24 days. 12 days. 54 men. 5. If 14 horses eat 56 bushels of corn in 16 days, in how many days will 20 horses eat 120 busl els ? Aus. 6. If 40 acres of grass be cut dwno by 8 men in 7 days,* in how many days will 480 acres be cudown br. 24 men ? Ans. 28 days. 7. If 12 inches of length, 12 of breadth, and 12 of thickness, make a bulid foot; what length of a plank that is 6 inches broad and 4 inches thick will make a solid foot ? Ans. 72 inches, 8. If 3000 lb. of bee serve 34 men 15 days, how many Ibs. will serve 120 men 25 days? Ans. 1764 lb. 1111 oz. 9. If 15 men eat 13s. worth bread in 6 days, when wheat is sold at 12s. per bushel, in how many days will 30 men eat 43s. 4d. worth of bread, when wheat is at 10s. per bushel ? Ans. 10% If 18 men build a wall 40 feet long, 3 feet thick and 16.et high-in 12 days, how many men will build a wall 360 for long, 8 feet thick and 10 feet high in 60 days? Ans. 11. If 12 men cast a ditch 30. feet long, 6 deep, and 3 proad in 15 days, when the day is 12 hours long; in how Finany days will 60 men cast a ditch 300 feet long, 8 deep, and 6 broad, when the day is but 8 hours long? Ans. 12. If 1 lb. of gold is about 14 times more valuable than 1 lb of silver, and the proportion of its weight to that of silver is as 19 to 10 : Required the vake of a bar of silver equal in bulk to one of gold worth £1000? Ans. 371. 11s. 10248d. 13. If 3 masters, who have each 8 apprentices, in 5 weeks, each week 6 days, earn $360 ;, how much will 5 masters, who have each 10 apprentices, earn in 8 weeks, each week 54 days, their daily wages being the same ? Ans. $1100. 14. How many pears can I have for $1 35cts. if 70 ches. nuts are worth 50 almonds, and 48 almonds 1 pomegranate, and 28 lemons 18 pomegranates, and 25 pears 10 lemons, and 108 chesnuts cost 24 cents ? Ans. 15. A.B. has a negotiable note for 876l. 145. 10d. due in 79 days but being in want of ready money, he has agreed with C.D. to discount it at the rate of 6 per cent per annum, How much has A. B. to receive? Ans. 9125 16. If a cistern of 171 feet long, 101 feet broad, and 13 feet deep, holds 546 barrels of water, how many barrels will a cistern hold that is 16 feet long, 7 feet broad, and 15 feet deep? Ans. 384 barrels. 120 days. 66 375 pears. 8651. 78. 1411 4092 17. If 12 shoemakers, in 2 weeks, make 36 pair of men's and pair of women's pes ; how many pair of each sort, would i8 shoemakers make in 5 weeks ? Ans 135 pair of men's, 90 pair women's. 18. If 12 oxen be maintained on 15 acres for 4 months, how many sheep will be maintained on 36 acres fo. 3 months, supposing 7 sheep to eat as much as 1 ox. Ans. 2683 sheep. 19. A certain sum of money was lent at simple interest, which in 8 months amounted to $297 60 cts. and in 15 months, to $306. I demand the principal and rate of interest ! Ans. $288 principal, $5 rate per cent. 20. If 80000 cwt. of ammunition were to be remod from a place in 9 days, and that in six day's time 4500 cwt. was carried away with 18 horses ; how many horses will be wanted to carry away the remainder in 3 days ? Ans. 604 horses: 21 A. raises goods worth $30 to $40 and gives 9 months credit, how high must B. raise goods worth $27 he agree. ing' to give 10 months credit ? Ans. $37. 