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42. How many acres in 4 farms, each of 201 A. 2 R. 15 P. ?

Ans. 806 A. 1 R. 20 P. 43. How many grains in 12 lb. 3 3 43 23 12 gr. ?

Ans. 70852 grains. 44. How many grains in 8 lb. 9 oz. 10 pwt. 8 gr.?

Ans. 50648 grains. 45. Divide 8 lb. 9 oz. 10 pwt. 8 gr. into four equal parts; how much in each part?

Ans. 2 lb. 2 oz. y pwt. 14 gr. 46. A man owns three tracts of land; the first tract contains 546.A. 3 R. 15 P., the second 612 A. 2 R. 25 P., and the third 408 A. 3 R. 12 P.; Le devises 212 A. to his wife, and the balance equally to his four children ; how much will each child get ?

Ans. 339 A. 13 P. 47. How many pills of 1 grain each, can a druggist make out of 1 lb. 9 3 5 3 27 15 gr. of morphia ?

Ans. 41740 pills. 48. A man has property valued as follows: one house £2145 9s. 8d., another £1576 16s. 4d., a third £654 15s. 10d.; he has a draft for £2176 9s. 6d., and cash £82 5s. 4d., all of which he wishes to divide into four parts as follows: the second to be double the first, the third once and one-half the second, and the fourth once and onethird the second; how much in each part ?

Ans. £663 11s. 8d. = 1st part;

£1327 3s. 4d. = 2d part; £1990 15s. = 3d part; £2654 6s. 8d. = 4th part.

RATIO.

Two fractions can be formed with any two integral numbers, the one a proper fraction and the other an improper fraction; thus, } and can be formed with ry and 9. When the proper fraction is a multiplier of any number, the product is less than the number multiplied; therefore, this fraction is termed a Diminishing Ratio. But when the improper fraction is a multiplier, the product is greater than the multiplicand; hence, the improper fraction is termed an Increasing Ratio.

PROBLEMS.

1. If 5 lbs. sugar cost 50 cents, what will 9 lbs. cost ?

It is evident that 9 lbs. will cost more than 5, and just as much more as is indicated by the increasing ratio formed by the two like terms, 5 lbs. and 9 lbs.

10

If 5 lbs. cost 50 cts., 9 lbs. will cost $8 cts. xf = 90 cts.; this may be further demonstrated thus,

5 lbs. = 50 cts.
1 lb.

= 10 cts.

9 lbs. = 90 cts. In a problem of ratios, the one ratio is given, and one of the terms of the other ratio, to get the second term; thus, in the above:

Given, 5 lbs. sugar and 50 cents.

Required, 9 lbs. sugar and ? The ratio of the money will be the same as of the sugar. As the required sugar is more than the given, the ratio must be increasing; that is, . .. 50 xf = 90, the ratio of the required money to the given, H = }, the same as

of the sugar.

EXAMPLES.

5) 40

1. If 5 bushels of wheat cost $6.25, what will 8 bushels cost?

Given 5 bu. and $6.25.
Required, 8 bu. and
$6.2$ x

= $10.00.
8 25) 1000

8
5
625

25 The ratios of the wheat and of the money is the same. REM.-Ratios can only be formed by two like terms.

2. If 5 bushels of oats cost $1.50, what will 21 bushels cost ? Given

5 bu. and $1.50.
Required, 21 bu. and
$8.$0 x = $6.30.

2; the ratio is the same. REM.Write the given terms in a line and the like term of the required immediately under that of the given. One term of the required is wanting, and the given like term may be called the term of demand, and should be placed first and multiplied by the ratio, having for its numerator the required term of the ratio, and for its denominator the given term.

630

= 150

As a general thing, an increase in the required term of the ratio will take more of the unknown to accomplish it; an increased amount of goods will cost a greater sum of money; an enlarged piece of work, an additional sum of money; and the greater the work, the longer time to perform it, etc. In examples of this kind, the ratios are direct, and the required term of the ratio holds the place of the numerator and the given term that of the denomi. nator, and the product of the ratio and the odd given term is the term required.

3. If a man travel 40 miles in 8 hours, how many miles will he travel at that rate in 18 hours ?

Given 40 miles. and 8 hours.
Required, ? miles and 18 hours.

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40 miles x the = 90 miles. 4. If 15 bushels of wheat yield 3 barrels of flour, how many bushels will yield 10 barrels of flour?

Given 15 bu. and 3 barrels of flour.
Required, ? and 10 þarrels of flour.

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5. If a man travel 30 miles in 2 days, how long will it take him to travel 240 miles ?

Given 30 miles and 2 days.
Required, 240 miles and ?

6. If a staff 4 feet long cast a shadow 3 feet, what is the height of a steeple which casts a shadow 90 feet?

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7. If the interest of $100 for one year is $5, what would be the interest of $500 for the same time?

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INTEREST.

PRINCIPAL.
Given

$100 and $5.
Required, $500

and ? 8. If of a barrel of flour cost $4, what will 4 barrels cost?

Given barrel and $4.
Required 4 barrel and ?

4 x

= $28.

4

X4

$4 x

3 REM. 4is a multiplier, and is a divisor; the į must be inverted.

9. If 41 bushels of wheat cost $5.40, what will 84 bu. cost? 91 bu.? 231? 313? 471 ? 394 ? 581? 974 ? 1064?

10. If 8 bushels of wheat cost $10, what will be the cost of 9j bu. ? 104 bu. ? 15% bu. ? 371 bu.? 95% bu. ? 125% bu. ? 1504 bu.? 279 bu. ?

11. If 5% acres of land cost $230, what is the cost of 61 acres ? 73 acres ? 124 acres? 133 acres ? 173 ? 183 ? 194 ? 208 ? 379 ? 497 ?

12. If 2} acres of land cost $110, what will be of an acre cost? į acre ? 4 acre? } acre ? acre ? f acre ? $acre? 11 acres ? 1% acres ?

13. If Pa of a yard of cloth cost % of a dollar, what will of a yard cost ? Given

yd. and to Required, 4 yd. and

?

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