwilling to pay 4 cents per quart, the cost price, for pure Guernsey milk ; he therefore mixes so much water that he can sell the mixture at 3 cents per quart, and make 20% on his outlay. How much water is there in every quart sold ? 791. If new-made soap sells for $4.75 per hundred- weight, and in drying loses 0.12 of its weight, what is a hundredweight of the dry soap worth ? 792. A St. Louis broker invested $10,000 in three per cents at 75, and when they rose to 78, he sold that stock, and bought bonds at $208 which paid 8%. What was the change in income ? 793. A druggist bought a stock of goods for $1643.50 cash. For what sum must his note be made, payable in 90 dys., that, when discounted at 6%, the proceeds shall yield the amount required ? 196 ARITHMETICAL EXERCISES. 794. The sugar-beet yields 6% of its weight in sugar. One acre of land will produce 25,000 lbs. of beet-root, worth $2.75 per ton. How many acres of land are needed to supply with beet-root a sugar factory whose annual produc- tion of sugar is 100,000 lbs., and what is the value of the beet-root supplied ? 795. Crystallized blue vitriol is composed of 63.3 parts, by weight, of copper, 32 parts of sulphur, 80 parts of oxy- gen, and 90 parts of water. Find its percentage composi- tion. How much copper is there in 200 lbs. of blue vitriol? 796. Two coal-dealers in Pittsburg sold an equal amount of coal. One received from a Boston merchant $6200 on the delivery of the coal ; the other took a note for $ 6800 for 2yrs. 6 mos., without interest, from a New York banker. If money commands 7%, which dealer received the greater price for his coal ? 797. $14,400 in 3% United States bonds at 101 J are transferred into a 4^% railway stock at 125J, the expenses of the operation amounting to $50.98. Find the alteration in the income produced. 798. Find the net cash amount of a bill of $750, dis- counts being -J^, 25, and 17^, and an additional discount of 5% for cash. 799. A milkman gains $1401.60 in 1 yr. by selling milk at 8 cents per quart. He sells on an average 42 gals, daily. What is his rate of profit per cent ? 800. A milkman gains $2102.40 in 1 yr. by selling milk at 8 cents per quart. He sells on an average 48 gals, of milk every day. What is his rate of profit per cent ? 801. A man has a sum of money due him at the end of 4 yrs., simple interest being reckoned at 5%. What frac- tion of the sum could he take off for payment at once ? PERCENTAGE. 197 802. Three pipes carry water into a tank. The first running alone can fill it in 4 hrs., the second in 5 hrs., and the third in 6 hrs. How long will it take them to fill the tank if they run together ? 803. A man has a bill for $1353.60 due him at the end of 4 yrs. Find what sum he could take for cash payment, simple interest being reckoned at 5%. 804. A vessel has a leak which admits 127-J gals, of water in 3 min. The pumps are just able to remove 209if' gals, in 5 min. Can the pumps keep the amount of water in the vessel from increasing? 805. A good harness oil is composed of f suet, -J- lard, ■J- turpentine, -I- beeswax, and the rest olive oil. Find the cost of 1 lb. of this oil, if the suet costs 12 cents per pound, the lard 19 cents, the beeswax 45 cents, the turpentine IdJ- cents, and the olive oil 28J- cents. 806. Reduce y|4jj to its lowest terms. 807. If a loaf weighing 4^ lbs. be sold for 6 cents when wheat is 72 cents per bushel, what should be the price of 150 lbs. of bread when 8 bu. of wheat bring $8.64? 808. One pipe can fill •§■ of a vessel in 1 hr. Another pipe can empty f of it in 3 hrs. If the vessel be empty, and both pipes are opened, in what time will the vessel be full? 809. A clock which gains 7-J- min. in 24 hrs. is 12 min. fast at midnight on Sunday. What o'clock will it indicate at 4 o'clock on Wednesday afternoon ? 810. At what point must the hands of a clock be placed at noon to indicate the true time at 7.30 p.m., if there be a daily gain of 3J min. ? 198 ARITHMETICAL EXERCISES. 811. A reservoir 10 ft. deep contains water to the height of 2 ft. It is supplied with water by a pump which could fill it if empty in 5-^ hrs. The water is taken from the reservoir by another pump, which is capable of empty- ing it, when full, in 9-| hrs. If both pumps are set in action, in what time will the reservoir be completely full of water ? 812. A steam pump, employed to raise water to a reser- voir, will fill the reservoir in 10 hrs. 25 min. when it works well. One day the efficiency of the pump was reduced ^ by an accident, just as the reservoir was -J- full. How long did it take the pump on this occasion to fill the reservoir ? 813. If $480 amounts to $648 in 10 yrs. at simple interest, what would $24,000 amount to in 20 yrs. at the same rate ? 814. A grist mill has 3 mill-stones. The first stone can grind 5 bu. of corn in 2 hrs., the second 10 bu. in 3 hrs., and the third 15 bu. in 4 hrs. How many bushels can all three grind in 1 hr. ? How many hours will it take them to grind 460 bu. ? 815. By selling out 3% bonds at 102f, and investing the proceeds in a railway stock which pays an annual divi- dend of 7%, a man finds that he can double his income. What is the price of the stock ? 816. A fountain can fill a fish basin in 2J- hrs. Another fountain can fill it in 3 hrs. If the basin is dry, and both fountains are turned on, in what time will it be f full ? If the basin holds 15,000 gals., how many gallons will each fountain empty into it in 1 min. ? 817. The weight of the water contained in a rectangular cistern 8 ft. long and 7 ft. wide is 93f cwt. of 112 lbs. each. What is the depth of water in the cistern if a cubic foot of water weigh 1000 oz. ? PERCENTAGE. 199 818. A ship 40 mi. from the shore springs aleak, which admits 3|- 1. of water in 12 min. 60 1. would suffice to sink her, but the ship's pumps can throw out 12 t. of water in an hour. Find the average rate of sailing, that she may reach the shore just as she begins to sink. 819. Two fountains empty into the same basin. The first can fill it in 3 hrs. and the second in 6 hrs. The first is allowed to play alone for 1 hr., and then the second for 1^ hrs. Both fountains are then turned on. In what time will the basin be filled ? 820. A certain district contains a rural' population of 3789 and a town population of 2364. Among the rural population, the births are 31 per thousand annually, and the deaths 25 per thousand. Among the town population the births are 42 per thousand, and the deaths 30 per thousand. What is the annual increase or decrease of the whole population ? 821. A dealer bought 2 horses giving ^ as much for one as for the other. He sold the more expensive horse at a gain of 15%, and the other at a loss of 5%, receiving $715.20 for both horses. What did he pay for each horse ? 822. In Fahrenheit's thermometer the freezing-point is marked 32°, the boiling-point 212°;. in the Centigrade the same points are respectively 0° and 100°. Express 4° C. in Fahrenheit's scale, and 62° F. in the Centigrade scale. 823. A certain zinc ore yields 55% of metallic zinc, and a certain copper ore yields 25% of metallic copper. In making brass from those two metals 5% of the metal is wasted, and the coals and labor cost as much as the metal. The zinc ore is worth $43.20 per ton, delivered, and the copper ore $81.60. What is the net cost per ton of brass consisting of a mixture of equal parts of the two metals ? CHAPTER VL PROPORTION. Miscellaneous Exercises (illuBtrating the applications of the Rule of Three). 1. Find a fourth proportional to 3, 15, 7. 2. Find a number which has the same ratio to 21 that 45 has to 9. 3. A's wealth is to that of B as 3 to 7. B is worth $ 63,000. What is A worth ? 4. In five years the population of a mining town increased from 200 to 16,000. If the rate of increase remain the same, what will the population be after five years more ? 6. If 75 men can do a piece of work in 12 dys., how many men could do it in 20 dys. ? 6. What must be paid for 12 lbs. of indigo, when 7 lbs. cost $12.75? 7. If twelve men reap a field in 4 dys., what time would be required for 32 men to reap it ? 8. A ship performs a voyage in 63 dys., sailing at the rate of 6 knots an hour. How long would it take her if she sailed 7 knots an hour ? 9. A milkman having failed, settled his accounts, and found he had property to the amount of $215, while he owed $1075. If his creditors demand immediate payment, how much will they receive on a dollar ? PROPORTION. 201 10. A gentleman gave to his daughter on her marriage ipl500, which was ^ the value of his interest in a silver mine. To his son he gave a sum equal to ^ of the same in- vestment. What amount was received by the son ? 11. A bankrupt's debts are $2520, and his assets over and above all expenses are $1890. What can he pay on a dollar ? 12. If 4 men reap a field in 6 dys., how many days will one man require for the same work ? 13. An English clergyman pays an income tax of £6 12 s. 6 d. on a £265 income. What is the tax on £1 ? 14. If $ 15.12 is paid for a bag of coffee weighing 56 lbs., what will 78 lbs. cost ? 15. How many cabbages can be planted on 25 sq. rds. of land, each plant occupying 180 sq. in. ? 16. If a train travel at the rate of 30 mi, per hour, how many feet does it pass over in a second ? 17. A cow gives 2408 qts. of milk in a year. How many gallons will 57 cows give, at the same rate ? 18. How much tea at 92 cents a pound must be given in exchange for 13 rugs at $6.90 each? 19. How many times can a three-peck measure full of corn be emptied into a bin which holds 8 J bu., before it will be full ? 20. If a wheel revolve 49,280 times in passing over 133 miles, what is its circumference ? 21. A stable-keeper bought 288 bu. of oats. How long will they supply 8 horses, if each horse eats 6 qts. a day ? 22. One of the wheels of a machine makes 91 revolu- tions in 3f sec. How many revolutions will it make in 5f hrs. ? 202 ARITHMETICAL EXERCISES. 23. How many dessert spoons, each weighing 2 oz. 3 dwt. 6 gr., can be made from 6 ingots of silver, each weighing 19 oz. 9 dwt. 6 gr. ? 24. If a field containing an acre and a half produces 180 bu. of potatoes, what yield may be expected from an adjoin- ing field which contains 5 A. 32 sq. rds. ? 25. A spring of water which yields 250 gals, an hour supplies a town containing 360 families. What is the aver- age daily supply for each family ? 26. What is the circumference of a wheel which makes 31,680 revolutions in passing over 87 mi. ? 27. If a dozen teaspoons weigh 10 oz. 12 dwt. 15 gr., how many can be made from an ingot of silver weighing 6 lbs. 5 oz. 19 dwt. 6 gr. ? 28. Three men, A, B, C, put a certain sum of money into business. A put in f of the sum, B f, and C the rest. In winding up the business, they found that the original sum had increased by exactly one-quarter, and now amounted to $60,500. Find each man's share of the profit. 29. A town in Massachusetts, divided into three school districts, pays a school tax of $4212. The property in District No: 1 amounts to $24,700; in No. 2, to $37,250; in No. 3, to $43,350. What school tax is paid by each district ? 30. In 1880 the Austrian Lloyds possessed 72 steamers, having a total of 17,100 horse-power. What was the aver- age horse-power per steamer ? 31. At 6% , what will be the interest on $130 for 8 mos. ? 32. A man bought a field containing 7 A. 4295 sq. yds., and divided it into equal lots, each containing 16 sq. rds. 25 sq. yds. How many lots were there ? PROPORTION. 203 33. In what time will $160 gain $37.50, interest at 6% ? 34. Light travels 184,000 mi. a second. How long does it take it to travel from the sun to the earth, assuming the distance to be 92,600,000 mi. ? 35. Provisions for 9 mos. have been furnished to a force of 2100 men. Before any of the provisions are used, a re- inforcement of 600 men is received. How long will the supply of food last ? 36. Find the value of f of a ship, if -J of it is worth $3264. 37. A man paid $2 for the hauling of 1200 lbs. of coal 36 mi. At the same rate, how many pounds could be car- ried 24 mi. for the same sum ? 38. How long would 4 horses be in eating 48 bu. 3 pks. of oats, at the rate of 6 qts. per day for each horse ? 39. If 2^ yds. of cloth cost one guinea, what must be paid for 183^ yds. of the same material ? 40. A man travels 540 mi. in 24 dys. by walking 6 hrs. a day. How many miles will he travel in 3 dys., if he walk 8 hrs. a day? 41. A young man in college spends $15.40 of his allow- ance every 35 dys., and saves $100 per year. What is his yearly allowance ? 42. A professor at Oxford paid £15 7 s. 6 c?. income tax at the rate of 6 d. to the pound. What was his income ? 43. The shadows cast of objects at a given instant vary directly as their heights. If a staff 6 ft. high cast a shadow 7 ft. long, how high is a tree whose shadow is 112 ft. long? 44. If a tower 36 ft. high cast a shadow 48 ft. long, what is the height of a mast casting a shadow 288 ft. long? 204 ARITHMETICAL EXERCISES. 45. If ^ of I of a cargo of raw silk be worth $4000, what will be paid for -J of -^ of the cargo ? 46. Seventy-two men dig a ditch in 63 dys. In how many days will 42 men perform the same work ? 47. One dozen silver spoons, weighing 3f oz. each, are valued at $13.50. What will be the cost of a silver tank- ard weighing 1 lb. 10 oz. ? 48. If a man can do a piece of work in 32 dys., by work- ing 10 hrs. a day, how many days will it take him to do the same piece of work if he works 8 hrs. a day ? 49. If I of a yacht be worth $9600, what will J of it cost? 50. If 8 cwt. of sugar cost $48, what will 74 cwt. be worth? 51. If the fare for 165 mi. be $4.29, what would it be for 630 mi. ? 62. If 24 lbs. of rice cost $1.02, what will 112 lbs. cost? 53. If 4 men do -J- of a piece of work in 15 dys., how many men will be required to finish it in 12 dys. ? 54. If a man spend $4453 in a year, how much will he spend in 117 dys. ? 55. If 11 lbs. of rags will make 8 lbs. of paper, how many pounds of rags are required to make 585 lbs. of paper ? 56. If 36 lbs. of flour will make 45 loaves of bread weighing 1 lb. each, how many such loaves can be made from 56 bags of flour weighing 19^ lbs. each? 57. A London merchant owes £ 3057 12 8, ; the net value of his assets are £2675 8 s. What will a creditor receive to whom he owes £ 100 ? PROPORTION. 205 58. If 12 rolls of paper 2 ft. wide will paper the walls of a certain room, how many rolls -J of a yard wide would be required ? 59. How many yards of lining -f of a yard wide are required to line 16 yds. of cloth | of a yard wide ? 60. A bookseller receives 91 volumes of a certain work, The price of the book is $3.20, but for every dozen taken one is allowed free of cost. What did the books cost him ? 61. A man sold a house lot so that he received for it $412.68. He thereby gained just 14%. What did the lot cost him ? 62. If a man can do a piece of work in 9^ dys. of 8^ hrs. each, how many hours per day must he work in order to do the same amount in 7^ dys. ? 63. If velvet ^ of a yard wide cost $9 per yard, what should be the price when it is |^ of a yard wide ? 64. If 39 yds. of silk f of a yard wide will make a cer- tain number of neckties, how many yards f of a yard wide would make the same number? 65. If an express train passes over 55 mi. in 53 min., how far would it go at the same rate in 2 hrs. 39 min. ? 66. One workman is paid f of the wages of another. How much will the second earn while the first earns $138 ? 67. If 7 men can do a piece of work in 13 dys., how long will it take 9 men to do the same work ? 68. Divide 90 into two parts proportional to 4 and 6. 69. Divide 300 into two parts such that the first may be to the second as 2 to 5. 70. Divide 780 into parts proportional to the numbers 3, 5, and 7. 206 ARITHMETICAL EXERCISES. 71. A bell-founder receives an order to cast a bell weighing 1000 lbs., and containing 77% copper, 21% tin, and the remainder zinc. How many pounds of each metal are required ? 72. Two men hire a pasture for $50, and pay $3.55 for repairing the fence. One man puts 20 horses into the pas- ture for 1'2 wks., and the other 15 horses for 18 wks. What ought each man to pay ? 73. A merchant goes into bankruptcy. His assets were $21,380, his liabilities $91,000, and expenses of settlement amounted to $3180. How much will his creditors receive on the dollar, and what sum will a creditor receive to whom the merchant owes $ 6200 ? 74. A man dies owing three creditors $8050, $2970, $7170, respectively. His assets, deducting all expenses, amounted to $13,646. What will each creditor receive, and also what per cent of his just dues ? 75. Divide 264 into three parts which shall be as the numbers ^, |, f . . 76. Divide 1270 into parts proportional to the numbers 3, ^, 5i, 6^. 77. Throe heirs receive from an estate, one $4700, an- otKor $3200, and the third $12,500, on condition that they together pay c debt of $2000. What amount net will each h:ir receive? 78. Four men engage in c business where the profi": is $ 1200. How much of it should each man receive, if the first man put in $3000, the second $5000, the third $4200, and the fourth $2400? 79. A merchant goes into bankruptcy with liabilities $ 40,000, and assets $ 24,000. What can ho pay on a dollar, the expenses of settlement amounting to $ 1800 ? PROPORTION. 207 80. A wine ioaerchant put into an empty cask 15 qts. of brandy costing him $1.10 per quart, 66 qts. costing $1.20 per quart, and 43 qts. costing $1.40 per quart. What must be his selling price per quart in order to clear 20% ? 81. A grocer mixes 120 lbs. of tea costing 50 cents per pound, with 180 lbs. costing 40 cents per pound. At what price per pound must he sell the mixture in order to make $80 on the whole? 82. Flint glass is composed usually of 72% sand, 14% soda, 12% lime, and 2% alumina. How much of each of these substances is there in 10,000 lbs. of flint glass ? 83. A master carpenter employs 7 men at $3.10 per day, 6 at $2.80, and 5 at $2.50. What is the average daily wage of the men ? 84. If 10 men can reap a field of 7-J- A. in 16 dys. of 9 hrs. each, how many men are required to reap a field of 4J- A. in 9 dys. of 12 hrs. each? 85. If 6 men can do a piece of work in 4 dys., how many more men must be employed to finish it 1 dy. sooner ? 86. What length has the same ratio to 1 ft. 7-J in. that 17| mi. has to 6 mi. 143 yds. ? 87. If 5 men earn $56.64 in 12 dys., how much will 18 men earn in 20 dys. ? 88. A grocer buys two kinds of tea wholesale at 20 cents per pound, and 28 cents per pound, respectively, and mixes them in the ratio uf 5 to 3. What is his profit if he sells 56 lbs. of the mixture at 42 cents a pound ? 