22. A meal-monger purchased 22 sacks of meal, each containing 280lbs. 7 sacks he bought at 50s. per sack, 10 at 60s. and the rest at 74s. per sack; this meal he mingles all togeth. er, and desires to know how he must sell it per stone of 14lbs. to gain 50 per cent by the mixtures ? Ans. 48. 6d. 23. A wall was to be built 700 yards long in 29 days ; now after 12 men had been employed on it for 11 days, it was found that they had completed only 220 yards of the wall. It is required then to determine how many men must be adred to the former, that the whole number of them may just finish the wall in the time proposed ? Ans. 4 men to be add 24. A ship being manned with 300 men, and provided with bread for 12 months, so that each man is allowed 30 ounces per day, but having been 6 months on their voyage, they find it will require 9 months more before they can find ish it, and having lost 50 of their number by death, now te.! me the daily allowance of bread for each man during the said 9 months ? 24 ounces. ܪ Ans The American Tutor's Guide, &c. ಆ. PART III. gr. 1 = 7= cwt.qo's. 10= 27 12 1 PRACTICE. PRAC RACTICE is a compendious method of performing ques.. tions in the Rule of Three by taking aliquot, or even parts. One number is said to be an aliquot part of another, when the former divides the latter without a remainder. TABLES. d. ll. 1=1? 2=SS 1. 8 8=1 d. 2 0 14=1 20= 2 6= 1637 2 2 3 4= 28 2: 4 0= 3 56 4 0= 5 0= 45 5 0= 10 0= 6 8 10 0 I. When the price of 1 lb. yard, &c. is less than a penny.. Rule-Take such aliquot part, or parts of the given quantity, as the price is of a penny, for the answer in pence ; which reduce to pounds. Note-When the complement of the given price, in any case, is an aliquot part, deduct the said aliquot part of the given quantity therefrom, and the remainder will be the an Of a Shilling: Of a Pound Of a Hund. wt. O O O Of a Ton, 8wer. EXAMPLES. 1. 2107 at Id. Ans. 21. 3s. 10d|4. 15312 at 1d. Ans. 157. 19s. 2. 1470 at d. 31. 1s. 2d. 15. 7656 at 11. 151. 198. 3. 1276 at d. - 31. 198.9d. 16. 9423 at d. 291. 8s. 114d II. When the given price of 1 lb. yard, &c. is a penny or more, but less than a shilling. RULE-Take such part or parts of the given quantity, as the price is of a shilling, for the answer in shillings, which reduce to pounds. EXAMPLES. 7.1762 at id. Ans. 71. 6s. 100| 9. 2462 at 12d. Ans. 151. 78. 9d 8.1400 at 14d. - 71. 58. 10a 10. 1041 at 14d. 71. 116.92 11.2490 at 2d Ans. 201. 155. 131. 1000 at 7d. Ans. 291. 38. 4d 12. 2408 at 2 d. - 221. 113. 6a 32. 1656 at 7}d. 501. Os. 6.1 13. 640 at 2 d. 61. 138. 4a 33. 1420 at 711. 441. 73. 60 14. 1740 at 2 d. 191.18s. 90 34. 674 at 7 d. 211.155.3.d 15. 746 at 3d. 91. 6s. 35.2170 at 8d. 721. 6s. 8d 16. 1417 at 3 d. 191. 3s. 91a 36. 1700 at 8fd. 581. 8s. 90 17.3091 at 3 d. 451. 1s. 6a|37. 1765 at 8 d. 621. 10. 211 18. 214 at 3 d. 31. 68. 101|38. 749 at 8 d. 271. 6s. 17d 19. 2000 at 4d. 331. 6s. 8d 39. 1417 at 9d. 531. 2s. 9d 20. 569 at 44d. 101. 1s. 6 a 40.2373-at 9 d. 911. 98. 210 21.1246 at 41d. 231. 7s. 3d 11. 1476 at 91d. 581. 88, od 22. 1426 at 4 d. 281. 45.510 42. 1760 at 9d. 711.10s. 23. 2740 at 5d. 571. Is. 8d. 43. 6000 at 10d-2501. 24. 2147 at 54d. — 461. 