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Had the compositors

Let us now analyze this statement. worked the same number of hours per day, and had the same work to do, the first would have been the true answer; and the second would have been the true answer had the time only been different and the work to be done been the same. The third proportion_accounts for the inequality of the work done, and gives the answer under all the suppositions. It is evident the same answer would have been obtained, had the first answer been substituted in the second proportion, and the second answer in the third proportion. Hence, the reason of the rule is obvious.

5. If a pasture of 16 acres will feed 6 horses for 4 months, how many acres will feed 12 horses for 9 months?

6. If 25 persons consume 300 bushels of corn in 1 year, how much will 139 persons consume in 7 years at the same rate?

7. If 32 men build a wall 36 feet long, 8 feet high, and 4 feet wide in 4 days; in what time will 48 men build a wall 864 feet long, 6 feet high, and 3 feet wide?

8. If a regiment of 1878 soldiers consume 702 quarters of wheat in 336 days, how many quarters will an army of 22536 soldiers consume in 112 days?

9. If 12 tailors in 7 days can finish 13 suits of clothes, how many tailors in 19 days of the same length, can, finish the clothes of a regiment of soldiers consisting of 494 men?

10. An ordinary of 100 men drank £20 worth of wine at 2s. 6d. per bottle; how many men, at the same rate of drinking, will £7 worth suffice, when wine is rated at 1s. 9d. per bottle?

11. If 60 bushels of oats will serve 24 horses for 40 days, how long will 30 bushels serve 48 horses at the same rate?

12. If a garrison of 3600 men, in 35 days, at 24oz. per

day each man, eat a certain quantity of bread, how many men in 45 days, at the rate of 14oz. per day each man, will eat double the quantity?

13. A garrison of 3600 men has just bread enough to allow 24oz. a day to each man for 35 days; but a siege coming on, the garrison was reinforced to the number of 4800 men. How many ounces of bread a day must each man be allowed, to hold out 45 days against the enemy?

14. If 336 men, in 5 days of 10 hours each, dig a trench of 5 degrees of hardness, 70 yards long, 3 wide, and 2 deep, what length of trench of 6 degrees of hardness, 5 yards wide, and 3 deep, may be dug by 240 men in 9 days of 12 hours each?

15. If 12 pieces of cannon, eighteen-pounders, can batter down a castle in an hour, in what time would nine twentyfour-pounders batter down the same castle, both pieces of cannon being fired the same number of times, and their balls flying with the same degree of velocity?

16. If 15 weavers by working 10 hours a day for 10 days, can make 250 yards of cloth, how many must work 9 hours a day for 15 days, to make 6073 yards?

17. If £3 be the wages of 13 men for 7 days, what will be the wages of 20 men for 15 days?

18. If a footman travel 294 miles in 7 days, of 12 hours long, in how many days, of 10 hours long each, will he travel 147 miles?

19. Bought 5000 planks, of 15 feet long and 2 inches thick; how many planks are they equivalent to, of 12 feet long and 12 inches thick?

20. If 248 men, in 5 days of 11 hours each, dig a trench of 7 degrees of hardness, 232 yards long, 3 wide, and 24 deep; in how many days, of 9 hours long, will 24 men dig a trench of 4 degrees of hardness, 337 yards long, 5 wide, and 31 deep?

PRACTICE.

199. PRACTICE is an easy and concise method of applying the rules of arithmetic to questions which occur in trade and business. It is only a contraction of the RULE OF THREE when the first term is unity.

For example, if 1 yard of cloth cost half a dollar, what will 60 yards cost? This is a question which may be answered by the rule called Practice. The cost is obviously $30.

200. One number is said to be an aliquot part of another, when it forms an exact part of it: that is, when it is contained in that other an exact number of times. Hence, an aliquot part is an exact or even part.

For example, 25 cents is an aliquot part of a dollar. It is an exact fourth part, and is contained in the dollar four times. So also, 2 months, 3 months, 4 months, and 6 months, are all aliquot parts of a year.

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QUEST.-199. What is Practice? If one yard of cloth cost $8, what will half a yard cost? What will one quarter of a yard cost? 200. When is one number said to be an aliquot part of another? What is an aliquot part? What are the aliquot parts of a dollar expressed in the table? What the aliquot parts of a year? What the aliquot parts of a month? What the aliquot parts of a pound? What are the aliquot parts of a shilling?

EXAMPLES.

1. What is the cost of 376 yards of cloth at $0,75, or

a dollar per yard ?

Had the cloth cost $1 per yard, the cost of the 376 yards would have been $376. Had it cost 50cts. per yard, the cost would have been of $376, or $188: had it

OPERATION.

3 of

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been 25cts. per yard, the cost would have been

of $376,

or $94; but the price being 75cts. per yard, the cost is 188 +94 $282.

2. What is the cost of 196 yards of cotton, at 9d. pcr yard?

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Therefore, 196yd. at 9d. or 3s. =147s. £7 7s. Ans.

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201. When the price in shillings is less than 20,

Multiply by half the number of shillings, and the figures to the left of the right hand figure will express the pounds, and this figure doubled will be the shillings.

11. What is the cost of 56 yards of cloth, at 16s. per yard? 16s. = 16 of a £: Hence

56 × 1080 6 = the amount in pounds.

But 56 × 100 8 = 56 × 1 = £44.8, in which the right hand figure 8 expresses tenths of pounds, and by doubling it, we obtain twentieths of pounds, or shillings: therefore, the reason of the rule is manifest.

QUEST.-201. When the price is in shillings and less than 20, how will you find the cost? What is the reason of the rule?

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