89. If 8 men can excavate 12,000 cu. yds. of earth in 36 dys. of 10| hrs. each, how many men will be required to excavate 8750 cu. yds. in 21 dys. of 7 hrs. each? 208 ARITHMETICAL EXERCISES. 90. If a man travel 360 mi. in 12 dys. of 8 hrs. each, how many hours a day must he travel to accomplish 450 mi. in 20 dys. if he increase his rate 20 % ? 91. If 102 knives are worth 163 forks, how many forks are worth 94 knives ? How many knives are worth 1000 forks ? 92. How many boys, each doing f of a man's work, must be engaged with 14 men to do in 24 dys. what 12 men could do in 36 dys. ? 93. A garrison of 6000 men provisioned for 179 dys. is, after 8 wks., diminished by 2000 men. How long will the food last the remainder of the garrison ? 94. A cup weighs 9^ oz., and is composed of gold and silver in the proportion of 15 to 1. What is the weight of each metal in the cup ? 95. If 10 men can reap a field of 7^ A. in 16 dys. of 12 hrs. each, how many hours a day must 8 men work to reap a field of 4^ A. in 9 dys., if they can work 20 % faster than the former men ? *'96. A can do 30 % more work in a day than B. How long will B take to do a piece of work which A can do in 4 dys. ? 97. If 15 men working 10 hrs. a day dig 450 yds. of a ditch in 18 dys., how many men will be required to dig 480 yds, in 8 dys., working 8 hrs. a day? 98. A grocer mixes 100 lbs. of tea which cost him 34 cents a pound with 27 lbs. of tea which cost him 60 cents a pound. He then sold the mixture at 49 cents a pound. How much did he make on the whole amount? 99. If 6 men can earn 1 97.20 in 21 dys. of 12 hrs. each, how much can 4 men earn in 35 dys. of 10 hrs. each? PROPORTION. 209 100. If 5 weavers can earn $152 in 18 dys., and 3 weavers can earn as much as 4 spinners, how much will 3 spinners earn in 24 dys. ? 101. If 4 loads of hay will serve 6 horses for 8 wks., how many horses will 5 loads serve for 5 wks. ? 102. If 27f mi. are travelled in 2| hrs., how long will it take to travel 11|^ mi. ? 103. If 32 meters equal 35 yds., how many meters are there in 56.35 yds. ? 104. If 32 meters equal 35 yds., and a brass rod 1.5 me- ters long weighs 19 lbs. 11 oz., find the weight of an inch of this rod. 105. If 7 men in 25 dys. of 10 hrs. each earn $219, how many hours a day should 12 men work to earn $262.80 in the same number of days ? 106. If a man can do -^^ of a piece of work in a day, how long would he take to do f of a piece of work 5^^ times as much in amount, if he work 1-J times as fast as before, but only ^ as long each day ? 107. Gun metal is composed of 11 parts of copper to 2 parts of tin. How much tin must be added to 209 lbs. of copper to make gun metal ? 108. A garrison of 1500 men has just provisions enough to allow 26 oz. of bread a day to each man for 38 dys. If the garrison is increased by 400 men, how much bread must be assigned to each man, in order that the provisions may last for 65 dys. ? 109. If 5 men and 8 boys can hoe 50 A. in 11 dys., working 10 hrs. a day, how long would it take 21 men and 15 boys to hoe 558 A., working 11 hrs. a day, supposing a boy does | the work of a man ? 210 ARITHMETICAL EXERCISES. 110. Three towns, A, B, C, agree to drain an unhealthy swamp, and to raise for this purpose $23,000, each town to contribute accprding to its population. If the numbers of inhabitants are 4995, 6993, and 10,989, respectively, what sum of money must each town raise ? 111. What can a bankrupt who owes $28,500, and whose assets are only $11,400, pay on a dollar? 112. Divide 1170 into three parts, such that the first shall be to the second as 2 to 3, and the second shall be to the third as 3 to 4. 113. A man dying left $7200 to be divided among three poor families according to the number of children in the families. The respective numbers being 6, 4, and 2, what sum will each family receive? 114. What per cent profit is made by buying a horse for $190 and selling him for $218.50? 115. If 4 men or 7 boys can do a piece of work in 6 dys., how long will it take 6 men and 9 boys to do it ? 116. If it requires 5600 lbs. of manure of a certain kind to fertilize a field of 7 A. properly, how much manure 20% richer than the former will be needed for a field of 4 J A. ? 117. An alloy of •§• copper, -^ zinc, and -J- nickel formi a substance strongly resembling silver. How much of each metal is there in 1000 lbs. of the alloy ? 118. By walking 8 hrs. a day a man performed the journey from Albany to Niagara in 18 dys. What time would have been required had he walked 12 hrs. daily ? 119. A shadow 5 ft. 8 in. long is cast by a pole 6 ft. high. What is the height of a spire that throws a shadow 156 ft. long at the same hour of the day ? PHOPORTION. 211 120. A tank containing 6000 gals, leaks 1 gal. 2 qts. in one minute. In how long a time will it be emptied ? 121. When $600 will earn $30 in 6 mos. 6 dys., how much will the same sum earn in 8 mos. 12 dys. ? 122. A young man borrowed of a friend $7000 for 40 dys. For how long a time should the young man lend this friend $1750 to return the favor ? 123. A piece of lining material 1\ yds. wide will line 35 curtains. How many curtains will be lined by a piece of the same length 2J yds. wide ? 124. When gold stood at 110, a clerk's salary paid in gold was worth $3570 in currency. What was the value of the salary in currency, with gold at 125 ? 125. A ship with a crew of .40 men had provisions for 3 mos. If the crew were reduced to 32 men, how long would these provisions last ? 126. The floor of a drawing-room is covered by 40 yds. of carpet 1 yd. wide. How many yards of carpet f of a yard wide would cover the same floor ? 127. If 32f yds. of raw silk 20 in. wide will make a portiere, how many yards of material 15 in. wide will be necessary ? 128. If in working capacity 6 men are equal to 7 women, and 8 women to 11 boys ; and if 5 men can do a piece of work in 10 hrs., how long will it take 1 man, 2 women, and 3 boys together to do the same piece of work ? 129. A paper company consisting of three partners has to expend $ 530 in repairs. The partners have invested in the business, respectively, $2500, $3000, $4200. What sum must each partner pay ? 212 ARITHMETICAL EXERCISES. 130. If the rent of 3 A. for ^ of a year be $4, what will be the rent of 40 A. for 1 yr. ? 131. The two large wheels of a tricycle are 6t ft. in cir- cumference, and make 3000 revolutions in going a certain distance. How many revolutions will the small wheel, 5 ft. in circumference, make in going the same distance ? 132. A certain quantity of coal will last 700 families 7 mos. ; how long will it last 1600 families ? 133. The interest *on a certain sum at a given rate for 4 yrs. is $63.40. What will be the interest for 8^ yrs. on the same principal at the same rate? 134. For 6 yrs. at 4%, on $964.75 the interest is $231.54. What will be the interest at 6% on the given principal for the same time? 135. If $6.03 interest is paid on $67 for a certain time and rate, what principal will yield $30.15 under the same conditions ? 136. If a bushel of flour make 52 ten-cent loaves of bread, what should be the price per loaf when 60 loaves are made from a bushel ? 137. If 8 cows eat 7 bu. of carrots in 9 dys., how many bushels will 17 cows eat in 12 dys. ? 138. By travelling 8 hrs. per day for 10 dys., a man performs a journey of 200 mi. Were he to travel 12 hrs. per day, how many days would be required for a journey of 300 mi. ? 139. If a baker can make 135 lbs. of bread with 180 lbs. of flour, how many pounds can he make with 920 lbs. of a kind of flour which will yield only -J-J- as much bread as the first? PROPORTION. 213 140. If it takes 288 lbs. of meal to last 7 horses 4 dys., how many pounds will support 27 horses 13 dys. ? • 141. A dry goods dealer paid $15,697.50 for 39 pieces of carpeting, each containing 175 yds. What should he pay for 78 pieces, each containing 180 yds., and the quality being better in the ratio of 15 to 14 ? 142. If 50 men working 9 hrs. a day require 6 dys. to dig a trench 100 yds. long, 2 yds. wide, and 3 yds. deep, how many men working 10 hrs. a day for 9 dys. will be required to dig a trench 50 yds. long, 6 yds. wide, and 5 yds. deep, at a place where the earth is twice as hard to handle ? 143. Three men engage in trade for 4 yrs. The first put in $5200, but withdrew it after 4 mos. The second put in $7000, and withdrew it after 1 yr. 8 mos. The third put in $8600 for the whole time. The profit amounted to $68,833. How should it be divided? 144. Two capitalists contribute, one $ 10,000, the other $12,000, to an enterprise which continues in operation for 10 yrs. ; 10 mos. after starting, a third man becomes a partner, and contributes $ 15,000, and 2 yrs. after this, a fourth man puts in $17,400. The total profit was $45,600. Find the share of each man. 145. An. alloy of f copper, -^ zinc, and the rest tin forms an alloy strongly resembling gold. How much of each of the metals is there in 1000 lbs. of the alloy ? 146. How many acres of wheat can be harvested in 3 dys. by 16 men, if 40 A. are harvested by 12 men in 9 dys. ? 147. If a twelve-cent loaf weigh 40 oz. when flour is $8 per barrel, what will be the weight of a five-cent loaf when flour is worth $6 per barrel? 214 ARITHMETICAL EXERCISES. 148. If $100 gain $2 in 3 inos., what sum will gain $4.40 Tn 11 mos. ? 149. How much will $103 gain in 12 mos., if $600 gain $45 in 18 mos.? 160. If 16 sheep eat 37 bu. of potatoes in 27 dya^ how many bushels will 74 sheep eat in 63 dys. ? 151. A garrison of 1500 men has provisions for 12 wks., at the rate of 20 oz. per day to each man. How many men will the same provision support 20 wks., if 8 oz. per day are allowed to each man ? 152. For 5 days' work, 8 men are paid $40. At the same rate, how much should 32 men receive for 24 days* work ? 163. How many horses will be required to draw 132 t, of hay in 18 dys. to a railroad station, if 12 horses draw 44 t. in 5 dys. ? 154. Find the wages of 9 workmen for 12 wks., if each man receive $1.80 per day. 165. If $2415 be a man's tax at the rate of 2^% on $1, what is the rate on $ 1 when his tax is $3078.75? 156. On a certain railway line the telegraph posts are placed 58 yds. apart, and a passenger counts as he passes 37 in 2 min. At what rate per hour is he travelling? 157. A tailor engages to furnish suits for 330 children. The cloth cost $2640. The buttons, etc., for each suit cost $ 1.40. If he wishes to make a profit of $ 1.20 on each suit, how much must he charge for each suit ? 158. Hay costs $22 per ton, and oats cost 60 cents per bushel. If one horse eat daily 25 lbs. of hay, and 10 qts. of oats, what will be the expense of keeping 5 horses from Dec. 1, 1883, to April 1, 1884? PROPORTION. 215 159. A man spent \ of his money, then ^, then J. He then had left $ 10.65. How much had he at first ? 160. If a canary bird eat 1 qt. of seed which costs 15 cents, in 3 mos., how much will it cost to keep 2 birds 1 J yrs. ? ^ 161» I count 16 ticks of my watch between the instant of seeing a flash of lightning and that of hearing the report. At what distance is the thunder cloud, if sound travels 1056 ft. a second, and my watch ticks 128 times each min- ute, assuming that light passes from one place to another instantaneously ? 162. I paid $200 for 135 yds. of cloth. With the same sum, how many yards could I have obtained of a cloth 3 yds. of which are worth 5 yds. of the kind purchased ? 163. Mary and Sarah can accomplish a given amount of sewing in 6f dys. ; Mary and Lucy can perform the same work in 4|^ dys. ; Mary, Sarah, and Lucy in 3| dys. How many days will Mary alone need for it ? 164. If a man in pacing steps 3 ft. at a time, how many rods will he go in taking 184 steps ? 165. If a teacher spend 30 min. each day on the classes in mental arithmetic, how many hours will be spent in a term of 12 wks. of 5 dys. each ? 166. The mean distances of the great planets in miles from the sun are as follows : Mercury, 35,393,000. Jupiter, 475,693,000. Venus, 66,131,000. Saturn, 872,135,000. Earth, 92,600,000. Uranus, 1,753,851,000. Mars, 139,312,000. Neptune, 2,746,271,000. If the distance of Mercury is represented by a line 1 ft. long, find to the nearest inch the lengths which will repre- Bent the oth^r distances, 216 AEITHMETICAL EXERCISES. 167. Railway companies almost always use for ties or sleepers young trees large enough to make only one tie for each cut. Trees of this size will not average more than two cuts each. Assuming 60 of these trees to the acre, the average distance apart of ties to be 2 ft., and the number of miles of track in the country to be 112,000, how many acres of woodland would be required to furnish all the ties? 168. The average duration of railroad ties has been found to be 7 yrs. Assuming the data in the last question, find how many ties are required each year for keeping the roads in repair, and also how many acres of woodland must be devoted to this purpose. 169. Assuming that it takes 30 yrs. for trees to grow to the size requisite for furnishing ties, how many acres of woodland are necessary to keep up the supply of ties for the existing rtTdds ? How many square miles of 640 A. each? 170. A vessel can be filled in 57 min. by one pipe which discharges 6 gals, a minute, and emptied in 38 min. by another. How many gallons a minute does the second pipe discharge? In how many minutes would the vessel be emptied if full, and both pipes were opened at the same instant ? 171. A bookseller supplies the scholars of a town with penSj penholders, and paper. He charges 10 cents per quire for paper, 3 cents apiece for penholders, and 5 cents for 6 pens. He pays $1.60 per ream for the paper, 25 cents per dozen for the penholders, and 75 cents per box for the pens, each box containing 12 doz. pens. What is his profit for 1 yr., if he sells 80 reams of paper, 60 doz. penholders, and 30 boxes of pens ? PROPORTION. 217 172. If there are 360 scholars in the town referred to in the last example, how many pens and penholders, and how much paper, does each scholar on the average use dur- ing the year? 173. A salt-dealer put up 56,000 lbs. of salt in 20-lb., 10-lb., and 5-lb. boxes, using of each size the same number. How many boxes of each size were there ? 174. Six men can reap a field 200 yds. long and 150 yds. wide, in 4 dys. of 12 hrs. each. In how many days of 10 hrs. each will 8 men reap a field 300 yds. long and 250 yds. wide ? 175. If a piece of work can be finished by 5 men in 12 hrs., or by 4 boys in 20 hrs., how much time will be required to perform the same work by a man and a boy working together ? 176. The interest on $24 for 5 yrs. at 4% is $4.80. What interest will accrue on $360 in 4i yrs. at 6% ? 177. In 6 yrs. at 5% £825 interest will accrue on £2750. At what rate will £ 1160 interest accrue on £3625 in 8 yrs.? 178. In 3 yrs. at 4i% $364.50 interest is paid on $2700. In what time will $8825 yield $2294.50 at 4% ? 179. $2675 principal at 4% in 3 yrs. yields $321 inter- est. What principal will yield $93 at 5% in 7| yrs. ? 180. With the understanding that a boy can perform only half the work of a man, how many hours per day must 42 boys work to accomplish as much in 45 dys. as 27 men would accomplish in 28 dys., working 10 hrs. per day? 181. A farmer can plant a field of corn in 8 dys. When his son works with him the work can be accomplished in 5 dys. In what time would the son alone perform the work? 218 ARITHMETICAL EXERCISES. 182. A German laborer can harvest a crop of oats in 7 dys., an Irishman in 6 dys., and a Chinaman in 5 dys. If the German and the Irishman work together for 2 dys., and then the Chinaman join them, in how many days will the remaining portion of the work be completed ? 183. Twenty horses working 14 wks., 6 dys. in the week and 8 hrs. a day, transport a certain quantity of coal from a mine to the nearest wharf. In how many weeks will 24 horses do the same work, if they be on the road 5 dys. in the week and 7 hrs. a day ? 184. Divide 60 into two parts proportional to 11 and 9. 185. A lady divided $2500 between her four children so that their respective portions, beginning with the oldest, were as the numbers 2, 3, 7, and 8. What was the share of each ? 186. Gunpowder is made of 75 parts of saltpetre, 10 of sulphur, and 15 of charcoal. How many pounds of each are contained in 1344 lbs. of gunpowder ? 187. Twelve women or 18 girls can make f of a dozen shirts in 6^ hrs. How much time must be allowed for 11 women and 9 girls to finish the remainder of the dozen ? 188. Three men engaged in a business in which the profit for one year amounted to $1275. What share of the profit is due to each man, if the respective amounts of capital which they furnished are as the numbers 3, 5, and 7? 189. If 3 mules are worth 5 sheep, what must be paid for 20 mules, when 4 sheep cost $17? 190. Three brothers having been together in business for one year, divide their gain, $837, in the proportion of }, -J, and }. What sum falls to the share of each ? PROPOETION. 219 191. Two neighbors in Florida carry on a fruit business, one furnishing $40 for 3 mos., and the other $75 for 4 mos. The profits are $ 70. Find the gain of each. 192. Express a speed of one mile per hour in terms of feet per second. 193. Three Frenchmen opened a restaurant in San Francisco, furnishing respectively $500 for 7 mos., $600 for 8 mos., and $900 for 9 mos. The profit is $410. What is the gain of each ? 194. Five workmen working together finish a piece of work in 20 dys. and receive as pay $260.75. One of the men was absent 5 dys. and another 2 dys. The foreman is to receive 25 cents per day more than the others. What was the portion of each man ? 195. If 120 men can make an embankment f of a mile long, 30 yds. wide, and 7 yds. high, in 42 dys., how many men would it take to make an embankment 1000 yds. long, 36 yds. wide, and 22 ft. high, in 30 dys. ? 196. Two men agree to do a piece of work for $63. They finish the work in 18 dys. ; but one of them was absent 5 dys. of this time on account of sickness. How should the pay be divided ? 197. Gilbert and Dan can hoe a piece of corn in 14 dys., Gilbert and Ernest can hoe it in 12 dys., Dan and Ernest in 15 dys. In what time can the work be done by the three working together ? 198. Three herdsmen hired a pasture to be used in com- mon, and paid $26.50. One put in 10 oxen for 3 mos. ; another, 12 oxen for 4 mos. ; and the third, 14 oxen for 2 mos. What rent should each pay ? 220 ARITHMETICAL EXERCISES. 199. The sum of the lengths of the three sides of a tri- angle is 480 yds., and these sides are as 3, 4, 5. What is the length of each side ? 