193.334 44.4652 at 10$d- 1981. 135.7d 25. 674 at 5d. 151. 8s. 110 45.2476 at 10 - 1081. 6s. 6d 26:1746 at 5 d. 411.168.744126. 2176 at 101.- 971. Os. 4d 27.1741 at 62. 431. 10s. Od 17. 1276 at 11d 581. 98. 8d 28. 2142 at 6 d. 551. 158.70 48. 2142 at 111 1001. 8s.110 29. 1040 at 6 d. 281. 35. 4d 19.4760 at 112 1 2282. ls. 8d 30. 1746 at 6 d. 491. 28. 12.150. 640 at 111d- 311. 6s. 8d III. When the price of 1 lb. yard, &c. is more than a shilling but less than two. Rui.E-Let the quantity given stand for so many shillings, to which add the amount in shillings of said quality at the overplus price, found by case 1st. or 2nd. EXAMPLES. 51. 2140 at 1s. Olda Ans, 1091. 43. 70. 52. 3715 at 1s. O d. 1931. 9s. 9 d. 53. 2712 at 1s. 03. 1441. 13. 6d. 54. 6100 at 1s. 111. 3431. 28. 6d. 55. 1210 at 1s. 2 d. 741. 78. 3 56. 1260 at 13. 3d. 781. 15s. 57. 7121 at 1s. 4 d. 4821. 35. 012. 58. 7890 at 1s. 6 d. 6161. 88. 13d. . 59. 7120 at 1s. 8 d. 6001, 15s. 60. 1074, at 1s. 10 d. 1011. 163. 111. 61. 19998 at 1s. 11d. 1978). 19s. 42. 62. 9999 at 1s. 11 d. 9897. 98. 8 d. IV. When the price of 1 b. yard, &c. is any number of shilo linge under 20. RULE-Multiply the quantity by the shillings in the price, and divide by 20 ; or if the price be even shillings, multiply by half the price, and double the first figure of the product for shillings, and the rest will be pounds; or, work by aliquot parts. EXAMPLES. 63. 486 at 23. Ans. 481. 12s169. 600 at 138. Ans. 3901. 64. 121 at 38. 181. 3 70. 430 at 14s. 3011. 65. 471 at 53. 1171. 1571. 171 at 16s. 1361. 168 66. 191 at 8s. 761. 8. 12. 3142 at 178. 26707. 148 67. 242 at 11s. 1331. 20173. 1621 at 18s. 14581. 188 68. 2101 at 128. 12601. 12s174. 101 at 19s. 951. 19 V. When the price of 1 lb. yd. &c. is shillings and pence, or shil. lings penee and farthings. Rile-Take such part or parts of the given quantity, as the price is of £1. or multiply the given quantity by the shil. lings and take parts for the rest, add them together and divide by 20. EXAMPLES. 75. 7150 at 1s. 8d. Ans. 5951. 16s. 8d. 76. 596 at 2s. 6d. 711. 23. 6d. 77. 525 at 3s. 4d. 871. 10s. 78. 438 at 6s. 8d. 1461. 79. 392 at 6s. 9d. 1321. 68. 80. 438 at 8s. 6 d. 1871. 10s. 41d. 81. 136 at 9s. 21!. 621. 12s. 4d. 82. 732 at 12s. 7d. 4601. 11s. 83. 370 at 14s. 2 d. 2632. 48. 94d. 84. 3210 at 158. 7 d. 25111. 38. 13d. VI.Whenthe price of 1 cwt. yd. &c. is pounds, or pounds shillings,&c. RULE-Multiply the given quantity by the pounds, and take parts for the shillings, &c. or, reduce the pounds and shillings into shillings, then, multiply the quantity by the shillings, take parts for the rest, add them together and divide by 20, EXAMPLES. 85. 120 at 41. Ans. 4801. 86. 142 at 71. 9941. 87. 127 at 11. 38. 4d. 1481. 38. 4d. 88. 327 at 11, 7. 60. 4491. 12s. 6d. 89. 536 at 11. 17s. 6d. 10051. 90. 2104 at 51.3s. 108351. 12s. 91. 7156 at 51. 6s. 379261. 165. 92. 2157 at 31. 15s. 2 d. 81081. 19s. 54d. 93. 2157 at 21. 78. 4jd. 51091. 7s. 103d. 94. 95 at 151. 14s. 71d. 14941. 7. 4.d. VII. When the price and quantity geven are of several denomi nations. RULE--Multiply the price, by the integers in the given quantity, and for the lower denominations, take parts, add them together, and the sum will be the ans ver. |