RULE.

Set the term in the first place, which is of the same kind with that in which the answer is required. Then determine whether the answer ought to be greater or 'less than the third term. If the answer ought to be greater than the third term, set the greater of the other two numbers on the left for a second or middle term; and the 1 ss number on the left of the second term, for a first term. If the answer ought to be less than the third term, the less of the two other numbers must be the middle term, and the greater must be the first term. 'After thus stating the sum, proceed to do it in the following manner, viz: Reduce the third term to the lowest denomination mentioned in it. Reduce, likewise, the first and second terms to the lowest denomination that either of them has. Then multiply the second and third terms together, and divide their product by the first term. The quotient thus obtained will be the

answer.

It will not be necessary to distinguish between direct and inverse proportion, because the foregoing rule is calculated for both.

• PROOF.

By reversing the statement.

EXAMPLES.

1. If 3 pounds of sugar cost 25 cents, what will 18 pounds cost at the same rate?

lbs. lbs. cts.

Thus, 318 : : 25

18

200

25

3)450

$1.50 Answer.

2. If 7 pounds of coffee cost 874 cents, what must I pay for 244 pounds?

3. If 450 barrels of flour cost $1350, what will 8 barrels cost?

bbls. bbls.

$

$

Thus-As 450 : 8 : : 1350: 24, Answer.* 4. If 15 yards of cloth cost £6, what number of yards may be bought for £125?

yds. yds.

As 6 125 : : 15: 312 Answer.

5. If twelve men can do a piece of work in 20 days, in what time will 18 men do it?

As 18 : 12 : : 20 13 Answer.

6. What will be the cost of 17 tons of lead, at 223 dellars 66 cents per ton?

T. T.

D. cts. D. cts

As 1 17 : : 223.66 : 3802.22 Ans.

::

7. What will 72 yards of cloth cost at the rate of 9 yards for £5 12s.

yds. yds. As 9 : 72

£ s. £ s.

: 5 12 44 16 Ans.

8. If 750 men require 22500 rations of bread for a month, what will a garrison of 1200 require?

Ans. 36000.

*The sum in the third example is read thus:-As 450 is to 8, so is 1350 to the answer. This is the manner of reading all sums when stated in the Rule of Three.

9. What must be the length of a board that is 9 inches in width, to make a surface of 144 inches, or a square foot? Ans. 16 inches. 10. How many yards of matting 2 feet 6 inches broad, will cover a floor that is 27 feet long, and 20 broad? Ans. 72 yards.

11. If a person's annual income be 520 dollars, what is that per week? Ans. 10 dollars.

12. If a pasture be a sufficient for 3000 horses for 18 days, how long will it be sufficient for 2000?

H.
As 2000

H.

D. D.

3000 : : 18: 27 Ans.

13. What must be the length of a piece of land 131 rods in breadth, to contain one acre?

Ans. 11 rods, 4yds, 2ft. 0 in. 14. If 8 men can build a tower in 12 days, in what time can 12 build it?

M. M.

D.

D.

As 12 : 8 : 12 8 Answer. 15. If a piece of land be 5 rods in width, what must be its breadth to make an acre?

16. How much carpeting that is 1

R.

As 5 : 160 : : 1 : 32 Answer. yards in breadth, will cover a floor 74 yards in length, and five yards in breadth?

By Decimal Fractions.

yds. yds.

yds.

As 1.5 : 5 : : 7,5 : 25 Answer.

17. What will one quart of wine cost at the rate of 12 dollars for 16 gallons?

gals. qts. qt. D. cts. As 16 or 64 : 1 12.00 183 Ans. 18. If 10 pieces of cloth, each piece containing 42 yards, cost 531 dollars 30 cents, what does it cost per yard? Ans. $1.281 19. If a hogshead of brandy cost 78 dollars 75 cents, what must be given for 5 gallons at the same rate? Ans. $6.25

20. If a staff 4 feet in length, cast a shade on level ground, 8 feet in length, what is the height of a tower, whose shade, at the same time, measures 200 feet?

ft. fl.

fl. ft.

As 8: 200: : 4 : 100 Answer. 21. I lent my friend 350 dollars for 5 months, he promising to do me the same favour; but when requested, he could spare only 125 dollars. How long ought I to keep it to balance the favour?

D. D.

M.

As 125 350 : : 5

M.

: 14 Answer.

22. If 7 oxen be worth 10 cows, how many cows will 21 oxen be worth?

Ox. Ox.

As 7

C. C.

: 21 : : 10 30 Answer. 23. If board for 1 year, or 52 weeks, amount to $182, what will 39 weeks come to? Ans. $135.50. 24. If 30 bushels of rye may be bought for 120 bushels of potatos, how many bushels of rye may be bought for 600 bushels of potatos? Ans. 150 bushels rye.

25. A gentleman bought a bag of coffee for the use of his family, weighing 127 lbs., for which he gave $15.25 cts.; what was it a pound? Ans. 12+cts. 26. If a gentleman spends 4 dols. 621 cts. every day, how much will that amount to in a year?

Ans. 1688.121. 27. A lady bought for the use of her family, a piece of cloth, containing 16 yds. 3 qrs. 2 na., at $1.25 cts. a yard; what was the amount of the whole?

Ans. $21.09+.

28. A, failing in trade, owes the following sums, viz. to B $1600.60, to C $500, to D $750.20, to E $1000, to F $230; and his property, which is worth no more than $1020.20, he gives up to his creditors; how much does he pay on the dollar? and what is the amount of loss sustained by all?

Ans. 25 cts, on $1; and the amount of loss is $3060.60. 29. A farmer inade from an orchard of apples, 146 barrels of cider, which he afterwards sold at $3.12 cts. a barrel; what was the amount of the whole?

Ans. $456.25.

30. A flour merchant sold 1574 bbls. of flour, at $5.12 cents a barrel, what was the amount? Ans. $8066.75. 31. A merchant failing, was able to pay his creditors only 62 cents in a dollar; how much will a person receive, whose claim is 746.25 cents?

Ans. $466.40,6,25. 32. A lady purchased a set of silver, weighing in the whole 5 lb. 6 oz. 5 dwt. at 1.50 cents an ounce; what was the cost of the whole? Ans. $99.37,5.

33. A lady, intending to make a bed quilt, containing 84 square yards, desired her daughter to inform her how much muslin 14 yard wide would be required to line the same; how many did it take? Ans. 6.8 yds. or 6 yds. 34. A certain field will afford pasture for 10 oxen, for 60 days; how long will the same pasture suffice for 24 oxen? Ans. 25 days.

35. A pipe will drain off a cistern of water in 12 hours; how many pipes of the same size will empty it in 30 minutes? Ans. 24 pipes.

36. Two persons travel on the same road, and in the same direction. One sets out 5 days before the other, and travels 20 miles a day; the other travels 25 miles a day; how long before the latter will overtake the former? Ans. 20 days.

37. If 48 men can build a fortification in 24 days, how many men can do the same in 192 days? Ans. 6 men. 38. A certain piece of work was done by 120 men in 8 months, how many men will it take to do another piece of work of the same magnitude in 2 months? Ans. 480.

39. A merchant failing in trade, owes 29475 dollars: he delivers up his property, which is worth 21894 dollars 3 cents; how much does this sum pay on the dollar towards what he owes? Ans, 74cts. 2m.+

40. If property rated at 28 dollars, pay a tax of 21 dollars, how much is that on the dollar?

Ans. 75 cents.

41. If of a yard cost 624 cents, what will of a yard Ans. $2.187.+

cost?