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14. If yard of cloth cost $2, what will 3 ells F. cost?

15. If

2 × 1 =

yard of cloth cost $2.25, what will 5 ells English cost? What will 5 ells French cost?

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1. If 12 bushels of wheat cost $15, what will 42 bushels

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2. If 15 bushels of oats cost $4.50, what will 75 bushels cost?

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3. If 12 bushels of wheat cost $15, how many bushels will $52 buy?

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4. If 15 bushels of oats cost $4.50, how many bushels

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5. If a man travel 48 miles in 6 hours, how many miles will he travel in 56 hours at the same rate?

Ans. 448 miles.

6. If 20 bushels of wheat yield 4 barrels of flour, how many bushels will be required for 15 barrels of flour? Ans. 75 barrels.

7. If 20 bushels of wheat yield 4 barrels of flour, how many barrels of flour will 75 bushels yield?

8. If a man travel 50 miles in 2 days, how long will it take him to perform a journey of 375 miles at the same rate?

9. If a staff 3 feet long cast a shadow 4 feet, what will be the length of the shadow of a steeple 180 ft. high?

3 ft., staff

Given
and 4 ft., shadow.
Required 180 ft., steeple and ?

Shadow of steeple 240 ft.

shadow.

10. If the interest of $100 for one year is $6, what is the interest of $500 for the same time?

Ans. $30.

11. If a man's salary amounts to $1500 in 3 years, how much will it amount to in 7 years?

12. If 12 bushels of wheat cost $15, what will 351 bushels cost?

35 × 2 = 71

12 × 2 = 25

15 × H

13. If of a barrel of flour cost $6, what will 5 barrels cost?

The 5 is a multiplier and the is a divisor.

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14. If 5 bushels of wheat cost $6.60, what will 37 bushels cost?

.20

6.60 × × 112 = $44.80.

15. If of an acre of land is worth $36.40, what is the value of 15 acres at the same rate?

15,138 = 273.

18

$36.40 × × 273.

16. If 7 acres of land cost $1560, what will of an acre cost? Ans. $150.

17. The assets of a firm are $48576 and the liabilities $97648; how much will a creditor receive to whom is owing $1654?

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Ans. $1.

18. If of a yard cost $, what will of a yard cost? 19. If of a ship cost £49, what is of it worth?

Ans. £32.

20. What will 57 acres 3 rods and 24 perches of land cost, if 5 acres 2 rods and 6 perches cast $224.64 ? Ans. $2348.83+. 21. If $1.50 will buy 6 lbs. sugar, how much sugar will $36.50 buy?

Reduce to perches.

22. If 5 yards of cloth cost $7.15, what will 721 yards cost? 87.15 x 145.

23. If 4 lbs. ham cost 87 cents, what will 354 lbs. cost? Ans. $6.79+. 24. If .75 of a ton of hay cost $15, what will 2.25 tons cost? Ans. $45.

25. If 160 acres of land cost $400, what will 830 acres cost?

26. If of a ship cost $4500, what will cost?

27. If .25 of an acre of land is worth $32, what is .875 of an acre worth?

28. If 5 yards of muslin cost 46 cents, what will 201 yards cost? Ans. 162 cents. 29. If 3 yards of cloth cost $15.75, what will 6 ells English cost? Ans. $39.37. 30. If 5 ells Fl. cost $15.15, what will 6 ells Fr. cost?

In the preceding examples, the ratios were all direct; as in those cases any increase in the required term of the ratio demanded a similar increase of the unknown; but there are cases which require the ratio to be inverted, such as, the more men employed, the less time will be required to perform a piece of work; the more hours employed in the day, the less days; the wider the material, the less yards it will take to make a garment, etc.

These cases of inverse ratio are readily detected by asking this question: "Will an increase of the required term of the ratio demand an increase in the unknown term?" If it does, the ratio is direct; but if an increase in the required term of the ratio demand a diminution of the unknown term, the ratio must be inverted; thus,

PROBLEM.

If 4 men can do a piece of work in 10 days, how long will it take 8 men to do the same work?

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COR.-It is evident that 8 men will do it in less time; that is, in one-half the time that it will take 4, which ratio is expressed by the diminishing ratio of 4 and 8, that is,, in which the given term is the numerator of the ratio and the required term the denominator.

EXAMPLES.

1. If 5 men can dig a ditch in 20 days, how many men will dig it in 25 days?

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REM.-An increase in the 25 will require less men.

2. If 6 horses eat a certain quantity of hay in 30 weeks, how many horses will consume the same quantity of hay in 9 weeks?

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3. If a man perform a journey in 12 days, when the days are 9 hours long, how many days of 12 hours will it take him?

Given
Required,

12 days and 9 hours.

?

and 12 hours.

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