200. In time of war 1921 men are to be quartered upon 4 towns whose respective populations are 4150, 12,450, 24,900, 29,050. How many men according to the popula- tion should be assigned to each town ? 201. 8% is lost by selling a roll of carpet for $38.64. What per cent would be gained by selling it for $57? 202. A manufacturer having in his employ 6 men, 7 women, and 14 boys, paid them all together in one month $ 52, in such proportion that each woman received -f- of the sum paid each man, and each boy received f of the sum paid each woman. Find the amount received for the month by the men, the women, and the boys. 203. Twenty-five lamps used 5 hrs. every evening for 20 dys. require a quantity of oil that costs $2,125. How many lamps used 4 hrs. every evening for 30 dys. can be furnished with oil at a cost of $ 7.65 ? 204. Five men and 7 boys can reap a field of rye con- taining 125 A. in 15 dys. In how many days will 10 men and 3 boys reap a field of 75 A. if the work of a boy be half that of a man ? 205. The money that will pay the wages of Henry Wads worth 61 i dys. will pay the wages of Milton Rogers 81 1 dys. For how many days will the same sum pay the wages of the two men ? 206. A New York iron-merchant sold a quantity of car rails for $1391 at a gain of 7%. Had the rails been sold for $1235, what would have been the gain or loss per cent? PROPOETION. 221 207. A tract of government land of 200 A. is to be divided among 4 soldiers according to the pensions received by each. If these pensions were respectively $500, $360, $800, and $90, what number of acres should each have? 208. Gerard Fiske and Hezekiah Wells together spend at a restaurant in 22^ dys. the same sum which would sup- port Fiske alone 38^ dys. For how many days would this Slim support Wells alone ? 209. If a man can walk 4 United States miles in one hour, how much time will he need to walk a German mile, one United States mile being 0.2136 of a German mile ? 210. A store and its stock of goods are worth $3190. The value of the goods is to that of the store as 9 to 2. What is the value of the goods ? 211. When hay is worth $ 15 per ton in Boston, 8 horses can be kept 12 dys. for a certain sum. For how many days can 6 horses be kept at the same cost when hay is $ 12 per ton? 212. On a Fahrenheit thermometer the temperature of melting ice is marked 32°, and that of boiling water 212°. On a Centigrade thermometer the corresponding tempera- tures are marked 0° and 100°. If the mercury in a Centi- grade thermometer stands at 35°, at what degree will it stand in a Fahrenheit thermometer ? 213. The temperature of a room is 59° Fahrenheit. What is the corresponding reading on a Centigrade ther- mometer ? 214. When water is 60° Fahrenheit, what temperature will be indicated by a Centigrade thermometer ? 215. Seven women in 8 dys. of 11 hrs. each can make 22 doz. shirts. In how many days of 10 hrs. each can 12 women make 360 doz. shirts ? CHAPTEK VIL MENSURATION. Note. In this chapter the pupil i& advised to draw neat and exact diagrams whenever the problem is one that admits of such illustration. Diagrams often make easy the solution ofprobleTns which without them would seem extremely difficult. Square each of the following numbers : 1. 7; 9; 28; 100; 1000. 5. 1500.81; 36.0018. 2. 76; 329; 101; 100,408. 6. J; i; |; |; |f 3. 0.6; 0.47; 0.009; 0.0604. 7. |i; ||; ^i; AVr- 4. 9.02 ; 27.8 ; 18.09 ; 90.008. 8. 2| ; 9^ ; 17f ; 149^. 9. 19; 1006; 0.8; 0.002; 31.06; ■^^; 16^. 10. 87; 3003; 0.101; 182.4; 4.001; 3^; 201/^. Extract the square root of the following numbers : 11. 1 ; 16 ; 49 ; 64 ; 81 ; 100 ; 400. 12. 144 ; 169 ; 625 ; 9025 ; 11,026. 13. 22,600; 32,400; 11,881; 4,004,001. 14. 0.04 ; 0.0026 ; 0.00013924 ; 0.40005626. 15. 6.26; 73.96; 16.4026; 266.672441. 17. Hf ; T^m ; i^V^ ; Mm- 18. 86tt ; 745^1^ ; 1750fM ; 3265f||M*. MENSURATION. 223 Find the square roots of the following numbers, correct to one decimal place : 19. 536. 21. 69,785. 23. 5,193,583. 20. 4376. 22. 875,042. 24. 20,439,995. Find the square roots of the following numbers, correct to two decimal places : 25. 53.2. 27. 100.052. 29. 95.767. 26. 49.24. 28. 9.254. 30. 6052.21. ^ Find the square roots of the following numbers, correct to three decimal places : 31. 4.532. 33. 8^. 35. 4^. 32. 3.55075. 34. |. 36. 15||. Find the square roots of the following numbers, correct to four decimal places : 37. 5.2. 39. 7.20051. 41. 9^, 38. 4.005. 40. 3053.172. 42. 19|i. 43. What number multiplied by itself gives for the product 121,801? 44. The product of two equal numbers is 122,500. Find the numbers. 45. What is ihe number whose square root increased by 17 is equal to 71 ? 46. The sum of $676 was divided among a certain num- ber of persons, so that each person received as many dollars as there were persons. How many persons were there ? 47. Find the mean proportional between 35 and 1260. 48. A silver dollar is 1-J- in. in diameter. How many silver dollars could be laid flat side down on the surface of a table measuring 4 ft. on each side ? 224 ARITHMETICAL EXERCISES. A Plane is a surface upon which straight lines can be drawn ia all directions. The surface of still water is a good example of a plane surface. A Plane Fig^e is a portion of a plane surface bounded by lines. The Area of a plane figure is the ratio of its magnitude to that of another plane figure assumed as the unit. For the units of area, see page 79. The unit most commonly used is the square foot. A Quadrilateral is a plane figure bounded by four straight lines. For example, A BCD is a quadrilateral ; AB, BC, CD, DA are its sides ; the points A, B, (7, D are its vertices ; the angles ABC, BCD, etc., are its angles ; AC and BD are its diagonals ; and AB + BC-\-CD + DA is its perimeter. H O / E F ^ B A Square is a quadrilateral haying all its sides equal and all its angles right angles. Thus, EFQH is a square. The area of a square is found by multiplying the length of one side by itself ; in other words. Area of a square =» square of one side. Find the area, in square yards and smaller "units, of a square, the length of whose side is : 49. 97 yds. 52. 372 ft. 55. 98 ft. 6 in. 50. 388 yds. 53. 19| ft. 56. 66 ft. 4 in. 51. 47f yds. 54. 87| in. 57. 69 ft. 2 in. Find the area, in acres, square rods, and square yards, of a square, the length of whose side is : 58. 54 rds. 61. 29^ rds. 64. 356 yds. 59. 43 rds. 62. 47^ rds. 65. 267 yds. 60. 38frds. 63. 89 yds. 66. 178 yds. MENSURATION. 225 Find the length of one side of a square whose area is : 67. 285,166 sq. yds. 73. 97ff sq. yds. 68. 1560.25 sq. yds. 74. 286^2^ sq. yds. 69. ff sq. yd. 75. 43 sq. yds. 3^ sq. ft. 70. -5^ sq. yd. 76. 781 sq. yds. 6^ sq. ft. 71. 2isq.yds. 77. 20 A. 49 sq. rds. 72. 4|^ sq. yds. 78. 13 A. 129 sq. rds. 79. Find in yards the side of a square field which con- tains just 10 A. 80. What is the length of one side of a square field con- taining 15| A. ? 81. A man owns a square lot containing 34 A. 36 sq. rds. What is the length of one side ? 82. Find the perimeter of a square whose area is 2^ A. 83. How many rods of fencing are required to enclose a square park containing 1000 A. ? 84. Find one side of a square field containing 22^ A. 86. A garden in the form of a square contains 4466 sq. ft. 100 sq. in. What is the length of one side ? 86. A square plot of land 127 yds. long has a path 1 yd. wide running round on the inside of it. Find the cost of gravelling this path, at 15 cents per square yard. 87. What will it cost to build a stone wall around a square field containing 3 A. 44 sq. rds. 25 sq. yds., at $2f per yard ? 88. A square room is 15^ ft. long. Find the length of a square piece of carpet that will just cover half the floor. 89. A walk 2J- ft. wide round the outside of a square court 30 yds. long is to be paved. Find the cost, at 18 cents per square foot. 90. How many tiles 4 in. square are required to cover a square court, one side of which is 16 ft. 8 in. long ? 91. The perimeter of a square is 684 yds. Find the area. 226 ARITHMETICAL EXEECISES. A Rectangle is a quadrilateral having all its angles right angles. ABCD is a rectangle. The opposite sides of a rectangle are equal ; that is, AB^CD, and AD = 30, The lengths of two adjacent sides, as AB and AD, give the dimensions of the rectangle ; AB is the length or base, AD the breadth or altitude. Area of a rectangle = length X breadth. Find the area of a rectangle, having given : 92. Length 37 in., breadth 27 in. 93. Length 4 yds., breadth 3 yds. 2 ft. 94. Length 10 ft. 7 in., breadth 9 ft. 6 in. 96. Length. 7 ft. 6 in., breadth 6 ft. 7 in. 96. Length 17 ft. lOJ in., breadth 6J in. 97. Length 4 yds. 2 ft. 6 in., breadth 2 yds. 1 ft. 4 in 98. Length 210 yds., breadth 180 yds. 99. Length 20 rds. 5 yds., breadth 12 rds. 1 yd. 100. Length 5 ch. 20 Iks., breadth 4 ch. 35 Iks. Find the breadth of a rectangle, having given : 101. Length 26 yds., area 572 sq. yds. 102. Length 19 J yds., area 331^ sq. yds. 103. Length 26 yds. 2 ft., area 622 sq. yds. 2 sq. ft. 104. Length 140 yds., area 3|- A. 105. Length IJ mi., area 5 A. Find the length of a rectangle, having given : 106. Breadth 18 in., area 36 sq. yds. 107. Breadth 78} yds., area 6733| sq. yds. 108. Breadth 190^ yds., area 32 A. 18sq. rds. 23J sq. yds. 109. Breadth 136 yds., area 7 A. 21 sq. rds. 28f sq. yds. MENSURATION. 227 110. A square floor measures 17 ft. along one side. How many bricks 9 in. by 4 in. will cover it ? 111. How many slates 14 in. by 11 in. are required to cover a roof 36 ft. by 22 ft. ? 112. A street -J- of a mile long bas on eacb side a side- walk 7^ ft. wide. Wbat will it cost to pave the sidewalk with stones each measuring 2 ft. 9 in. by 1 ft. 8 in., and worth 75 cents each ? 113. A wall 23 yds. long and 13 yds. high is to be built of stones measuring 16 in. by 11^ in. outside face. Find the cost of the material at $37.50 per hundred. 114. A lawn measures 72 yds. by 49 yds. Turfs meas- ure 18 in. by 14 in., and cost, labor included, 75 cents per dozen. What will it cost to turf the lawn ? 115. A floor is 27 ft. 6 in. long and 8 yds. wide. Planks are 11 ft. by 9 in. How many planks are needed to cover the floor, and what will they cost at 20 cents per square foot ? 116. What will it cost to pave a courtyard 18^ yds. by 15^ yds. with flagstones 31 in. by 18 in., and costing $75 per hundred ? 117. A house has 24 windows; 11 of them measure S^ ft. by 6J ft. each, the rest 2f ft. by 4^ ft. each. The former are filled with panes 13 in. by 10-J- in., and the latter with panes 13-J- by 8 J in. How many panes of each size will be required ? 118. A path 8 ft. wide surrounding a rectangular court 60 ft. long and 36 ft. wide is to be paved w^ith tiles 9 in. long and 4 in. wide. How many will be required ? 119. A street -^ of a mile long covers IJ A. What is the breadth of the street ? 120. How many yards of paper 27 in. wide are required to paper a room 18 ft. long, 12 ft. wide, and 11 ft. high ? 228 ARITHMETICAL EXERCISES. 121. A carpet 15 ft. 6 in. long and 10 ft. 8 in. wide is put in the middle of a floor 20^ ft. by 16 ft. How many- yards of carpet 27 in. wide will be required to cover the remaining part of the floor ? 122. Find the cost of carpeting a room 18 ft. 9 in. long and 17 ffc. 6 in. wide with carpet 2 ft. wide, running length- wise, and costing $1.90 per yard. 123. A room is 23^ ft. long and 17^ ft. wide. Find the cost of carpeting the room with carpet at 75 cents per square yard, and whitening the ceiling at 6 cents per square yard. Find the cost of carpeting and papering the following rooms, the carpet running lengthwise in each case : 124. Koom 39 ft. by 23 ft., and 17 ft. high; with 3 win- dows, each 9^ ft. by 8 ft. ; 2 doors, each 10 J ft. by 6 ft. ; and 2 fireplaces, each 6^ ft. by 4 ft. Carpet is 24 in. wide, and costs $1.50 per yard ; paper is 24 in. wide, and costs 75 cents per roll of 10 yds. 126. Room 19 ft. by 17 ft., and 13 ft. high; with 2 win- dows, each 7 ft. by 4 ft. ; 2 doors, each 9^ ft. by 4 ft. ; and one fireplace 6^ ft. by 4 ft. Carpet is 22 in. wide, and costs $1.65 per yard ; paper is 22 in. wide, and costs $1.65 per roll of 12 yds. 126. Room 29^ ft. by 21^ ft., and 16 ft. high ; with 6 win- dows, each 5^ ft. by 6 ft. ; 2 doors, each 7-J- ft. by 9 ft. ; and fireplace 7^ ft. by 6 ft. Carpet is 21 in. wide, and costs $1.26 per yard ; paper is 21 in. wide, and costs 35 cents per roll of 10 yds. 127. Room 32^ ft. by 21^ ft., and 16 ft. high"; with 5 win- dows, each 7|- ft. by 6 ft. ; 3 doors, each 9^ ft. by 6 ft. ; 2 fireplaces, each 7^ ft. by 6 ft. Carpet is 22 in. wide, and costs $2.08 per yard ; paper is 28 in. wide, and costs 70 cents per roll of 10 yds. MENSURATION. 229 128. A room is 16 ft. by 16 ft., and 13 ft. high. It has 3 windows, each 3^ ft. by 7 ft. ; 2 doors, each 4 ft. by 7^ ft. ; a fireplace 3 ft. by 6^ ft. ; and a base-board 18 in. high. What will it cost to whiten the walls and ceiling, at 5 cts. a sq. yd., and paint the floor and base-board, at 6 cts. a sq. yd. ? 129. What must be the breadth of a rectangular piece of wood 3 ft. 9 in. long, that its area may be the same as that of a piece 2 ft. 6 in. square ? 130. An orchard containing 2 A. is rectangular in form, and its length is 5 times its breadth. Find the dimensions. 131. A square and a rectangle have the same perimeter, 100 yds. The length of the rectangle is 4 times its breadth. Which contains the greater area, and by how much ? 132. Two fields contain each 12 A. One is in the form of a square, the other is a rectangle whose length is equal to 3 times its breadth. At $4 per rod, what will be the difierence in the cost of fencing the two fields ? 133. A man wishes to cut from a square field a rectan- gular lot containing a quarter of an acre. If one side of the field be taken for one side of the lot, and measures 3^ chains, find the length of the other side. 134. How many planks, each 10 ft. long and 8 in. wide, will cover a floor 14 ft. 3 in. long and 13 ft. 4 in. wide? 136. A man wants 3^ sq. ft. of wood, and has only a plank 18 in. wide from which to cut it ofi*. Find the length of the piece, he must cut ofi". 136. What will it cost to line with lead, at 1 cent per square inch, the inside of an open cistern 10 ft. long, 6 ft. wide, and 4 ft. deep ? 137. If it costs $448 to fence a square field, at $4.40 per rod, what would it cost to fence the same amount of land in the shape of a rectangle 196 yds. long ? 230 ARITHMETICAL EXERCISES. A Rhombus is a quadrilateral having all its sides equal, but its angles not right angles. ABCD is a rhombus ; AB is called its base, and the line DE, drawn from D perpendicular to AB, is called its altitude. D C P O A E B M Q N A Rhomboid is a quadrilateral having its opposite sides equal, and its angles not right angles. MNOP is a rhomboid ; MN is its base or length ; PQ drawn per pendicular to MN is its altitude. A Parallelogram is a quadrilateral having its opposite sides par- allel. The square, the rectangle, the rhombus, and the rhomboid are all of them parallelograms. The opposite sides of a parallelogram are equal, and the opposite angles are also equal. The sum of the four angles of any parallelogram is equal to four right angles, or 360°. Area of any parallelogram = base X altitude. Find the area of a parallelogram, having given : 138. Base 18 in., altitude 13 in. 139. Base 26 yds. 2 ft., altitude 23 yds. 1 ft. 140. Base 93 yds. 1 ft., altitude 106 yds. 2 ft. 141. Base 26 yds. 2 ft. 8 in., altitude 23 yds. 1 ft. 4 in. 142. Base 16 ft. 6 in., altitude equal to 4 times the base. 143. Base 1 furlong 10 rds., altitude 25 rds. 144. Base 6 ch. 25 Iks., altitude 5 ch. 40 Iks. 145. Base 12 ch. 50 Iks., altitude 9 ch. 146. The area of a parallelogram is 4 A. 79 sq. rds., and the base is 7 ch. 19 Iks. Find the altitude. MENSURATION. 231 A Triangle is a plane figure bounded by three straight lines. The figure ABC is a triangle. A triangle, ABC, has three sides, AB, BO, AQ and three angles, ABQ BOA, OAB. The side AB is called the base, ^ q the opposite corner C the vertex, and \ > the perpendicular CD, drawn from \ / to AB, the altitude. Either one of \ / the other sides might be taken as the \ X base. If ilC is taken as the base, the \ / opposite corner B would be the ver- \/_ tex, and the perpendicular drawn A from B to -AC would be the altitude. The sum of the angles of a triangle is equal to two right angles, or 180°. Any triangle, ABO, is equal in area to one-half of a parallelo- gram, ABOE, having the same base AB as that of the triangle, and also the same altitude OD : therefore. Area of a triangle = J ijbase X altitude). If the three sides of a triangle are given, the area is found as fol- lows : From the half-sum of the sides subtract each side separately. Multiply the half-sum and the three remainders together. The square root of the product is the area of the triangle. Find the area of a triangle, having given : 147. Base 17} yds., altitude 4f yds. 148. Base 53 yds. 1 ft., altitude 46 yds. 2 ft. 149. Base 20 ft. 6 in., altitude 10 ft. 4 in. 150. Base 148 rds. 2 yds., altitude 69 rds. IJ yds. 151. Base 10 ch. 35 Iks., altitude 8 ch. 32 Iks. 152. Sides 50 ft., 40 ft., and 30 ft. 153. Sides 104 ft., Ill ft., and 175 ft. 154. Sides 380 yds., 420 yds., and 765 yds. 156. Sides 2 ch. 73 Iks., 4 ch. 25 Iks., 6 ch. 28 Iks. 232 ABITHMETICAL EXEBCISES. A Right Triangle is a triangle having a right angle. In the right triangle ABC, the right angle is at £ ; the sides AB^ BC, which form the right angle, are called the legs, and the side AC is called the hypotenuse. The sum of the two acute angles of a right triangle is equal to on« right angle, or 90°. If one of the acute angles is equal to 30°, the opposite side is equal to half the hypotenuse. Q The sum of the squares upon the two legs of a right triangle is equal to the square upon the hypotenuse ; or, + J5(7 =^C^ If one of the legs, as AB, be taken for the base, then the other leg 5 C will be the altitude ; therefore. Area of a right triangle = half the product of its legs. The diagonals of a rhombus MNPQ bisect each other at right angles, and divide the rhombus into four equal right triangles ; hence Area of a rhombus — half the product of its diagonals. Find the hypotenuse and the area of a right triangle if ; 156. The two legs are 3 ft. and 4 ft. 157. The two legs are 16 ft. and 12 ft. 168. The two legs are 108 ft. and 81 ft. 159. The two legs are 332 ft. and 249 ft. 160. The two legs are 23 rds. and 37} rds. 161. The two legs are 30 rds. and 220 yds. MENSUBATION. 