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24 days.

12 days.

54 hen.

5. If 14 horses eat 56 bushels of corn in 16 days, in how many days will 20 horses eat 120 busdls ?

6. If 40 acres of grass be cut dwn by 8 men in 7 days, in how many days will 480 acres be cudown bv 24 men ?

Ans.

28 days. 7. If 12 inches of length, 12 of breadth, and 12 of thickness, make a ulid 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 beef serve 340 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 128. 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 dîtch 30 feet long, 6 deep, and 3 proad in 15 days, when the day is 12 hours long; in how Finany days will 60 mèn 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 value of a bar of silver equal in bulk to one of gold worth £1000?

Ans. 371. 11s. 1026 d. 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 51 days, their daily wages being the same ? Ans. $1100.

14. How many pears can I have for $1 35cts. if 70 chesnuts are worth 50 almonds, and 48 almonds 1 pomegranate, and 28 lemons 18 pomegranates, and 25 pears 10 lemons, and 108 chesnuts cost 2. cents ?

Ans. 15. A.B.has a negotiable note for 876l. 14s. 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 bas A. B. to receive ?

Ans. 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.

375 pears.

8651. 78. 1411

17. If 12 shoemakers, in 2 weeks, make 36 pair of men's and pair of women's ges; how many pair of each sort, would i8 shoemakers make in 5 weeks ?

Ans135 pair of men's, 90 pair wornen'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 manyáhorses will be wanted to carry away the remainder in 3 days ?

Ans. 604 horsese 21 A. raises goods worth $30 to $40 and gives 9 month 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. d. 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 added to the former, that the whole number of them may just finish the wall in the time proposed ?

Ans. 4 men to be added 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 fin. ish it, and having lost 50 of their number by death, now tel me the daily allowance of bread for each man during the said 9 months ?

Ans 24 ounces.

PART III.

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of id.

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7=16

of a Shilling.

of a Pound

Of a Hund. wt.

Of a Ton,

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. gr.

d.

16. 1 =

1, 8=ia d..

8=1 1 l= 2 0

14=

2 0 2 6.

16

2 2 3 4:

28

4 0= 2 3

56: 4 0

5 0 5 0

10 0 6=

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 quan. tity, 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

EXAMPLES. 1. 2107 at Id. Ans. 21. 3s. 104d14. 15312 at 1d. Ins. 151. 195. 2. 1470 at id. 31. 1s. 2d. 5. 7656 at 21. 151. 198. 3. 1276 at d. 31. 198.9d. 6. 9423 at d. 291. 8s. 1140 II. When the given price of 1 lb. yard, &c. is a penny or more,

but less than a shillingRule-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. 10d| 9.2462 at 12d. Ans. 151. 7s. 9d. 8.1400 at 14d. - 71. 58. 10a 10. 1041 at 14d. 71. 116.9.4

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11.2490 at 2d Ans. 201. 155. 31.1000 át 17d. Ans. 291. 38. 44 12: 2408 at 2 d. 221. 113. 6a 32. 1656 at 7%d. 501. 0s. 6:1 13. 640 at 2 d. - 61. 138. 4a 33. 1420 at 71 1. — 441. 78. 6d 14. 1740 at 2 d.- 191.18s. 934. 674 at 7 d. 211.158. 3d 15. 746 at 3d. 91. 6s. 35.2170 at 8d. 721. 6s. 80 16. 1417 at 3 d. 191. 3s. 91a 36. 1700 at 8 d. 581. 8s. 94 17.3091 at 3 d. 451. 1s. 6td 37. 1765 at 8 d. 621. 10s. 231 18. 214 at 3 d. 31. 6s. 1038. 749 at 8 d. 271. 6s. 170 19. 2000 at 4d. 331. 6s. 8d|39.1417 at 9d. 531. 28. 9d 20. 569 at 44d. 101. 1s. 640 40.2373-at 94d.- 911. 98. 2.d 21. 1246 at 43d. 231. 78. 3d 11. 1476 at 9:1d. 581. 88, 6d 22. 1426 at 4 d. 281. 48.51442. 1760 at 9 d. 711.108. 23. 2740 at 5d. 571. Is. 8d. 43. 6000 at 10d-2501. 24. 2147 at 5$d. 461. 195.370 44.4652 at 10d- 1981. 138.70 25. 674 at 5 d. 151. 8s. 11d 45. 2476 at 104d-1081. 6s. 6d 26:1746 at 5 d. 411.168.71d! 16. 2176 at 1044 971. Is. 4d 27. 1741 at 60. 431. 10s. 60 17. 1276 at 11d 581. 98. 8d 28. 2142 at 6 d. 551.158.714 48.2142 at 111 1001. 8s. 1} 29. 1040 at 6d. 281. 38. 4d 19. 4760 at 111 1 228. 1s. Sd 30.1746 at 6 d. 491. 28. 12.150. 640 at 11d- 311. 6s. 8d III. When the price of 1 lb. yard, &c. is m 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. Old.

Ans. 1091. 43. 7d.

1931. 93. 9d. 53. 2712 at 1s. 03.

1441. 18. 6d. 54. 6100 at 1s. 111.

343/. 28. 6d. 55. 1210 at 1s. 2 d.

741. 78. 31. 56. 1260 at 13. 3d.

781. 15s. 57. 7121 at 1s. 4 d.

4821. 35. 04d. 58. 7890 at 1s. 6 d.

6161. 8s. 11d. • 59. 7120 at 1s. 8 d.

6001, 15s. 60. 1074, at 1s. 10 d.

1011. 16s. 111. 61. 19998 at 1s. 114d.

19784. 19s. 421. 62. 9999 at 1s. 11 d.

9891. 9s. 840. IV. When the price of 1 lb. yard, &c. is any number of shil.

ling: 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 lialf the price, and double the first figure of the product for shillings, and the rest will be pounds; or, work by ali. quot parts.

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EXAMPLES. 63. 486 at 23. Ans. 481. 12s 69. 600 at 138. Ans. 3902. 64. 121 at 38.

181. 3. 70. 430 at 14s. 3011. 65. 471 at 53. 1171. 15. 71. 171 at 16s. 1361. 166 66. 191 at 8s.

761. 8. 12. 3142 at 178. 26702. 148 67. 242 at 11s. 1331. 2. 73. 1621 at 18s. 14581. 188 68. 2101 at 128. 12601. 12:174. 101 at 19s. 951. 198 V. When the price of 1 lb. yd. &c. is shillings and pence, or shil.

lings penee and farthings. RÜLE_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. 163. 8d. 76. 596 at 2s. 6d.

711. 28. 6d. 77. 525 at 3s. 4.d.

871. 10s. 78. 438 at 6s. 8d.

1461. 79. 392 at 6s. 9d.

1321. 666 80. 438 at 83. 6 d.

1871. 10s. 41d. 81. 136 at 9s. 211.

621. 12s. 4d. 82. 732 at 12s. 7d.

4601. 11s. 83. 370 at 14s. 2 d.

2631. 45. 91d. 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. 3s. 4d.

1481. 38. 4d. 88. 327 at 11. 7. 6d.

4491. 12s. 6. 89. 536 at 11. 17s. 6d.

10057. 90. 2104 at 57. 3s.

108351. 12s. 91. 7155 at 51. 68.

379261. 16s. 92. 2157 at 31. 15s. 21d.

81081. 198. 54d. 93. 2157 at 21. 78. 4 d.

51091. 7. 10}d. 95 at 151. 14s. 74d.

14941. 7s. 44d. 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, ada them together, and the sum will be the ans ver.

94.

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