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5. If 14 horses eat 56 bushels of corn in 16 days, in how many days will 20 horses eat 120 bushels ? As. 24 days.

6. If 40 acres of grass be cut down by 8 men in 7 days,” in how many days will 480 acres be down by 24 men? Ans. 28 days.

7. If 12 inches of length, 12 of breadth, and 12 of thickness, make a lid 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 lbs. will serve 120 men 25 days? Ans. 1764 lb. 11 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. 12 days.

10 If 18 men build a wall 40 feet long, 3 feet thick and 16et 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.

54men.

11. If 12 men cast a ditch 30 feet long, 6 deep, and 3 road in 15 days, when the day is 12 hours long; in how nany days will 60 men cast a ditch 300 feet long, 8 deep, and 6 broad, when the day is but 8 hours long?

Ans. 120 days.

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. 377. 11s. 10148d.

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 5 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 24 cents? Ans. 375 pears.

15. A.B.has a negotiable note for 8767. 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 has A. B. to receive? Ans. 8657. 7s. 14092

16. If a cistern of 17 feet long, 10 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.

17. If 12 shoemakers, in 2 weeks, make 36 pair of men's and pair of women's es; how many pair of each sort, would 18 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 for 3 months, supposing 7 sheep to eat as much as 1 ox. Ans. 2683sheep.

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 together, and desires to know how he must sell it per stone of 14lbs. to gain 50 per cent by the mixtures?

Ans. 4s. 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 added 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 fin. ish‍it, and having lost 50 of their number by death, now też me the daily allowance of bread for each man during the said 9 months? Ans 24 ounces.

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PART III.

PRACTICE.

PRACTICE 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.

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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

swer.

2. 1470 at d.

3. 1276 at d.

EXAMPLES.

1. 2107 at 1d. Ans. 21. 3s. 103d4. 15312 at 4d. Ans. 157. 19s. 31. 1s. 2d. 5. 7656 at d. 157. 19s. 37. 198.9d. 6. 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.

7.1762 at 1d. Ans. 71.
8. 1400 at 14d. — 71.

EXAMPLES.

6s. 10

9.2462 at 1d.Ans. 157. 7s. 9d 58. 10a 10. 1041 at 1ąd. — 77. 118. 92

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131.1000 at 7d.Ans.291. 3s. 4d

22/. 11s. 6a 32. 1656 at 74d.

6. 138. 44 33. 1420 at 7. 197. 18s. 9a 34. 674 at 7 d.

91. 6s...
19/. 3s. 9a

35.2170 at 8d.

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501. Os. 64

441. 7s. 6d

217. 15s. 3 d

721. 6s. 8d

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451. 18.6

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31. 6s. 10
331. 6s. 8d 39. 1417 at 9d.

38. 749 at 8 d..

271. 6s. 1 d

531. 2s. 9d

917. 98. 24d

11.2490 at 2d Ans. 201. 15s.
12.2408 at 24d.
13. 640 at 2d.
14. 1740 at 2 d.
15. 746 at 3d.
16. 1417 at 3d.
17.3091 at 3 d.
18. 214 at 3d.
19.2000 at 4d.
20. 569 at 44d.
21. 1246 at 44d.
22. 1426 at 4 d.
23.2740 at 5d.
24. 2147 at 54d.
25. 674 at 54d.
26.1746 at 5d.
27.1741 at 6d.
28. 2142 at 6 d.
29. 1040 at 6}d.
30.1746 at 61d.

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10. 1s. 6a40. 2373 at 94d.
231. 7s. 3d 11. 1476 at 93d.
281. 48.5d 2. 1760 at 9 d.
571. Is. 8d. 43. 6000 at 10d-
46l. 19s. 32d 44. 4652 at 104d-
157. 8s. 11a 45. 2476 at 104d
417. 16s. 7d 16. 2176 at 104d-
431. 10s. 6d 17.1276 at 11d
551. 15s. 748. 2142 at 11

581. 88. 6d
717.10s.
2507.
1981. 13s. 7d
1087. 6s. 6d
971. 9s. 4d

581. 9s. 8d 1007. 8s.12d

281. 3s. 4d 19.4760 at 11-2281. 1s. 8d 491. 28. 1150. 640 at 114d- 31. 6s. 8d III. When the price of 1 lb. yard, &c. is more than a shilling but less than two.

RULE-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.

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

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.

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V. When the price of 1 lb. yd. &c. is shillings and pence, or shillings pence and farthings.

RULE-Take such part or parts of the given quantity, as the price is of £1. or multiply the given quantity by the shillings and take parts for the rest, add them together and divide by 20.

EXAMPLES.

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VI. When the 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.

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VII. When the price and quantity given are of several denomi

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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.

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