233 Find one leg of a right triangle, having given : 162. Hypotenuse 10 ft., one leg 8 ft. 163. Hypotenuse 60 ft., one leg 30 ft. 164. Hypotenuse 31 ft. 6 in., one leg 12 ft. 8 in. 166. Hypotenuse 945 yds. 1 ft., one leg 345 yds. 1 ft. Find the area of a right triangle, having given : 166. Hypotenuse 25 in., one leg 15 in. 167. Hypotenuse 95 ft., one leg 76 ft. 168. Hypotenuse 207} ft., one leg 124i ft. 169. Hypotenuse 37} rds., one leg 25 rds. 170. Hypotenuse 173i rds., one leg 104} rds. 171. Hypotenuse 13 ch. 79 Iks., one leg 9 ch. 85 Iks. 172. The legs of a right triangle are each equal to 12 ft. Find the hypotenuse. 173. The side of a square is 100 ft. Find the diagonal. 174. The hypotenuse of a right triangle is 28 ft. long, and the two legs are equal to each other. Find their lengths. 176. The diagonal of a square is 33 ft. 4 in. What is the length of each side ? 176. The diagonal of a square room is 37 ft. Find the cost of a carpet IJ yds. wide, at $1.80 per square yard. 177. The diagonal of a square field measures 340 yds. What will it cost to fence it at $2 per rod? 178. The diagonal of a rectangle is 46 ft. 5 in., and length is 44 ft. 4 in. Find its breadth. 179. A ladder 45 ft. long just reaches a window when placed with its foot 27 ft. from the side of the house. How high is the window above the ground ? 180. The hypotenuse of a right triangle is 95 yds. ; the two legs are as 3 tQ 4, Find the legs and the area. 234 ARITHMETICAL EXERCISES. Find the area and side of a rhombus, having given: 181. The diagonals 12 in. and 16 in. 182. The diagonals 26 yds. and 341 yds. 183. The diagonals 11 ft. and 9 ft. 184. The diagonals 29 rds. and 21f rds. 185. The diagonals of a diamond-shaped pane of glass are 12 in. and 16 in. Find the number of square feet in 300 such panes. 186. The side of a rhombus is 31 yds. 2 ft. ; one diagonal is 50 yds. 2 ft. Find the area and the other diagonal. 187. One side of a right triangle is 30 ft., and the oppo- site angle is 30°. Find the other two sides. 188. The acute angles of a rhombus are each equal to 60°, and the shorter diagonal is 16 ft. Find the area. 189. The acute angles of a rhombus are each equal to 60°, and the longer diagonal is 108 yds. Find the area. 190. Two vessels start at the same time from the same place, and sail, one due north, the other due east, at the rates of 6 and 8 mi. per hour respectively. How far apart will they be at the end of 6 hrs. ? 191. What distance will a man save, if, instead of walk- ing along the sides of a rectangular field 640 yds. long and 480 yds. wide, he crosses the field in a straight line from one corner to the opposite corner ? 192. The breadth of the gable end of a house is 56 ft. ; the distance of the ridge-pole from the ground is 75 ft. ; the height of the eaves is 54 ft. Find the slant height of the roof. 193. A room is 20 ft. long, 15 ft. wide, and 12 ft. high. Find the distance from one corner of the floor to the oppo- site corner of the ceiling. MENSUBATION. 285 An Isosceles Triangle is a triangle haying two eqnal sideB. In the isosceles triangle ABQ AC and BC are the eqnal sides, AB is called the bascj and C the vertex. The angles opposite the eqnal sides are equal. The altitude CD bisects the base, and also the angle at the vertex C. a ^ A D B E H F An Equilateral Triangle is a triangle having its sides all equal. The triangle EFG is an equilateral triangle. The angles of an equilateral triangle are also eqnal, and each angle is equal to 60°. The altitude GH bisects the base EF, and also the angle at the vertex G. Find the area of an isosceles triangle, having given : 194. Base 16 in., altitude 13 in. 196. Base 3 ft., each of the equal sides 5 ft. 196.* Equal sides each 96t yds., altitude 58 yds. 197. Equal sides each 40 ft., angle at vertex 90^. 198. Base 40 ft., angle at vertex 90**. 199. Base 80 ft., angle at base 45®. 200. Base 150 ft., angle at base 30**. 201 . The width of a house is 47 ft. ; height to ridge 67} ft. ; height to eaves 39 ft. Find the cost of painting the side of this house at 2 cents per sq. ft., allowing 240 sq. ft. for windows. 202. The side of an equilateral triangle is 14 yds. Find the area. 203. How much larger is a square than an equilateral triangle having the same perimeter ; namely, 60 ft. ? 236 ABITHMETICAL EXEBCISES. A Trapezoid is a quadrilateral having two of its sides parallel, but the other two sides not parallel. p: K -1 The figure ABCD is a trapezoid. /I ^N^ \ ! The parallel sides AB, CD are /I ^^^ \ I called the bases. The distance DE / I ^^^ \ I or BF between the bases is called / i ^^N \ ' the altitude. / ! lai The diagonal BD divides the trap- ^ -E B ezoid into two triangles, having for their respective bases the bases of the trapezoid, and having equal altitudes {DE and BF) ; hence, Area of trapezoid = J X sum of bases X altitude. Find the area of a trapezoid, having given : 204. Bases 37 ft. and 25 ft., altitude 19 ft. 206. Bases 1 ft. 5 in. and 1 ft. 11 in., altitude 4 ft. 8 in. 206. Bases 19J yds. and 26} yds., altitude 62 yds. 207. Bases 256 yds. and 144 yds., altitude 85 yds. 208. Bases 26} rds. and 33} rds., altitude 79 rds. 209. Bases 12 ch. and 8 ch., altitude 10 ch. 40 Iks. 210. Find the altitude of a trapezoid if the area is 2990 sq. yds., and the bases are 76 yds. and 54 yds. 211. A field has the shape of a trapezoid. The parallel sides are 6 ch. 45 Iks. and 3 ch. 55 Iks. respectively, and the distance between them is 4 ch. 20 Iks. Find the value of the field at $ 780 per acre. 212. A man paid $2262 for a field having the shape of a trapezoid. The parallel sides are 119 yds. and 200 yds., and the distance between them is 110 yds. What did the field cost him per acre ? 213. Find the altitude of a trapezoid if the sum of its parallel sides is 231 rds., and its area is 115} A. MENSURATION. 237 A Trapeziam is a quadrilateral having no two of its sides parallel to each other. The usual method of finding the area of the trapezium is to measure the lengths of a diagonal, as AC^ and also the lengths of perpendicu- lars to this diagonal dropped from the opposite corners B and D \ then to compute the areas of the triangles ABD, ACD\ and add the two results together. A Find the area of a trapezium ABCD, having given : 214. AC-= 35yd8., J5^=- 19 yds., Z)i^= 17 yds. 215. 4C= 23 yds., ^^= 38yd8., Z)i^= 27 yds. 216. AC= 47 yds., J5^= 56 yds., Z)i^--- 49 yds. 217. AC= 48ft., J5^=24Ht., DF^lb^it. 218. ^C=34ift., J5^=19ift., DF=U\ii. 219. ^0^= 400 yds., J5^= 120 yds., i)i^= 80 yds. 220. AC-= 79rds., ^^= 67 rds., DF= 63 rds. 221. Find the cost of a lot of land in the shape of a trapezium, at 25 cents per square foot, one diagonal being 108 ft., and the perpendiculars uj on it from the opposite corners being 55 ft. 3 in. and 60 ft. 9 in. 222. Find the area of a trapezium ABCD (see fig.), if AB = 87 ft., BC= 119 ft., CD = 41 ft., DA = 169 ft., and the diagonal AC= 200 ft. 223. Find the area of the trapezium ABCD, if AD = 145 ft., CB = 135 ft., AF= 87 ft., FC= 81 ft., AC= 368 ft. 224. Find the area of a trapezium ABCD, if AB = 48 ch., BC= 20 ch., AC= 52 ch., DF= 30 ch. 226. One diagonal of a quadrilateral is 10 ch., and the perpendiculars upon it from the opposite angles are 6 cb 27 Iks. and 8 ch. 6 Iks. Find th^ are^. 238 ARITHMETICAL EXERCISES. A Polygon is a plane figure bounded by straight lines. A poly- gon having three sides is called a triangle; having /owr sides, a quad- rxlateral; having /ve sides, 2t, pentagon; having «ia; sides, a hexagon; having eight sides, an octagon; having ten sides, a decagon; having twelve sides, a dodecagon. The area of any polygon may be found by dividing it into trian gles by means of diagonals, computing the areas of these triangleb, and adding the results. 226. Find the area of the polygon ABCDE, having given : AB, 61 yds., AE, 69 yds., BC, 140 yds., BD, 159 yds., CD, 23 yds., BE, 100 yds. BE, 91yds., 227. Find the area of the polygon ABODE, having given : BE, 108 yds., EC, 96 yds., AF, 49 yds., DH, 35 yds. CG, 67 yds., 228. Find the area of the polygon ABCBEF, having given : AB, 85 yds., AF, 105 yds., BC, 76 yds., AC, 105 yds., CD, 87 yds., CE, 143 yds., i)^,100 yds., AE, 116 yds, EF, 17 yds., MENSUBATION. 239 229. Find the area of the polygon ABODE, having given: AC, 476 yds., BO, 160 yds., AF, 175 yds., AH, 420 yds, ^i^, 160 yds., DH, 90 yds. ^G, 320 yds., (Note that the figure EF HD is a trapezoid.) 230. Find the area of the polygon ABCDEF, having given : AC, 312 yds., FO, 63 yds., BK, 116 yds., EG, 54 yds., AF, 125 yds., i^^, 283 yds., CF, 323 yds., DH, 60 yds. 231. When it is difficult to enter a polygonal field for the purpose of measuring lines, the area may be found by surrounding the polygon by a rectangle, as shown below, and subtracting from the area of this rectangle the areas of the parts outside the polygon. Find the area of the swamp ABCDEFQ, having given : ^Jf,88rd8., JlfJ5,94rds., BR, 94rds., EC, 28rds., jRiV^, 40rds., PS, 45rds., 8E, 20rds., ST, 65rds., TF, 48 rds., TG, 58 rds.. iVD, 107 rds., OQ, 60 rds., DP, 104^ rds., QA, 123^ rds. 240 ABITHMETIOAL EXEBCISES. --Jf- " D A Regular Polygon is a polygon having all its sides equal and all its angles also equal. There is in every regular polygon a point equidistant from the corners and also equidistant from the sides ; this point js called the centre. The distance from the centre to any corner is called the radius, and the distance from the centre to any side is called the apothem. The figure ABCDEF is a regular hexagon ; is the centre, OA the radius, Olfthe apothem. The radii of a regular polygon divide the figure into equal isos- celes triangles ; hence it follows that, Area of a regular polygon = J X perimeter X apothem. The radius of a regular hexagon is equal to one side, and the radius of an equilateral triangle is equal to twice the apothem. The apothem of a regular polygon bears a constant ratio (usually irrational) to one side ; for most purposes the following values are sufficiently accurate : No. of sides. Apothem. No 1. of sides. Apothem. o . . . . one side x 0.2887. 7 • • • • • one side x 1.0382 4 ^ • • • • one side X 0.5000. o . . . . one side X 1.2071 o . . . . one side X 0.6882. 10 ... . one side X 1.5388, 6 . . , , one side X 0.8660. 12 one side X 1.8660. Find the area of: 232. An equilateral triangle, if one side = 2J- ffc, 233. A regular pentagon, if one side = 3 ft. 234. A regular hexagon, if one side = 60 ft. 235. A regular heptagon, if one side = 30 ft. 236. A regular octagon, if one side = 30 ft. 237. A regular decagon, if one side = 38 ft. 238. A regular dodecagon, if one side — 10 ft. MENSURATION. 241 239. What angle is formed at the centre by two adjacent radii of an equilateral triangle ? a square ? a regular hexa- gon? a regular octagon? a regular decagon? a regular dodecagon ? 240. Show that the apothem of a regular hexagon =: 0.866 X the side. 241. The perimeter of a regular hexagon is 25^ ft. Find the area. 242. A park has the shape of a regular hexagon. Each side is 500 ft. long. What is the assessed valuation of the park at 8 cents per square foot ? 243. Each side of a lot in the shape of a regular decagon measures 80 Iks. Find the area. 244. How much land will be covered by a tent, the base of which has the shape of a regular heptagon, and measures 20 ft. on each side ? 245. Find the side of a square having an area equal to that of a regular hexagon whose side is 4 ft. 246. What area can be paved with 1000 tiles in the shape of regular octagons, the side of each octagon being equal to 3 in.? 247. The radius of a regular decagon is 24 yds., the apothem is 22J yds. Find the area (to the nearest square yard). 248. How many hexagonal paving-stones measuring 1 ft. on each side, are required to pave the floor of a hall 60 ft. long and 20 ft. wide, allowing 5% extra to fill corners? 249. A field has the shape of a regular hexagon, and one side is 247 yds. Find its value at $ 242 per acre. 260. Find the cost of carpeting a regular octagonal floor, one side of which is 12 ft., with carpet 29 in. wide, and costing $1.70 per square yard. 242 ABITHMETICAL EXEECISES. A Circle is a plane figure bounded by a curved line called a cir- cumference, every point of which is equally distant from a point within called the centre. A line drawn from the centre to the cir- cumference is called a radius, and a line drawn through the centre and limited by the circumference is called a diameter; therefore a diameter is equal in length to two radii. The circumferences of two circles have the same ratio to each other as their radii, or as their diameters. Thus, if the radius of a circle be doubled, the circumference will also be doubled ; or, if the diam- eter be trebled, the circumference will also be trebled ; and so on. It follows that the ratio of the circumference of a circle to its diam- eter is the same for all circles. The exact value of this ratio cannot be expressed by numbers, but the value near enough for most prac- tical purposes is -^. Concentric circles are circles having the same centre. Circumference of a circle = ^X radius. Radius of a circle = /j X circumference. Area of a circle = -^ X {radiysf. Radius of a circle = V^ X area. Pind the circumference and area of a circle, having given: 261. Radius 21 ft. 262. Radius 7 ft. 263. Radius 40 ft. 10 in. 254. Radius 7.7 yds. 265. Radius 28 rds. 256. Radius 4 ch. 62 Iks. 257. Diameter 77 yds. 268. Diameter 49 ft. 269. Diameter 19J rds. 260. Diameter 115| rds. 261. Diameter 32 yds. 2 ft. 262. Diameter 18 yds. 2 ft. MENSUEATIOK. 243 Find the radius and the area of a circle, having given : 263. Circumference 132 yds. 264. Circumference 198 yds. 266. Circumference 396 yds. 266. Circumference 15 ft. 7 in. 267. Circumference 91 yds. 2 ft. Find the radius and circumference, having given : 268. Area 2464 sq. ft. 269. Area 6237 sq. yds. 270. Area 6 A. 271. Find the area of a circle if the diameter is 18t yds. 272. Find the diameter of a circle if the area is 616 sq. in. 273. Find the area of a circle if the circumference is 2 mi. 274. A carriage- wheel whose diameter is 3} ft. made 1200 revolutions in going a certain distance. Find the distance. 275. The circumferences of two concentric circles are 440 ft. and 330 ft. respectively. Find the width of the ring. 276. How deep is a well, if the wheel whose diameter is 2 ft. 4 in. makes 30 revolutions in raising the bucket ? 277. Find the cost of building a wall around a circular garden containing 22,176 sq. ft. at $6.20 per yard. 278. The side of a square is 11 ft. Find the diameter of a circle equal in area to the area of the square. 279. The diameter of a circle is 7 ft. Find the side of a square having an area equal to that of the circle. 280. Find the area of a circular ring 4 ft. wide, if the radius of the outer circle is 32 ft. 281. What will it cost to gravel a walk 6 ft. wide, run- ning around a circular fish-pond whose diameter is 70 yds., at 20 cents per square yard? 244 ARITHMETICAL EXERCISES. An Arc is any part of a circumference, as ACB. A Chord is a straight line joining the ends of an arc. Thus, AB is the chord of the arc ACB. The diameter COE, drawn through the middle point D of the chord AB, bisects also the arc ACB, and is perpendicular to the chord ; AD is half the chord AB, and ACi& the chord of half the arc ACB ] CD is called the height of the arc ACB. It may be proved that AC 18 & mean proportional between CD and GE, and that AD is a mean proportional between CD and DE ; in other words, AC =CDxCE; and AD* =^ CD x DE. C The arch of a bridge often has the form of a circular arc ; in this case, AB is the span, CD the height or rise above the piers. The angle AOB is the angle at the centre subtended by the arc ACB. Every circumference is regarded as composed of 360 equal arcs, called degrees; and an arc ACB contains the same number of degrees, minutes, and seconds as the angle at the centre AOB ; also, Length of an arc ^ Number of degrees in arc Circumference 360° 282. Given AC- 283. Given AC- 284. Given AD 285. Given CD 286. Given CD 287. Given AJB- 25 ft., CD 15 ft, OC 8 ft, AC 5 in, AD 9 in, CE 48 ft, CD: 15 ft. ; find CU, 20 ft. ; find CD. 10 ft. ; find OC. 12 in. ; find CK 25 in.; find ^C. 18 ft. ; find 00. MENSURATION. 245 288. Given A0= 17 ft., CI)= 7ft.; find UO. 289. Given AC=^ 12 ft, (7^= 36 ft.; find OZ). 290. The chord of half an arc is 28 ft., and the radius of the circle is 28 ft. Find the height of the arc. 291. The chord of an arc is 4 ft. 4 in., and the height of the arc is 1 ft. 1 in. Find the diameter of the circle. 292. The span of a bridge in the form of a circular arc is 78 ft., and the rise above the piers is 12 ft. Find the radius of the circle. 293. The height of the circular arch of a bridge is 24 ft., and the radius with which it is described is 312 ft. Find the span of the arch. Find the length of an arc, having given : 294. Circumference 50 in., angle at centre 30**. 295. Radius 28 in., angle at centre 45®. 296. Diameter 35 in., angle at centre 36**. 297. Radius 84 ft., angle at centre 11** 15'. 298. The radius of a circle is 5 ft. 3 in. Find the whole perimeter of a sector the angle of which is 45°. 299. What angle at the centre is subtended by an arc 6 ft. 5 in. long, if the radius of the circle is 8 ft. 2 in. ? 300. The radius of a circle is 7 in. Find the angle at the centre subtended by an arc whose length is also 7 in. 301. An arc of a circle is 5 ft. 6 in. The angle which it subtends at the centre is 72°. Find the radius. 302. If in a certain circle an arc cf 120° is 88 ft. long, what is the length of an arc of 30° in a circle whose radius is 6 times that of the first circle ? 303. A chord in a circle is 4 ft., and the corresponding angle at the centre is 90°. Find the length of the arc. 246 AEITHMETICAL EXERCISES. A Sector is a portion of a circle bounded by two radii and the arc contained between them. The figure AOBC is a sector ; the angle AOB is the angle of this sector. A Segpnent is a portion of a circle bounded by an arc and its chord. The figure ADBGi& a segment. Every diameter divides a circle into two equal parts called semi- circles ; and two diameters perpendicular to each other divide a circle into four equal parts called quadrants. The area of a sector has the same ratio to the area of the entire circle that the arc of the sector has to the entire circumference ; hence it follows that : Area of sector _ Angle of sector Area of circle 360° The area of the segment ADBC is found by subtracting that of the triangle AOB from that of the sector AOBC. An inscribed polygon is a polygon whose sides are chords of the circle, and a circumscribed polygon is a polygon whose sides touch the circle. The radius of a circle is equal to the radius of every inscribed regular polygon, and to the apothem of every circum- scribed regular polygon. Find the area of a sector, having given : 304. Radius 14 in., angle at centre 45®. 305. Radius 2 ft. 11 in., angle at centre 24®. 306. Radius 56 ft., angle at centre 22|-^ 307. Radius 10 in., angle of sector 18°. 308. Radius 10 in., arc of sector = the radius. MENSURATION. 247 309. The area of a sector is 882 sq. yds. ; the radius of the circle is 42 yds. Find the length of the arc. 310. The angle of a sector is 60**, and the chord joining the ends of the arc is 14 ft. Find the area of the sector. 311. In a circle whose radius is 18 yds. 2 ft., find the area of a segment bounded by an arc of a quadrant and the corresponding chord. 312. The chord of a segment is 43 yds., and the angle subtended at the centre is 90°. Find the area of the segment. 313. The chord of a segment is 28 yds. ; the angle at the centre is 60**. Find the area of the segment. 314. In a circle whose radius is 1 ft., what is the length of the arc subtended by one side of the inscribed regular decagon ? 816. Find the area of a circle inscribed in a square whose area is 196 sq. ft. 316. Out of a square piece of wood 6 ft. 10 in. long is cut the largest possible circle. Find its area. 317. Out of a circular piece of wood whose radius is 3 ft. 4 in., is cut the largest possible square. Find its side. 318. The radius of a circle is 4 ft. Find the area of the inscribed regular hexagon. 319. The radius of a circle is 4 ft. Find the area of the circumscribed regular hexagon. 320. The side of a square is 42 yds. Find the areas of the inscribed and the circumscribed circles. • 321. The diagonal of a square is 54 yds. Find the area of the inscribed circle. 322. The radius of a circle is 9 yds. Find the areas of the inscribed and the circumscribed equilateral triangles. 248 ABITHMETICAL EXERCISES. Two polygons are similar if they are equiangular with respect to each other, and have their homologous sides proportional. The homologous sides are the sides opposite the equal angles. Thus, the triangles ABC^ A^B'Cy are similar triangles, and AB'.A'B' = BG.Bf(y', AB:A'B'=^AC.A^(y; BC'.B'Cy ^-ACiA'C/; All regular polygons having the same number of sides are similar to each other. The areas of two similar figures are proportional to the squares of any two homologous sides. The radii of two regular polygons of the same number of sides are proportional to their sides ; and the same is true of their apothems. The areas of two regular polygons of the same number of sides are proportional to the sqiuires of their sides, or the aqvarea of their radii, or the squares of their apothems. The areas of two circles are as the sqv^ares of their radii, or as the squares of their diameters. 323. If a rod 3 ft. high casts a shadow 2 ft. long, how high is a tree which casts a shadow 60 ft. long ? 324. If a triangular lot of land, one side of which is 80 ft., is worth $1000, what is a similar lot worth, the homologous side of which measures 240 ft. ? 325. To what extent is the area of a polygon altered if its sides are all of them quadrupled ? 326. The sides of two regular octagons are as 2 to 6. The area of the first is 80 sq. ft. Find the area of the other. 327. To what extent is the area of a regular polygon altered if its radius is reduced to one-fifth of its original value ? The radius of a circle is 3 ft. Find : 328. The radius of a circle 25 times as large. 329. The diameter of a circle 3 times as large. MENSURATION. 249 Cube the following numbers : 330. 4; 7; 9; 37; 75. 331. 39; 130; 276; 100; 1000. 332. 109; 2007; 10,000; 29,045; 371,908. 333. 0.7; 0.29; 0.008; 0.7175; 0.10091. 334. 9.3; 24.8; 375.012; 80.0027. 335. 17.05; 2945.6; 13,005.91; 23.0014. 336. i; i; |; |; |; jf ; ff. ||. 337. 2|; 9|; 18f ; 168Jf ; 10,000ff. Extract the cube root of the following numbers : 338. 1 ; 125 ; 343 ; 512 ; 729. 339. 1000; 2197; 3375; 27,270,901. 340. 35,937,000; 512,000,000; 1,003,003,001. 341. 0.001; 0.125; 0.064; 0.512. 342. 0.001728; 0.000000343; 0.000010529664. 343. -^j'y yf^; ^] -J-^; -flf. 344. -mi^-^; iWi^iW^; 709|i|f|; 1221|i^. Find the cube roots of the followiog numbers, correct to one decimal place. 345. 419. 347. 8988. 349. 1,765,789. 346. 2038. 348. 307,504. 350. 513,175,785. Find the cube roots of the following numbers, correct to two decimal places. 351. 29.2. 353. 97.005. 355. f 352. 410.23. 354. 109.0126. 356. 3|. Find the cube roots of the following numbers, correct to three decimal places. 357. 4.531. 359. 0.63. 361. 9||. 368. 1.5046. 360. fj. 362. 926^|. [50 ABITHHETICAL A Solid ie anything wHicli has three dimenaioDs, leogtii, breadth, and thickness. The boundary of a solid is called its tarface. If the sarface consiBt of planea, they are called the /aces. The faoea of a solid meet in linea called the edgu. A Cnbe ia a solid bounded by sii equal ^, Tlie three dimeosiona of a cnbe are The most convenient units of volume are cubes -whoBB edges are □nits of length. The whic /ooi and the cubic inch are examples of such unite. (For other unite, see page 80.) VolvTne of a eiibt = eabt of one edge. Find the volume and also the entire surface of a cube, having given : 363. Side 3 in. 367. Side 1 ft. 2 in. 364. Side 8^ in. 368. Side 2 ft. 3 in. 366. Side 8 ft. 6 in. 369. Side 20 ft. 3G6. Side 2 yds. 1 ft. 3 in. 370. Side 5 yds. 2 ft. 6 in. Find the length of one edge of a, cube, having given : 371. Volume 343 cu. in. 373. Volume 2 cu. ft. 1457 on. in. 373. Volume 16 cu. ft. 1080 cu. in. 374. Volume 68 ca. ft. 145 cu. in. 375. Find the weight of tlie water in a cubical cistern each aide of which measures 6 ft. {See bottom of p. 80.) 376. How much lead is used in lining the bottom and eides of a cubical vessel that contains 729 cu. ft. of water? 377. A man wishes to construct a cubical vessel that will hold exactly 1 ton of water. What must be the lengtli of one edge ? MENSURATION. 251 A Rectangular Parallelepiped is a solid bounded by six rectan- gular faces, each of which is equal and parallel to the face lying opposite. The annexed figure represents ^ ^ a rectangular parallelopiped. The face An CD is equal and parallel to the face EFOH. The lengths of the three edges which meet at any one of the corners are the dimensions of the solid; thus, AB is the length, AH the breadth, AD the thick- ness or height. The face ABEH is also called the base ; and then the edge AD is called the height. The entire surface of a rectangular parallelopiped is the sum of the six rectangles of which it is composed, and the Volume = length X breadth X thickness -= base X height. Find the surface and the volume of a rectangular paral- lelopiped, having given : 378. Length 10 in., breadth 8 in., thickness 6 in. 379. Length 9f ft., breadth 7^ ft., thickness 6^ ft. 380. Length 6| ft., breadth 5^ ft., depth 4^ ft. 381. Length J. 7f yds., breadth 13^ yds., depth 11| yds. 382. Length 4^ ft., breadth 1^ yds., depth 54 in. 383. Length 4 ft. 8 in., breadth 3 ft. 10 in., height 3 ft. Find the volume, having given : 384. Base 97 sq. in., height 10 in. 385. Base 3 sq. ft. 20 sq. in., height 1 ft. 3 m. 386. Base 11 sq. ft. 40 sq. in., height 5 ft. 3 in. Find the height of a rectangular parallelopiped, given : 387. Volume 378 cu. in., length 9 in., breadth 7 in. 388. Volume 236,612^ cu. yds., base 1114| sq. yds. 252 ARITHMETICAL EXERCISES. 389. A cellar which measures 12 ft. by 9 ft. is flooded to a dfepth of 4 in. Find the weight of the water, suppos- ing that 1 cu. ft. of water weighs 1000 oz. 390. What weight of water will a rectai^ular cistern hold, its length being 4 ft., breadth 2 ft. 6 in., depth 3 ft. 3 in., and 1 cu. ft. of water weighing 1000 oz. ? 391. How much lead is required to line an open cistern 4 ft. 6 in. long, 2 ft. 8 in. wide, and containing 42 cu. ft. ? 392. How many bricks 9 in. by 4i in. by 3 in. are re- quired to build a wall 90 ft. long, 18 in. thick, and 8 ft. high? 393. A book is 8 in. long, 6 in. wide, and li in. thick. Find the depth of a box 3 ft. 4 in. long, and 2 ft. 6 in. wide, that it may hold 400 such books. 394. Find the expense of covering a flat roof 17 ft. 4 in. long and 13 ft. 4 in. wide with sheet lead ^ in. thick, if a cubic inch of lead weighs 6^ oz., and 1 lb. of lead costs 14 cents. 396. Marble is 2.716 times as heavy as water, and 1 cu. ft. of water weighs 1000 oz. Find the weight of a block of marble 9 ft. 6 in. long, 2 ft. 3 in. wide, and 2 ft. thick. 396. Iron weighs 7.2 times as much as water, and 1 cu. ft. of water weighs 1000 oz. What will an open cistern made of iron 1 in. thick weigh when empty, if its external dimensions are 5 ft., 4 ft., and 3 ft. ? 397. A cistern is 6 ft. 6 in. long, 3 ft. 9 in. wide, and 1 ft. 3 in. deep. How many gallons of water will it hold ? What weight of water will it hold ? (1 gal. of water = 231 cu. in., 1 cu. ft. of water weighs 1000 oz.) 398. Rain has fallen to the depth of half an inch. How many cubic feet of water have fallen on an acre of land ? MENSURATION. _ 253 A Prism is a solid bounded by two ei^aal and parallel polygons called the bates, aad by parallelograms called the lateral facu'. The iotaraectioDB of the lateral faces with one another are called the laieral edges. A prism is called inangnlaT, quadrangular, hexagonal, etc., accord- ing as the bases are triangles, quadrilaterals, hexagons, etc. A Right Prism is a priam all of whose lateral faces are rectangles. The lateral faces and edges of a right prism are perpendicular to the bases. n A Cylinder is a solid bounded by two equal and parallel circles called the bates, and a curved surface called the lateral surjace. The line joiniug the centres of the bases is called the asis. A Right Cylinder is a cylinder whose axis is perpendicular to the bases. The kdght of a prism or a cylinder is the distance between its bases. The height of a right cylinder ia equal to the length of its axis. The lateral surface of a right prism or a right cylinder is found by multiplying ihe perimeter of the base by the height. Volxime of a pritm or cylinder — bate x height. (All the prisms and cylinders mentioned in the following examples ate supposed to be right prisms and right cylinders.) Find the Tolomee of the following prisms : 399. Base 23.5 sq. in., height 5.4 in. 400. Square base, side of base 13 in., height 19 in. 401. Triangular base, «ide3 10, 17, and 21 ft., height 16 fb. 402. Base an equilateral triangle, side 5 ft,, height 2S ft. 254 ARITHMETICAL EXERCISES. 403. Base a regular hexagon, side 4 ft. 9 in., height 25 ft. 404. Base a regular hexagon, side 10 in., height 10 ft. 405. Base a regular octagon, side 6 in., height 4 ft. 8 in. 406. Base a rectangle 3^ ft. by 2^ ft., height 15| ft. Find the volume and also the lateral surface of the fol- lowing cylinders : 407. Radius of base 7 in., height 10 in. 408. Radius of base 1 ft. 2 in., height 5 ft. 409. Diameter of base 8 ft. 2 in., height 4 ft. 6 in. 410. Diameter of base 9 ft. 4 in., height 12 ft. 411. Circumference of base 7 ft. 4 in., height 10 ft. 412. Find the radius of the base of a cylinder if the vol- ume is 1540 cu. in., and the height is 10 in. 413. Find the height of a cylinder if the volume is 114 cu. yds. 2 cu. ft., and the radius of base 7 ft. 414. How many cubic yards of earth must be dug out to make a well 3 ft. in diameter, and 20 ft. deep ? 415. The diameter of a well is 4 ft. 8 in., its depth is 30 ft. Find the cost for digging it at $3.75 per cubic yard. 416. How many cubic yards of earth must be dug out in making a tunnel 100 yds. long, whose section is a semi- circle with a radius of 10 ft. ? 417. The bill for digging a well 45 ft. deep, and 3 ft. 9 in. in diameter was $82.50. Find the charge per cubic yard. 418. If a cubic foot of brass is drawn into a wire -^ of an inch in diameter, what will be the length of the wire ? 419. What will it cost to sink a well 50 ft. deep and 3 J ft. in diameter, at $3.48 per cubic yard? 420. A cylindrical well is 119 ft. deep, and measures 4 ft. across the top. How many cubic feet of earth had to b^ dug out? MENSURATION. 255 421 . Is a cube a right prism ? Why ? Is a rectangular parallelepiped a right prism ? Why ? 422. What change in the volume of a cylinder is pro- duced by doubling its height ? By doubling the diameter of its base ? By doubling both ? 423. Two cylinders have the same height, but the radius of the base of one cylinder is 6 times that of the other. Compare their volumes. Compare also their lateral surfaces. 424. Find the cost of cementing the side and bottom of a cylindrical tank 20 ft. deep, and 18 ft. in diameter, at 32 cents per square foot. 425. How many gallons of water are there in a cylin- drical well 7 ft. in diameter, if the water is 10 ft. deep ? 426. How many inches will the water sink in a well 7 ft. in diameter, if 310 gals, of water are pumped out ? 427. How many cylindrical pieces of lead f of an inch in diameter and -J- of an inch thick must be melted, in order to form a cube whose edge is 3 in. long? 428. What length of wire 0.08 of an inch thick can be formed out of a cubic inch of metal ? 429. If a square iron rod 1 in. thick and 1 yd. long weighs 10^ lbs., what would a round iron rod of the same length and thickness weigh ? 430. How many revolutions must a roller 3 ft. long and 1^ ft. in diameter make, in order to go completely over a grass plot half an acre in extent ? 431. How large a cylinder can be made by rolling up a rectangular sheet of tin 80 in. by 60 in., so that the height of the cylinder is 80 in. ? How large, if the height is 60 in. ? { 256 ARITHMETICAL EXERCISES. A FTTamid is & solid bonaded by a polj-gon called the hiue, and by triangles called lateral faces, which all terminate in one point called thfl vertex. A pyramid is irvmffuiaT, hexagonal, etc., according aa the base is a triangle, a beiagon, eh:. A RigM Fytaadd is a pyramid all of whose lateral faces are isosceles triangles. If the base of a right pyramid is a ragalar poly- gon, the vertex is in the perpendicular erect«d at the centre of the 4 A done is a solid bounded by a circle called the baie, and by a curved surface called the lateral mrjaee, which terminates in a point called the vtrtex. A Right Cone is a cone whose vertex is in the perpendicular erected at the centre of the base. This perpendicular is called the amt of the right cone. The A«i^Aj of a pyramid or cone is the distance from the vertex to the base. The elanl height of a right cone Is the distance from the vertex to the drcumference of the base. The lateral surface of a right cone Is found by multiplying the circumference of the base by half the slant height. Volumt of a pyramid or cone = | base x height. (All the following questions refer to the right pyramid and right Find the volumes of the following pyramids: 432. Area of base 64 sq. io., height 1 ft. 9 id. 433. BaBS an equilateral txiangle, aide 4 ft., height 15 ft. 434. Base a regular hexagon, side 6 ft., height 30 ft. 436. Base a regular octagon, side 24 ft., height 74J yds. MENSURATION. 257 Find the volume of a square pyramid, having given: 436. Side of base 3 ft. 4 in., height 9 ft. 437. Diagonal of base 78 yds., height 30 yds. 438. Altitude of one face 18 in., height 13 in. 439. Lateral edge 29 in., height 17 in. Find the whole surface of a square pyramid, having given: 440. Side of base 8 ft., altitude of each face 20 ft. 441. Side of base 26 ft., altitude of each face 84 ft. Find the volume and also the curved surface of the following cones ; 442. Radius of base 7 in., height 3 ft. 6 in. 443. Diameter of base 7 ft., height 10 ft. 444. Radius of base 3 ft. 6 in., slant height 6 ft. 10 in. 445. Radius of base 12 ft., slant height 37 ft. 446. Circumference of base 44 ft., slant height 25 ft. 447. Find the cost of covering a conical spire measuring 40 ft. round the base, and whose slant height is 30 ft., with lead \ of an inch thick, if 1 cu. in. of lead weighs dj- oz., and lead is worth 12 cents per pound. 448. How much canvas is needed to make a conical tent 8 ft. high, and 7 ft. in diameter at the base ? 449. If 132 sq. ft. of canvas are formed into a conical tent whose slant height is 12 ft., find how much ground this tent will cover. 450. What length of canvas f of a yard wide is required to make a conical tent 12 ft. in diameter and 8 ft. high? 461. A right triangle whose sides are 3 in., 4 in., and 5 in. in length, is made to describe a cone by turning round on the side 4 in. as an axis. Find the curved surface, and the volume of the cone thus generated. 258 ARITHMETICAL EXERCISES. A Fmstniii of a pyramid or cone is the part which remains after the top has been cut off by a plane parallel to the base. The base and the section made by the cutting plane are called the bases of the frustum. The hdght of a frustum is the distance between the bases. The slant height of the frustum of a right cone is the distance from a point in the circumference of one base to the circumference of the other base. The lateral surface of the frustum of a right pyramid is composed of trapezoids. The lateral surface of the frustum of a right cone is found by multiplying the sum of the circumferences of the bases by half the slant height. To find the volume of a frustum, add together the areas of its bases and the square root of their product ; then multiply the sum by one-third of the height. Find the volumes of the following frustums : 452. Square pyramid, sides of bases 21 and 15 yds., height 84 yds. 453. Square pyramid, sides of bases 45 and 25 yds., height 96 yds. 454. Square pyramid, sides of bases 36 and 18 yds., height 120 yds. 455. Eight cone, radii of bases 86 and 68 yds., height 57 yds. 456. Right cone, radii of bases 8 ft. and 6 ft., height 15 ft. 457. Right cone, radii of bases 5 ft. and 4 ft., height 6 ft. MENSURATION. 259 468. How many square feet of tin will be required to make a funnel with the radii of top and bottom 14 in. and 7 in. respectively, and the height 24 in. ? 459. A church spire has the shape of a frustum of a regular hexagonal pyramid ; each side of the base is 5 ft., and of the top 2 ft ; the altitude of each trapezoidal face is 20 ft. How many square feet of tin roofing are required to cover the lateral faces and the top ? 460. Find the expense of polishing the curved surface of a marble column in the shape of a frustum of a right cone, slant height 12 ft., radii of bases 3 ft. 6 in. and 2 ft. 4 in., at 60 cents per square foot. 461. A round stick of timber is 20 ft. long, 3 ft. in diameter at one end, 2.6 ft. at the other. How many cubic feet does it contain ? 462. A bucket is 16 in. deep, 18 in. wide at the top, and 12 in. wide at the bottom. How many gallons of water will it hold, reckoning 7^ gals, to the cubic foot? 463. The mast of a ship is 51 ft. high, and the circum- ferences of its ends are 5 ft. 6 in. and 1 ft. 10 in. Find its value at 60 c^nts per cubic foot. 464. Find the volume of the frustum of a square pyra- mid, the sides of its bases being 40 ft. and 16 ft., and the altitude of a lateral face being 20 ft. 465. The chimney of a factory has the shape of the frus- tum of a square pyramid ; its height is 180 ft., and the sides of its upper and lower bases are 10 ft. and 16 ft. respectively ; the section of the flue is throughout the entire length a square whose side is 7 ft. How many cubic feet of brick does the chimney contain ? 260 ARITHMETICAL EXERCISES. A Sphere ia a solid boanded by s. curved bdt&co all points of which are equally distant from a point within called the centre, A straight line drawn from the centre to the Bur&ce ii called a Todiui, and a straight line drawn through the centre and terminated each way by the eurfcice is called a diameter. The Bircumicribing cylinder of a sphere is a, cylinder whose height and the diameter of whose base are both eqnal to the diameter of the .ptoi. (..a Fig.). It can be proved that the surface of a sphere is just equal to two- thirds the laierat surface of the circumscribing cylinder, and that the volume of a sphere is just equal to two-thirds the volnme of the cir- cumscribing cylinder. Hence it follows that (assoming t to be equal toy), Surface of a ephere - ^ x (radius)*. Volume of a aphere = 5J X (radius)'. Find the surface of a sphere, if the radius is : 466. 5 in. 468. 1 ft. 2 in. 470. lOi ft. 467. lOi in. 469. 3 ft. 6 in. 471. 4060 mi. Find the volume of a sphere, if the diameter is : 472. 14 in. 475. 10 ft. 6 in. 478. 42 ft. 473. 3 ft. 6 in. 476. 17 ft. 6 in. 479. 84 ft. 474. 6 ft. 10 in. 477. 4 ft. 8 in. 480. 126 yda MENSURATION. 261 481. The circilmference of a dome in the shape of a hemisphere (half a sphere) is 66 ft. How many square feet of tin roofing are required to cover it ? 482. If the ball on the top of St. Paul's Cathedral in London is 6 ft. in diameter, what would it cost to gild it at 7 cents per square inch ? 483. How many gallons of water will a hemispherical vessel hold whose diameter is 21 in., reckoning 7J gals, to the cubic foot? 484. If one cubic inch of iron weighs 4i oz., what will be the weight of an iron ball 5 in. in diameter ? 485. Find the weight of a spherical shell 10 in. in diameter and 2 in. thick, composed of a substance 1 cu. ft. of which weighs 216 lbs. 486. If an iron ball 4 in. in diameter weighs 9 lbs., what will an iron shell weigh whose external and internal diameters are 8 in. and 5 in. respectively ? 487. If a cubic inch of lead weigh 7 oz., what will be the weight of a spherical shell made of lead i of an inch thick, and measuring 7 in. external diameter ? 488. How many square feet of tin are required to make 16 hemispherical bowls, each to be 2 ft. 4 in. in diameter ? 489. A shell is 7 in. in external diameter, and 2 in. thick. What weight of powder will fill it, if 30 cu. in. of powder weigh 1 lb. ? 490. A circular room has perpendicular walls 15 ft. high ; the diameter of the room is 28 ft. ; the roof is a hemispherical dome. Find the cost of plastering the whole surface at 36 cents per square foot, and the cost of a mould- ing round the base of the dome, at 60 cents per foot. 262 ARITHMETICAL EXERCISES. Two cubes are to each other (in volume) as the cubes of their edges. Two spheres are to each other as the cubes of their radii, or as the cubes of their diameters. The surfaces of two spheres are as the squares of their radii, or as the squares of their diameters. If the heights of two right cylinders, or two right cones, are pro- portional to the radii of their bases, the volumes of the cylinders, or of the cones, are as the cubes of the heights, or as the cities of the radii of the bases ; and the lateral surfaces are as the squares of the heights, or the squares of the radii of the bases. 491. The edges of two cubes are 6 in. and 7 in. What is the ratio of their volumes ? If the volume of the smaller cube is 24 cu. ft., what is that of the larger? 492. The diameters of two spheres are 5 in. and 20 in. respectively. What is the- ratio of their surfaces ? What is the ratio of their volumes ? 493. The radii of the earth, the moon, and the sun are as the numbers 1, -^, and 112 respectively. If the volume of the earth be taken as unity, what would be the volumes of the moon and the sun ? 494. A ball 9 in. in diameter is turned down in a lathe till the diameter is 8 in. What part of the whole volume is removed ? 495. The diameter of an iron ball is 6 in. What is the diameter of an iron ball weighing -^ as much ? 496. If the height and radius of base of a cylinder are both trebled, to what extent is the volume altered? 497. The inside diameter of a hemispherical dome is 20 ft., and the uniform thickness is 2 ft. If it costs $5 to paint the inside surface, what will it cost at the same rate to paint the outer surface ? MENSURATION. 263 Miscellaneous. 498. What is the diagonal of a square whose area is 7 sq. in. ? 499. A square field is 37 yds. long. What is the side of a square field 4 times as large ? 500. A rectangular field 100 yds. wide contains 3-J A. What is its length ? 601. A rectangular cistern is 12 ft. 9 in. long, 8 ft. 3 in. broad, and 6^ ft. deep. Find the expense of lining the sides and bottom with lead weighing 8 lbs. per square foot, and costing 6 cents per pound. 502. The dimensions of a rectangle are 45 yds. and 28 yds. Find its diagonal. Also find the diagonal of a square having the same area. 503. How many square yards of painting are there in a room 20 ft. long, 14-^ ft. wide, and lOJ ft. high, with a fire- place 4 ft. by 4 ft. 4 in., and 2 windows each 6 ft. by 3 ft. 2 in.? 504. The length of each side of an equilateral triangle is 120 ft. Find the altitude. 505. Find the cost, at $6.75 per yard, of building a wall around a garden in the shape of a right triangle whose hypotenuse is 97 yds., and one leg 72 yds. 506. The hypotenuse of a right triangle is 40 ft., and one angle is 45°. Find the other two sides. 607. A mast is partly broken by the wind at the height of 20 ft. from the deck, and the top touches the deck so as to form the angle 30*. Find the entire length of the mast. 264 ARITHMETICAL EXERCISES. 508. One leg of a right triangle is 50 ft., and the oppo- site angle is 30°. Find the other leg. 509. A field has the shape of a parallelogram. Its base is 13 ch. 75 Iks., its altitude is 6 ch. 25 Iks. What is its value at $ 70 per acre ? 510. Find the area of a rhombus whose diagonals are 66 yds. and 120 yds. respectively. 611. Find the cost, at $2 per square yard, to pave a courtyard in the form of a rhombus, if its diagonals are 45 yds. and 24 yds. respectively. 512. Find the area of a parallelogram whose adjacent sides are 64 ft. and 36 ft., and one of whose angles is 45°. 513. The diagonals of a rhombus are 90 yds. and 120 yds. respectively. Find each side and the altitude. 514. A triangular lot of land was sold for $8208. Its sides are 25 yds., 101 yds., and 114 yds. respectively. What was the price per square foot ? 516. Compare the areas of a square and an equilateral triangle, if the perimeter of each figure is 60 ft. 616. The legs of a right triangle are 40 ft. and 30 ft. respectively. If a perpendicular be dropped from the vertex ,of the right angle to the hypotenuse, find the length of the parts into which the hypotenuse is divided, and the area of each part of the triangle. 517. A field has the shape of a right triangle, and the two legs are 100 yds. and 200 yds. respectively. How many acres does the field contain? And if a perpendicular be dropped from the vertex of the right angle to the hypotenuse, find the area of each of the parts into which the field is divided. i MENSURATION. 266 518. Find the value of a triangular field whose sides measure, respectively, 87 yds., 100 yds., and 143 yds., at 66 cents per square foot. 519. The diagonal of a trapezium is 54 ft., and the length of the perpendiculars to the diagonal from the opposite corners are 23 ft. 9 in. and 18 ft. 3 in. Find the area of the trapezium. 520. A field is bounded by four straight lines of which two are parallel. If the sum of the parallel sides is 1235 Iks., and the distance between them is 240 Iks., find the area of the field. 621. If a cai:riage- wheel make 220 revolutions in travel- ling half a mile, what is its diameter ? 522. There are two concentric circles. The circumfer- ence of the inner circle is 16 ft. 6 in., and that of the outer circle is 18 ft. 4 in. Find the width of the ring. 523. The minute-hand of a clock is 5 in. long. How far does its point move in one hour ? 524. Find the area of a semicircle if the radius of the circle is 14 ft. 525. The diameter of a circle is 56 ft. Find the side of a square equal to the circle in area. 526. The diameter of a circular grass-plot is 28 ft. What must be the diameter of a similar plot, in order that it may be just twice as large as the first ? 527. Compare the areas of a circle, a square, and an equilateral triangle, if they all have the same perimeter ; namely, 132 ft. 528. Find the cost of paving a circular court 30 ft. in diameter, at $1.35 per square foot, leaving in the centre a he;?iagonal space ^ach side of which measures 2 ft. 266 AEITHMETICAL EXERCISES. 529. The chord of half an arc is 17 ft. 9 in., and the height of the arc is 6 ft. 3 in. Find the diameter of the circle. 630. The chord of half an arc is 60 ft., and the diameter of the circle is 125 ft. Find the height of the arc. 531. How many cubic feet of stone are required to build a dam 1000 ft. long, 20 ft. high, 10 ft. wide at the bottom, and 4 ft. wide at the top ? 532. The distance around a reservoir in the shape of a regular hexagon is 360 ft. If the average daily loss from evaporation amounts to a layer of water 2 in. deep, how many cubic feet of water must be supplied daily to main- tain the water at a constant level? 633. How many square feet of sheet iron are required to make a funnel 2 ft. in diameter and 40 ft. long ? 634. I wish to have made a cylindrical pail 14 in. high, and holding exactly 4 cu. ft. What must be the radius of the base ? 535. Iron weighs 7.2 times as much as water, and 1 cu. ft. of water weighs 62-J- lbs. Find the weight of a cylindrical iron shell 1 in. thick and 2 ft. long whose inner radius is 7 in. 536. Find the expense of polishing the curved surface of a marble column 7 ft. 4 in. in circumference, and 15 ft. high, at $1.50 per square foot. 537. A cubic inch of gold weighs 11 oz. How many ounces of gold will be required in making a solid- gold ornament in the shape of a right pyramid 6 in. high, witk a square base each side of which is 3 in. ? 638. A conical mound of earth measures 264 yds. around its base, and the slant height is 70 yds. Find how many cubic yards of earth it contains. MENSUBATION. 267 539. The volumes of two spheres are as 1 to 3. The diameter of the first is 7 in. Find the diameter of tha other. 640. A bullet 3 in. in diameter is melted and then cast into a cylinder 2 in. in diameter. What is the height of this cylinder? 541. A plank is 23-J- in. wide. What length must be taken in order that the area of the part cut off may be 188 sq. ft. ? 542. A room is 38 ft. by 29 ft. What will it cost to plaster the walls to the height of 19 ft., at 2J cents per square foot? 643. A street is f of a mi. long, and 35 ft. wide. What will it cost to pave it with stones 11 in. by 3 in. upper sur- face, at $62J- per 1000? 644. How many persons can have lots of 2^ A. out of a field containing 2^ sq. mi. ? 545. A railway 22^ mi. long is double-tracked with rails weighing 24 lbs. to the foot. Find the cost of the rails at $50 per ton. 646. A lot containing 73f A. of land is for sale. A offers 20 cents per square foot, and B 9 cents per square link. Which offer is the best for the seller, and by how much? 547. A lawn 35 yds. by 27 yds. is to be covered with turfs 21 in. bv 18 in. What will the turfs cost at 3 cents each? 548. Garden A is 40 yds. by 30 yds., and garden B is 96 yds. by 72 yds. If A is lengthened 10 yds. and B 12 yds., how much must the width of each be diminished in order ihattbe areas may be unaltered? 268 ARITHMETICAL EXERCISES. 649. The area of a floor is 588 sq. ft., and its length and breadth are as 4 to 3. Find them. 550. The sides of three squares are 4 ft., 5 ft., and 6 ft., respectively. Find the side of a square equal in area to their sum. 651. A concert-room measures 21 yds. by 16 yds., and ^ of the floor is occupied by the orchestra. Benches 15 in. wide are placed for the audience across the room 2 ft. 3 in. apart, leaving a passage 4 ft. wide up the centre. Allow- ing 22 in. of bench to each person, how many can be seated ? 662. A room is 31^ ft. by 17 ft., and 12^- ft. high, with 3 windows each 5^ ft. by 6 ft., 2 doors each 7^ ft. by 4 ft., and a fireplace 7 ft. by 6^ ft. The carpet is 27 in. wide, costs $2.50 per yard, and is laid lengthwise across the floor. The paper is 27 in. wide, and costs $1.80 per roll of 10 yds. Find the cost of the carpet and the paper. 563. Two ships, making 6 mi. an hour each, sail from the same point. A starts at noon due west. At 3 p.m. B sails north. How far apart are they at midnight ? 664. A tree is partially broken by the wind at the height of 38 ft. from the ground, and the top touches the ground at an angle of 45°. Find the height of the tree. 666. How many diamond-shaped panes of glass, meas- uring 6 in. and 5 in. diagonally, will fill a window 18 ft. by 12^ ft. ? 666. Find the value of a triangular lot whose sides are 40 yds., 40 yds., and 48 yds., at 27 cents per square foot. 567. A, B, and are the corners of a right triangle right-angled at B, which is 176 yds. from C, and 189 yds. from A. In walking from A to 0, how much is saved by going direct, instead of going round by B ? MENSURATION. 269 658. A barn is 49 ft. long. The roof is 32 ft. span, and rises 4 yds. perpendicular from the eaves, and makes a right angle at the ridge. Find the cost of slating it, at 15 cents a square foot. 659. If a box will hold 1200 balls 1 in. in diameter, how many balls 2 in. in diameter will it hold ? 560. A meadow 120 yds. by 84 yds. is drained by tiles 18 in. long laid in rows 9 ft. apart. Find the cost at $7.20 per thousand. 561. Around a circular basin 17 ft. 6 in. wide is a walk 3 ft. 6 in. wide. What will it cost to gravel it at 30 cents per square yard ? 662. A piece of land 100 yds. by 78 yds. is surrounded by a ditch which occupies 1880 sq. yds. What would be its dimensions if the ditch were filled up ? 563. The gable end of a building is 41 ft. wide, 46^ ft. from floor to eave, and 15 ft. perpendicular from eave to ridge. Find the number of bricks 9 in. by 3 in. required for its facing. 664. What different areas will a cord 16 yds. long en- close, if arranged in the form of (i.) a square, (ii.) a circle, (iii.) an equilateral triangle, (iv.) an isosceles triangle with base 4 yds. ? 665. A grass-plot has the shape of an equilateral triangle with side 12 yds. A circular basin is made in its centre touching each side. Find the area of the basin. 566. How many medals 2\ in. diameter can be struck out of a square sheet .of metal one side of which is 15f ft. long ? And how much metal will then be left ? 667. What must be the length of a tether to enable a QOW to graze over just 10 sq. rds. ? 270 ARITHMETICAL EXERCISES. 568. Allowing 7 ft. as a cow's length from horns to tail, how much more surface may she graze, if a rope 35 ft. long be tied to her tail instead of to her horns ? 569. A table has the shape of a regular octagon, side 3 ft. ; and another table has the shape of a regular hexagon, side 4 ft. What will it cost to paint both their surfaces, at 8 cents per square inch ? 570. A single circular valve is required to replace three smaller ones containing severally 10, 20, and 30 sq. in. Find its diameter. 571. A boiler needs a safety-valve 10 in. in diameter, but has only an 8-in. one. Find the diameter of a second valve required to make up the deficiency. 572. A measuring wheel is 3J ft. diameter, and turns exactly 168 times in going round a circular pond. Find the area of the pond. 573. How must a circular lot of land 343 ft. diameter be laid out so that a fish-pond in the centre, a flower-garden round the pond, and a walk around the garden, may each occupy ^ of the entire area ? 574. The piston of a pump is 16 in. in diameter, and moves through a space of 46 in. How many cubic feet of water will be thrown out by 1000 strokes ? 575. A body is placed under water in a right cylinder 60 in. in diameter, and the level of the water is observed to rise 30 in. Find the volume of the body. 576. How much will a brass cylinder weigh under water if the height is 10 in., and the diameter of the base is 7 in.? Brass is 7.8 times heavier than water, and a body when immersed in water loses a weight equal to the weight of the water displaced. CHAPTER VIII. MISCELLANEOUS EXERCISES. 1. The chief items of expense in converting 450 bu. of Dakota wheat into bread ready for sale in Boston, accord- ing to Mr. Atkinson's book on " The Distribution of Prod- ucts," are as follows: price paid the Dakota farmer for the wheat, 80 cents per bushel; railroad freights, $200; milling at Minneapolis into 100 bbls. of flour, $ 50 ; cost of barrels, $40; commissions and cartage, $30; total cost of converting 100 bbls. of flour into 30,000 lbs. of bread, $420. If each loaf of bread weighs 1-J- lbs. and is sold for 8 cents, what per cent profit can a Boston baker clear above all expenses by buying Dakota wheat and converting it into bread ? 2. The change in the deposits in the savings banks of Massachusetts between 1865 and 1885 is shown by the following figures : 1865. 1885. Population, 1,267,330, 1,941,465. Number of accounts, 291,488, 848,787. Total amount deposited, $59,936,482, $274,998,412. Find for each date the average deposit on each account, and also the average deposit per head of population. 3. A man has 50 qts. of wine which cost him 62 cents per quart. After adding 12 qts. of water, he wishes to sell it so as to make 2h^o on his outlay. What should be his selling price ? 272 ARITHMETICAL EXERCISES. 4. In round numbers the population of this country was 34,750,000 in 1865, and 57,000,000 in 1885. • The total grain crop was 1,127,500,000 bu. in 1865, and 3,000,000,000 bu. in 1885. Which has increased more rapidly during the period between the dates mentioned, the population or the production of grain ? If the number of bushels of grain per head in 1865 be represented by a line 1 in. long, how long a line would represent the number of bushels per head in 1885 ? 5. The wheat crop of the United States in 1884 was in round numbers 500,000,000 bu. Land of good quality in Texas will produce 20 bu. of wheat per acre. The area of Texas is 275,000 sq. mi. very nearly. How much good land would be required to raise the entire wheat crop of 1884, and what per cent of the area of Texas would suffice for this purpose ? 6. The cotton factories of the world now require about 12,000,000 bales of cotton. Good land in Texas produces 1 bale to the acre, and Texas contains in round numbers 275,000 sq. mi. What per cent of the area of Texas would be sufficient for producing all the cotton required ? 7. The wages of mechanics in Massachusetts are now (1886) about 25% higher than in 1860, and the prices of things are on an average about 20% lower. If a mechanic now receives $90 per month, how much money could he save in a year, supposing that he saved nothing in 1860, and that he has the same standard of living now as then, with no additional expenses? 8. When water is heated from the freezing-point to the boiling-point it expands -^ in volume. If a cubic foot of water at the freezing-point weigh 62^ lbs., what will a cubic foot of boiling water weigh ? MISCELLANEOUS. 273 9. A merchant imports to New York goods which cost him £616 sterling in London. He pays an ad valorem duty of 12 9& on the goods, and a commission of 7% to agents for selling them. The goods realize $ 7800. What is the merchant's net gain, the pound sterling being equal to $4.86? 10. A circular plate of lead 8 in. diameter and 2 in. thick is converted without loss into spherical shot each 0.05 in. radius. How many shot does it make ? 11. A tailor buys 38 yds. of cloth at $2.45 per yard. Sponging causes a shrinkage of 4%. What must be his selling price in order that he may gain 10% ? 12. Two men perform a piece of work in 18 dys., and receive for it $189. One of the men was absent 5 dys. What amount of money should each man receive ? 13. Six men undertake to do a piece of work in 15 dys. They work 10 hrs. a day, but at the end of 8 dys. they find that only half of the work is accomplished. How many hours a day must they work during the remaining time in order to finish the work in the time agreed upon ? 14. A wine merchant imported 1315 gals, of wine at a cost of $3.33J- per gallon. After adding water in the ratio of a quart of water to each gallon of wine, he bottled the wine in bottles costing 5 cents each and holding a pint and a half. At what price per bottle must he sell the wine in order to make 50% profit on his money? 16. Five men have performed a piece of work in 20 dys., and have received for it $521.50. One of the men was absent 5 dys., and another was absent 2 dys. Another man receives 60 cents a day extra for directing the work. What should each man receive ? 274 ARITHMETICAL EXERCISES. 16. A milliner bought 275 bonnets at $14.40 apiece. She sold "I of them at 15 ^^ advance, and the rest at $13.75 each. What did she make by the transaction ? 17. Hay costs $22 per ton, and oats cost 80 cents per bushel. If 1 horse eat daily 20 lbs. of hay and 8 qts. of oats, what will it cost to feed 10 horses from Dec. 1, 1889, to Mar. 31, 1890, both dates included? 18. A boy sells paper at 20 cents a quire, and 6 pens for 5 cents. The paper costs him $3.25 per ream of 20 quires, and the pens cost $1.10 per box containing 18 doz. What is his profit in selling 80 reams of paper and 30 boxes of pens? 19. An ore contains 18% of pure lead, but 14% of this lead is lost in reducing the ore. What weight of ore must be treated in order to obtain 1 t. of pure lead ? 20. A hall is lighted by 58 gas-jets every evening except Sunday from 5.45 p.m. to midnight ; each jet burns 6 cu. ft. per hour. The price of the gas is $1.25 per 1000 cu. ft. Find the cost of lighting the hall for the month of January, if the month begins on Friday. 21. From a pipe full of wine -I of the contents are drawn away, and then 35 gals, are added. The pipe is then just half full. How many gallons will it hold ? 22. If a wheel revolves 91 times in 3f sec, how many times will it revolve in 5f hrs. ? 23. If f of a yard of velvet cost $3, what will ^ of a yard cost? 24. A locomotive travels ^^ of a certain distance in 3^ hrs. In how many hours will it travel at the same rate ^ of the same distance ? MISCELLANEOUS. 276 25. A schoolroom is 40 ft. long, 26^ ft. wide, and 19 J ft. high. If at least 80 cu. ft. of space and 8 sq. ft. of floor must be provided for each scholar, what is the maximum number of scholars which the room can provide for ? 26. On a certain map the linear scale is one inch to five miles. How many acres are represented on this map by a quarter of a square inch ? 27. If 1 lb. of dry oak wood gives out | the heat fur- nished by 1 lb. of coal, and if a cord of the oak wood weighs 2700 lbs. and costs $9, what should be the price of the coal per ton in order that it may be just as cheap as the wood? 28. A reservoir holding 6000 gals, is supplied by two pipes. One conveys 100 gals, in 1^ hrs., the other 200 gals, in 4^ hrs. If both pipes are turned on, in what time will they fill the reservoir ? 29. An ore contains -^ of its weight of iron, but 7% of this is lost in smelting. How many tons of ore must be handled annually in order that the daily output of iron may be 7-| t., the number of working days in the year being 310? 30. Divide $4832 among three persons in proportion to their ages, which are respectively 20 yrs., 24 yrs., and 26 yrs. 31. A man holds a note for $1800 payable July 18. On May 7 he ofi'ers to cancel it for a note for $500 pay- able May 25, another note for $600 payable Sept. 4, and the remainder in cash. How much in cash should he receive when money is worth 6% ? 32. Find the total proceeds of three notes, the first for $1550 payable in 6 mos. 20 dys. ; the second for $1990 payable in 3 mos. 10 dys. ; the third for $2480 payable in 5 mos. 25 dys., all three notes being discounted at 4^%. 276 ARITHMETICAL EXERCISES. 33. A man invested in a business $216,800. The first year he lost 9% of his capital; the second year he lost 4f % of what remained; but the third year he gained 44% of what was still left. How much capital did he have at the end of the third year ? What rate per cent simple interest did his money yield for the whole period ? 34. The base of the great pyramid near Cairo is a square 764 ft. on a side, and its height is 486 ft. What is the altitude of one of the triangular faces ? 35. Find the length of the side of a cubical vessel that shall contain twice as much as one whose side is 8 in. 36. If a wall 42 ft. long, 10 ft. high, and 2^ ft. thick contains 12,800 bricks, how many bricks of the same kind will be required for a wall 112 ft. long, 6 ft. high, and 2 ft. thick ? 37. A ship valued at $51,200 belongs to A, B, and 0. A owns y^ of it, and B owns \ of the remainder. What should C pay them for their joint shares to make a profit of 20% by the purchase? 38. Copper is bought at $306 per ton, payable in 6 mos. At what price should it be sold the same day, giving 8 mos. credit, in order to gain 25%, money being worth 4% ?^ 39. Two towns, A and B, are 30 mi. apart. The road between them goes over a hill the summit of which is 6 mi. from A. Two men set out at the same time from A and B ; the former walks 4 mi. per hour up hill and 5^ mi. per hour down hill, the latter 3^ mi. up and 4J mi. down. How far from A will they meet ? 40. Water expands 10% in freezing, and a floating body displaces an amount of water equal in weight to the body. What per cent of an iceberg is above water ? MISCELLANEOUS. 277 41. Four postmen deliver the letters in a certain city, two working 14 streets, and the other two 17 streets. The work of each of the latter streets is 20% less than that of each of the former streets. If a fifth man is brought in to help them in such a way that all five shall have equal work, in what ratio should he assist the two pairs of men ? 42. Find the amount at compound interest of $735 in 18 mos. at 6% per annum, interest payable semi-annually. 43. A man sold a horse at a loss of 20%. If he had received $60 more, he would have gained 10%. What did the horse cost him ? 44. Find the compound interest on $ 216 for 9 mos. at 5%, interest to be paid quarterly. 45. A, B, and C respectively invested $25,652, $20,988, and $16,324 in a business which yielded in one year a net profit of $5849.21. What was the share of each ? 46. A hatter bought 363 straw hats for $484. He sold f of them at a gain of 12^%, and the remainder at a loss of 6J%. What was his gain or loss per cent on the whole ? 47. Find the amount of $5553^ in 6f yrs. at 2J%, simple interest. 48. If a ship be lost which is insured for 88^% of its value, and its value be $83,650, what would a man lose who owns f of the ship ? 49. If 3% bonds are at 89f , what must be the price of 5 per cents that there may be no loss of income in selling out the former and buying the latter, allowing for a broker- age of ^% in each transaction ? 50. The average length of 10 sticks is 2 ft. 10^ in. ; one is 27^ in. long, another 37^ in. long. Find the average length of the remaining 8 sticks. 278 ARITHMETICAL EXERCISES. 51. How many boys, earning $1.10 per day, would earn in 12 dys. as much as 15 men would earn in 22 dys. at $1.40 per day? 52. If 400 meters equal J of a mile, how many square meters are there in J of an acre ? 53. If 2 cu. in. of mercury weigh 1 lb., and 100 cu. in. of air weigh 31 grs., how high must a column of air be to weigh as much as a column of mercury 29.388 in. high, standing on a base of the same area? Give the answer in miles and yards. 54. A ship-owner insures his ship so that in the event of loss he may recover the value of the ship and the pre- mium. The vessel is worth $64,350, and the premium is 2^%. Find the amount for which he must insure, and the premium he must pay. 55. A puts $5000 into a business, and B $6000, the partnership dating from Jan. 1, 1884. On May 26, B withdraws f of his capital. The whole profits for the year amounted to $573.68. What was B's share ? 56. Find the difference between the simple and the compound interest on $5208J for 4 yrs. at 5%. 57. If 1 lb. Troy of silver is worth $13.20, and if 2^ lbs. avoirdupois equal 1 kilogram, find the value of a lump of silver weighing 2.64 kilograms. 58. The average age of the boys in four classes is 18.4, 17.9, 17.7, 17.8 yrs., and the numbers respectively are 29, 33, 33, 34. Find the average age of the whole number of boys. 69. What is the greatest interval of time which is con- tained an integral number of times in 22 dys. 11 hrs. 15 xnin. 3 sec. and in 35 dys. 7 hrs. 23 min. 39 sec? MISCELLANEOUS. 279 60. Find the cost of papering the walls of a room 30 ft. 6 in. long by 21 ft. 4 in. wide, and 10 ft. 6 in. high, with paper 1 ft. 9 in. wide at 60 cents per roll of 10 yds., allow- ing 260 sq. ft. for windows, etc. Also find the cost of painting the ceiling at 10 cents per square yard. 61. An agent is allowed 8% commission for selling pianos, on condition of his making good any bad debts. If he sell 367 pianos at an average price of $ 170.54 each, and the bad debts amount to $59.53, what clear profit does he make? 62. What must be the price of a stock paying 7-^% per annum, so that a man may take it in exchange for a 4% stock worth 112J- without altering his income, allowing J-% brokerage both in selling and in buying? 63. If the planet Venus and the earth revolve round the sun in 224.7 dys. and 365.25 dys. respectively, at what intervals will the three bodies be in a straight line ? 64. Simplify lAof(4f + l|-6|-2| + 3A) P ^ 6f of H of If - li 65. A man receives $8754-| for the sale of goods upon which he has a commission of 5 % . What amount does he clear if his expenses are 15^% of his commission ? 66. If 0.0645 of a mile be travelled in 0.00301 of an hour, what is the rate in yards per second ? 67. If 10 negroes can dig a trench 100 yds. long, 2 yds. wide, and 4 ft. deep in 6 dys. of 8 hrs. each, in how many days of 10 hrs. each will 12 Irishmen dig a trench 80 yds. long, 3 yds. wide, and 2-^ ft. deep, an Irishman being sup- posed able to do ^ as much again as a negro ? 68. A pound weight of brass contains 3.3 cu. in., and a pound weight of antimony contains 6.27 cu. in. Find the weight in pounds of a mass of 313^ cu. in., containing equal weights of the two metals. 280 ARITHMETICAL EXERCISES. 69. A vertical glass tube contains water and oil. The height of the column of oil is 0.7 of that of the water, which is 25 in. If 16% of the oil be removed, by what per cent is the height of the whole column diminished ? 70. For doing a paper of 16 questions, 84 min. are allowed. If a boy spend 1-J- min. on the first question, 4f min. on the second, 6|- min. on the third, and 8 min. on the fourth, what is the average time which he can give to each of the others ? 71. If an ore lose 43.2% of its weight in roasting, and 39.5% of the remainder in smelting, how many tons of ore must be raised to produce 50 tons of metal ? 72. A pays B five $100 shares which sell at 10|-% pre- mium as the present worth of a note for $638 due in 1 yr. 4 mos. at 12%. Which gains by the payment, and how much ? 73. A grocer buys a barrel of sugar containing 336 lbs. at 5 cents per pound, and 2 bbls. each containing 336 lbs. at 4 cents per pound, and 2 bbls. each containing 392 lbs. at 5|- cents per pound. He then mixes the sugar and sells 1008 lbs. of the mixture at 6 cents per pound. Find the selling price per pound for the remainder, in order that he may gain 42% on his whole outlay. 74. Two trains travelling in opposite directions pass each other in 3-J- sec. Their lengths are 261 ft. and 201 ft. respectively. If the first train is travelling at the rate of 50 mi. per hour, what is the rate of the other ? 75. One-fourth part of some goods was destroyed by fire, and one-third part of what remained was sold at a loss of 10%. By what per cent must the cost price of the remaining goods be increased, in ord^r thfl^t no loss may b^ sustained? MISCELLANEOUS. 281 76. A person wishing to determine tlie length of an iron bridge, and knowing the velocity of sound in iron to be (roughly) 15 times that of sound in air (1120 ft. per sec- ond), places his ear at one end and notices an interval of 0.4 of a second between the two sounds received, one through the air, the other through the iron of the bridge, from a blow at the other end. What was the length of the bridge ? 77. If a cubic inch of water converted to steam will produce mechanical force sufficient to raise 2200 lbs. a foot high, how many meters high would the conversion into steam of a cubic centimeter of water raise one kilogram ? (Take 1 in. = 2.5 centimeters, and 1 kilogram = 2.2 lbs.) 78. A man owns two houses worth $5930 and $13,275 respectively. If the first rise in value 10%, and the second fall 3%, find the change per cent in the value of his whole property. 79. A can beat B by 6 yds. in 300 yds., andC can beat B by 9f yds. in 300 yds. By how much will C beat A in a mile race ? 80. If pure spirit cost $2.80 per gallon, in what ratio must spirit and water be mixed in order to clear 25% profit by selling the mixture at $2.50 per gallon ? 81. If $100 be invested at the beginning of each of 5 yrs. at 5% compound interest, find the total amount at the end of the 5 yrs. 82. If the work of 3 men is equal to that of 5 women, or to that of 7 boys, and if 3 men, 3 women, and 8 boys do ■| of a piece of work in 7 dys., working 8^ hrs. per day, how many days will it take 4 men, 11 women, and 7 boys to finish the work, working 9 hrs. a day ? 282 ARITHMETICAL EXERCISES. 83. In what proportion should tea at 90 cents per pound and tea at 45 cents per pound be mixed, so that by selling the mixture at 80 cents per pound there should be a gain of 26%? 84. Of three traders, A, B, and 0, A sells goods 16% dearer than B, and C 16% cheaper than B. What per cent does one of B's customers lose by dealing with A, and gain by dealing with 0? 85. A man finds that he can row 20 mi. down a river in 4 hrs., but that it takes him 6 hrs. to row back again. Find the rate of the stream, and his rate of rowing in still water. 86. If a man pronounce 9 syllables per second, and sound travel 1120 ft. per second, at what distance from a high rock ought he to stand, that the echo may be heard to repeat the last four syllables ? 87. A tradesman's price is 20% above what the goods cost him, but he deducts 5% for cash payment. What profit does he make on cash payments ? 88. The exact weight of a cubic foot of water being 62.36 lbs., find the error made in calculating the weight of 1000 cu. ft. of water on the supposition that 1 cu. ft. of water weighs 62^ lbs. 89. By selling a mixture of coiFee and chiccory in the ratio 7 : 3, a grocer gains 22^%. He then alters the ratio to 11 : 5, and sells the mixture at the same price as before. What does he now gain per cent, supposing the coflPee cost him 4 times as much as the chiccory ? CHAPTER IX. THE METRIC SYSTEM. I. Length. The names of the nnits of length, beginning with the largest, ar» as follows : kilometer^ hekiometer^ dekameteTf meter, decimeter, centi- meter, millimeter. Abbreviations : km, hm, dhm, m, dm, cm, mm. Each unit is 10 times as large as the next smaller unit. 1. How many millimeters are there in 1^? 2. Reduce 4*™ to each of the other units. 3. Reduce 8300"^ to each of the other units. 4. Reduce 126" to kilometers ; to millimeters. 5. Add 2*" 28°* 40*°^ ; 6254*'°" 96*" ; 163'°" 29*^"; 1000*^" gjdkm^ Give the answer in meters. 6. Subtract 4000^ 9"^ 6*" from 6,146,676°". Give the answer in meters. 7. The lengths of two roads are 24**" 8«" and 2540*" 42"". How many meters is one road longer than the other? 8. A lady bought 145"" of flannel at $0.80 per meter, and 3.25" of plush at $0.62 per decimeter. What was the amount of her bill ? 9. Multiply 39*^™ 8°" by 9, subtract from the product 2511m ^mm^ g^j^^ g^yg ^jjg answer in decimeters. 10. If 10 paces measure 8° 8*", how many centimeters are there in 2045 paces? 11. By what number must you divide 603,107*" in order that the quotient may be ll**"? 284 ARITHMETICAL EXERCISES. II. Surface. The units of surface are squares whose sides are units of length. Abbreviations : qkm, qhm, qdhn, qm, qdm, qcm^ qmm. Each unit is 100 times as large as the next smaller unit. In measuring land, the square meter is called a centar (ca) ; the square dekameter, an ar (a) ; the square hektometer, a hektar (Jia). 12. Reduce 1**° to each of the other units. 13. Reduce 1****™ to each of the lower units. 14. Express S****"* 3***''°* 4^°* T****" in square meters. 15. Reduce 25,000,000**"° to square hektometers. 16. Reduce 1545.7368 ars to each of the other units. 17. Reduce 39**'™ to centars, ars, and hektars. 18. Two fields contain, one 45*, the other 4500". Which is the larger field ? 19. Add 138* to 3615**, and give the answer in ars. 20. What must be added to 17,453**'" to obtain 3*^» 9'? 21. The area of Paris is about 700,000*, and that of London about 100***°. What is the difference in ars ? 22. What is the difference in hektars between 9,674,248**'"" and 5,423,967,400* ? 23. What cost 2.7**' of land at $0.49 per square meter ? 24. What cost 3,457,675***"" of land if 5'"» cost $4.80? 25. If 8.704'^' of land cost $17,451.52, what is the cost of 1**'^" ? of 1 ar ? of I**"" ? 26. What costs l***^'" of land if 1128» cost $16,920? 27. What is the price per center, if 1**'™ is valued at $20,000,000? THE METRIC SYSTEM. 285 III. Volume. The units of volume are cubes whose edges are the units of length. Abbreviations : ckm^ chm, cdhm^ cbm, cdm, ccm, cmm. Each unit is 1000 times as large as the next smaller uait» In measuring wood, the cubic meter is called a ster (sQ. 28. Reduce 1°*" to cubic centimeters. 29. Reduce 640,000^ to cubic meters. 30. What part of a cubic decimeter are 200*^" ? 31* In making a canal the total amount of earth raised was 1^ 2°^" 8"^ T''*"^ IS''^ 45«»". Express this in cubic meters. 32. 19"'*" + 28 fiW^ = how manj cubic meters ? 33. Reduce 0.1 of a ster to cubic millimeters. 34. One piece of wood contains 0.1 of a ster, and another piece contains 100°*" ; which is the larger ? 36. How many cubic centimeters must be added to O.S**"" to obtain 1319"^? 36. From TOSO"^" take 16,756*^. Give the answer in cubic meters. 37. What is the cost of 29,500*'" of box-wood at $0,55 per cubic decimeter ? 38. Three blocks of stone contain, one 3.9°'*", another 1815^*", the third 0.000002*^*". What will the three blocks cost at $26.55 per cubic meter? 39. A man buys at one time 90"*" of guano, and at another time 12,040°^. What is the amount of his bill if V^ of guaoo costs $7.50? 40. A man buys the following quantities of marble: 9«i«i. 150o«im. 0.000031'"'"; 170,000,000~". Find the total cost to him of the marble at $ 22.50 per cubic meter. 286 ARITHMETICAL EXERCISES. IV. Capacity. The nnitB are the kilolUer, hektoliter, dekaliter^ liter, deciliter, ceTUi- liter, millUiter, 1 liter = l^^i » lOOO«^. Abbreyiations : kl, hi, did, I, dl, cl, ml. Each unit is 10 times as large as the next smaller unit. ' These units are used for measuring liquids, gases, and solids in small pieces (as wheat, potatoes, sand, etc.). 41. Express in liters 316" ; 7" 24^; 4015»». 42. Reduce 100,040^ to hektoliters. 43. Express in cubic decimeters the following : 24" 8' ; 22.9"; 17,005"^. 44. Add 245^, 4", 9**", 136"", and express the result in kiloliters. 45. What is the value in deciliters of 3019 half-liters + 452 double dekaliters ? 46. What is the value of 30" + 225.56*" in cubic meters ? 47. How many centiliters in 31,675«'°» + 2" 65"? 48. Reduce 2.25" + 2045'«°» to deciliters. 49. Express in hektoliters the value of 0.04°*" + 315" + 50 half-liters. 50. Two casks contain, the first 2" 4°*, the second 203,060~°*. What is the capacity in liters of both casks? 51. A cooper makes three casks having the following capacities : the first, 0.03" ; the second, 28"^ ; the third, 179.25°^. Find their total capacity in hektoliters. 52. How many cubic centimeters must be added to 0.8" in order that the sum may be 1.3" ? 53. If 1" of wine costs $37.50, what is the cost of 0.08" + 15 double dekaliters + 7"? 54. If 24,050" of wine are worth $9740.25, what is the value of 1 dekaliter ? THE METEIO SYSTEM. 287 V. Weight. The units of weight are the kilogram, hektogram, dekagram^ gram, decigram, centigram, milligram, Abbreviatirons : kg, hg, dkg, g, dg, eg, mg. Each unit is 10 times as large as the next smaller unit. 1 gram = weight of l'^*'" of pure water at 4° centigrade. 1 kilogram = weight of 1 liter of water. 1 ton =■ 1000 kilograms. 55. Reduce 1* to decigrams, centigrams, and milligrams. 66. Reduce 20'^« 4'»« 25*8 to dekagrams. 57. Reduce 1 ton 30^* to hektograms. 58. What fraction of a kilogram are 50**? 59. Reduce 60'^« to dekagrams, and 26,000,000** to tons. 60. What is the weight of 1*** of pure water ? 61. What is the weight of I*'*" of pure water ? 62. What volume of water in hectoliters will weigh IGOS"^* ? 63. A bar of iron weighs 20''* 4*** 8* 1** 5°**; express the weight of the bar in grams. 64. Find the value in kilograms of 39.28** + 170*^* + 1100*'^* + 8"^* + 25**. 65. Find in grams the value of 22,545°* + 20'^* + 6*^* + 0.07 of a ton. 66. How many grams must be added to 8.29^* in order that the sum may be 13'^* 24'5** ? 67. If indigo is worth $2.25 per half-kilogram, what will be the cost of a quantity of indigo weighing as much as 2.8«>" of pure water? 68. Express in dekagrams the weight of 8*" + 235°* + 450°°" of pure water. 69. If 2^ of quinine cost $15.00, what costs 1**^*? 288 ABITHMETIOAL EXEBCISES. VI. Miscellaneous Exercises. 70. A rope-maker makes 6*" 4**° 3*" 8™ 4**°* 2r 5™" of rope. How many meters does he make ? 71. If 19" of silk cost $123.50, what is the value of 1 decimeter? 72. Reduce 13,000,000*^ to square dekameters. 73. Two fields contain, the one 457'" 8^*", the other 0.00075*»'°". Which is the larger field ? What is the dif- ference in square meters between their areas? 74. If 41.5 ars of land cost $1045.80, what is the value of 1 square meter ? 75. If 51.04°^°* of guano cost $18,119.20, what is the value of 1 cubic centimeter? 76. What is the value of 49,000*«» + 39«* of olive oil at $1.75 per liter? 77. A man buys at the rate of $225 per hektoliter the following quantities of brandy : 1" 6*^^ ; 14*^ ; 14,040«*» ; 0.03". What was the total cost ? 78. If V of oil costs $1.10, what is the value of 500,000^^" + 0.24*;^" + 4.0008" ? 79. Find the value of the following sum in hektograms : 0.4 of a ton + 20.029" + 32,144«« of water. 80. Two vessels, when empty, weigh 95^* 8^* each ; fiill of pure water they weigh, the one 45***, the other :523,415*'. How many decimeters will one vessel hold more ^han the other ? 81. If a freight train travels 80^° in 15 minutes, how far will it go in 5} hours? THE METRIC SYSTEM. 289 82. If a man pays 10 cents for 25** of wine and 12 cents for Ti*** of brandy, wliat is the value, at the same rate, of 1 liter of each article ? 83. If a man's pace has an average length of 0.7", and he takes 100 paces in a minute, how long will he be in going 28^"*, supposing that he rests half an hour on the road ? 84. The annual production of coal in England is about 32,000,000 tons. "What is the volume of this coal in heko- liters, if 1" of coal weighs TS.S'^^ ? 85. Wood yields about i of its bulk of charcoal and about \ of its weight. If 1 ster of oak wood weighs TSS""*, and 1 ster of beech wood weighs 620''*, find the volume and the weight of charcoal furnished by 6 sters of each kind of wood. 86. A fountain furnishes 17°^ of water per second. How many hours will be required to fill a tank holding S*"^™ 87. In order to find the capacity of a glass vessel, it may be weighed, first when empty, and then when full of pure water. The difference between these two weights in kilo- grams will be the same as the capacity of the vessel in liters. Hence find the capacity of a vessel which weighs empty 2.8''«, and full of water 15,825''«. 88. A lot of land containing 63.21', worth $0.35 per square meter, is exchanged for another lot containing P* 5*. What is the value per ar of the second lot ? 89. Light travels from the sun to the earth in 8 minutes 13 seconds. The distance is 153,624,000,000"". What is the velocity of light in kilometers per second ? 90. A bag weighs when empty, 213*, and when full of silver iive-franc pieces, 20''* 35*** 13*. A five-franc piece weighs 25*. How many five- franc pieces will the bag hold ? 290 ARITHMETICAL EXERCISES. 91. What is the value of 28*»^" Id^^^^ of cloth at $3.50 per square meter ? 92. How many square centimeters of surface has a table which is 1.1"* long, Q.85" wide ? 93. A garden in the shape of a rectangle is 235.08" long and 117.25°* wide. Find its value at $0.22 per square meter. 94. Find what the air in a balloon holding 725.85* weighs, knowing that water is 770 times heavier than air. 95. A vessel weighs when empty 2.7**, and when full of water 4235*'^*. What would it weigh if filled with milk, which is 1.03 times as heavy as water? 96. If milk is 1.03 times as heavy as water, and yields 15 9& of its weight in cream, and the cream yields 25% of its weight in butter, how many liters of milk are required to make a kilogram of butter ? 97. A landowner was offered $40,000 for a lot contain- ing 3.25 ars. He refused the offer. The land appraisers then allowed him $ 124 per square meter. Did he gain or lose by refusing the offer, and how much ? 98. Sound travels 340° per second. How far is a cannon from a man who hears the report 13 seconds after seeing the flash, assuming that light travels the distance instan- taneously? 99. If 34.19 ars of land are worth $1540, what is the value of 237.21^°*? 100. What is the price of a block of Carrara marble 2.6™ long, 1.85° wide, and 0.95° thick, at $2.45 per cubic deci- meter? 101. What is the cost, at $3.75 per ster, of a pile of wood having the following dimensions: length, 6.5°; breadth, 2.3°; height, 1.25°? THE METRIC SYSTEM. 291 102. Four vineyards furnish, the first, 1300*" of wine ; the second, T^"* & ; the third, 26,143*' ; the fourth, 15,000,- QQQoom pijj^ ^^q value of the entire quantity at $7.25 per double dekaliter. 103. If 1*" of walnuts yields V of oil, how much oil can be extracted from 4.08°^°* + 672' of walnuts, and what is it worth at $0.85 per half-liter? 104. If 6" I*' of Rhine wine are worth $480, what is the value of 1 dekaliter ? 105. An empty vessel weighs 27** 35**, and full of pure water, it weighs 243''*. What is its capacity in dekaliters, and in cubic decimeters ? 106. At the rate of $1.50 per kilogram, what is the price of 8135** + 143*** of tea ? 107. A trader buys at one time 9.85** of nut oil, and at another time 1,345,675"*. Find the cost of the whole at $0.19 per hektogram. 108. A druggist buys 3 boxes of fancy soap. »The first box weighs 75.25**; the second 80.39**; the third 90**. The empty boxes weigh 13.85**. What is the cost of the soap at 88} cents per kilogram ? 109. If 0.002 of a ton costs $15.75, find the price of a dekagram. 110. If 13** 6*** costs $105,133, find the price of a hektogram. 111. The weight of a body floating in a liquid is equal to the weight of the liquid displaced. What is the weight of a block of wood 1.6™ long and 0.8"* wide, which, lying horizontally in the water, sinks to a depth of 0.12"? 292 ARITHMETICAL EXERCISES. 112. A pile of wood containing 20.88 sters is 4.8" .long and 2.9™ wide. What is its height ? 113. A silver five-franc piece weighs 25*, and is com- posed of 9 parts pure silver and 1 part pure copper. A silver two-franc piece weighs 10«, and is composed of 635 parts of pure silver and 165 parts pure copper. A silver twenty-centime piece weighs 1*, and has the same composi- tion as the two-franc piece. Find the total weight of pure silver and of pure copper contained in 272 pieces of five- francs, 145 pieces of two-francs, and 179 pieces of twenty- centimes. Find also the total value, knowing that 100 cen- times = 1 franc. 114. A pile of wood 5.6" long, 3.7" wide and 1.85" high, supplies 4 fires. How long will it last, if each fire con- sumes 0.045 of a ster per day ? 115. What will it cost at the rate of $4.55 per 100 kilo- grams, to send 102,850 francs in silver five-franc pieces from Paris to Canton ? (See Ex. 113). 116. A floor, 5.4" long and 4.25" wide, is paved with square tiles 0.16" long, and costing $32.50 per thousand. Find the cost of the tiles. 117. If 1~" of a certain oil weighs 925"«, what is the value of 54^* 7* of the oil at $1.95 per kilogram ? 118. If a hektoliter of coal weighs 87.5^*, what sum will be obtained by selling 298''^" of the coal at $5 per ton ? 119. If a hektoliter of olive oil weighs 91.5**, and costs $120.25, what is the value of P« ? also of 1 liter? 120. If 1" of coal yields 1854°^" of gas, and 1 burner consumes 139* of gas in an hour, how many hektoliters of coal are required to supply 2600 burners going for 1440 hours ? THE METRIC SYSTEM. 293 121. A wheat-field contains IS.TQ"', and yields 301" of wheat, which is sold at the rate of $7.03 for 120^«. One hektoliter of wheat weighs 76^*. How much wheat is ob- tained from each square dekameter, and what is its value ? 122. A wood-lot contains 35**' 7* 4°' of land, and it is estimated that the quantity of wood will average 122 sters per hektar. Upon this basis find the value of the wood at $4.10 per ster. 123. If 2&"^ of flour yields 35*« of bread, and P" of wheat yields G''* of flour, find (1) how many hektoliters of wheat in one year a family of 6 persons will require, if each person on the average eats 7*"* of bread per day ; (2) the daily cost of the bread for the family, if 1" of wheat costs $3.72. 124. A grocer buys 3 boxes of fancy soap weighing, the first 210^« 7*^; the second 23,500*''« ; the third 0.37 of a ton. The empty boxes weigh 7.25**. The price paid is $17 for 100*^* of soap. Find the total weight of the soap and its cost. 125. A certain gas-burner consumes, on the average, 120* of gas per hour. Find the cost of lighting a room for 3 months, if there are 4 of these burners, and the room is lighted for 2 hours on 20 evenings during each month, and the gas costs $0.07 per cubic meter. 126. How much silver must be combined with 897* of copper, to form an alloy suitable for making five-franc pieces? (See Ex. 113.) Find the number of francs that can be made from the alloy. 127. By selling spice at $4.25 per kilogram which cost $0,372 per hektogram, a merchant makes a profit of $66.25. How many kilograms of spice did he sell ? 294 ARITHMETICAL EXERCISES. 128. A rectangle is 123.2" long and 74.6™ wide. Find its area (1) in square dekameters, (2) in centars. 129. Find in ars the areas of four rectangles whose di- mensions are as follows : the first 0.25" and 0.07" ; the second 49.03" and 29.9" ; the third 135.85" and 94.06" ; the fourth 210.42" and 115.7". 130. The base of a triangle measures 136.25", and its altitude 48.2". Find its area. 131. Find the altitude of a triangle, if the base is 82", and the area 51,373 ars. 132. The bases of a trapezoid are 83.45" and 57.55" respectively ; the altitude is 33.6". Find the area. 133. The diagonals of a rhombus are 8.6" and 6.85" respectively. Find the area. 134. Find the area of a circle the radius of which is 18" (take IT = 3.1416). 135. The radius of a circle is 0.75". Find the circum- ference and the area (take ir = 3.1416). 136. Find the area of a triangular field whose base is 950.75" and altitude 357.8". 137. If the area of a rectangular field is 95.8016 ars, and the base is 107.2", what is the altitude ? 138. A rectangular field is 278" long and 112.85" wide. I wish to take from one end of the field a rectangular lot that shall contain 78 ars. What will be its width, and what will be the area of the remainder of the field ? 139. What is the altitude of a field in the shape of a trapezoid the sum of whose bases is 231" and whose area is 0.924»'»? THE METRIC SYSTEM. 295 140. If a hektar yields 23J-" of wheat, what is the yield of a rectangular field 187.65"* long and 135.2" wide ? 141. What is the volume of a cube whose edge is 2.35"? 142. What weight of water will a rectangular tank hold, if its length is 1.6", its breadth 1.25", and its depth 0.85"? 143. The base of a cistern has an area of 22.4*i", and the cistern will hold, when full, 56,000*^* of water. What is the depth of the cistern ? 144. What is the price of 4 oak beams, each 10.8" long, and 0.45" square at the end, and sold at the rate of $30 per cubic meter ? 146. A pile of wood is made between two posts 0.82" apart. The sticks are 1.25" long. What must be the height of the pile in order that it may have a volume of 1 ster ? 146. The mean depth of a pond is 1.8", and it occupies a surface of 3.4 hektars. How many cubic meters of water does the pond contain when full ? 147. A heavy rain caused the water in a cistern 5.4" long and 2.6" wide to rise 0.53". How many liters of water fell into the cistern ? 148. Find the volume of a cylinder whose height is 5.38", and the diameter of whose base is 2.4" (take ir = 3.1416). 149. Find the volume, in cubic decimeters, of a cylinder whose height is 0.53" and the circumference of whose base is 155«" (take ir = 3.1416). 160. The radius of a cylindrical log is 0.25" and its length is 2.16". Find its volume in sters (take tt = 3.1416). 161 . A cylindrical vessel, the circumference of whose base is 2.2" and whose height is 2.1", is four-fifths filled with pure water. Find the weight of this water (take tt = 3.1416). 296 ARITHMETICAL EXERCISES. 152. Find the height of a square pyramid if a side oj the base is 3.05"^ and the volume is 37.21*^". 153. Find the surface of a sphere whose diameter is equal to 1.8"» (take tt = 3.1416). 164* Find the volume of a sphere whose radius is equal to 23.5" (tate ir = 3.1416). 166. Find the diameter of a sphere whose volume is equal to 240"^"^ (take tt = 3.1416). 156. If the circumference of a cannon-ball is 52^, find the surface and volume of the ball (take ir = 3.1416). 157. The meter was originally defined as i o o o^o o o o ^^ the distance from the equator to the north pole. Taking the circumference of the earth to be 24,855 mi., find the value of 1" in inches, correct to four decimal places. 158. Reduce 236 mi. to kilometers (1^ = 0.6214 mi.). 159. If the height of a barometer is 76"", and we take 1" as equal to 39.37 in., find the height of the barometer in inches. 160. On a map of France drawn to the scale ^(^^^^(^ the distance between two cities is 16.734 in. Taking 32™ as equal to 35 yds., find to the nearest kilometer the actual distance between the cities. 161. If 1 oz. = 28.35*, how many kilograms are there in 1 avoirdupois ton ? 162. One gallon contains 231 cub. in. Taking 1 in. as equal to 2^"°, find the weight in grams of a gallon of water. 163. A merchant imports 20" of wine, which he wishes to put into quart bottles. Deducting 5% of the wine as waste, how many bottles are required ? (1* = 0.261475 gal.) *™^ ^ 1 MATHEMATICS. ■ OomstOCk- BftTdy; Mom.'. -■ ■ Blllt Taylor: ■ Pll.ui ■ Ani.i-i ■ •',11 H ■ Weatwortb & Ol.l J II !■:>:.: r' ■H • •' Wentworth, Mcl,^:: 1 :■ f Wheeler !-lu,„ ;t, T™.-A. M /w i-V ^ 1 GINN & COMPAisi. ' — • ^^J IL BOSTON. KEW VORK. OMIC^Ob. ■- j ^^^1 1^ _3^^^^J^^H^^^^^^^^^HI H