EXAMINATION ON CHAPTER IX.

Ans. 11

Ans. .

Ans. $9

1. Find the ratio of 21 to 7, and of to . Ans. † and 13 2. Find the inverse ratio of of to 5. 3. Find the ratio of 3 qr. to 1 cwt. 2 gr. 20 lb. 4. Find the inverse ratio of 2 cwt. to 3 qr. 5 lb. Find the 4th term in each of the following proportions. 5. 3 days 10 days: $37: 4th term. 6. 7 men 13 men 21 days: 4th term.

224.

Ans. $1074.

Ans. 11 days.

7. 3 cwt. 1gr.: 7 cwt.:: $25.12: 4th term.

Ans. $54.115'.

8. 30 miles 100 miles #14 T. 1 cwt.: 4th term.

Ans. 4 T. 6.407' cwt. 9. If 13 yards of broadcloth cost $65.25, what should be paid for 17 yd. 24 gr. of cloth at the same rate?

Ans. $86.794'. 10. Allowing 9 barrels of flour to suffice a family for 12 months, how many barrels would the same family require for 2y. 4m.? Ans. 221 barrels.

11. If $100 will supply a number of horses with oats, for 3 months, when oats is at 25 cts. per bu., how long will the same sum supply them with the same article, when it is at $0.37 per bushel? Ans. 2 months. 12. Supposing a company of workmen to erect a building in 30 days, by working 8 hours per day; in how many days ought the work to be accomplished, if they employ 10 hours per day? Ans. 243 days.

13. A farmer bought 100 A. of land for $5500, and afterwards sold 37 A. 3 R. 29 P. at the same price per acre. What did the portion sold amount to? Ans. $2086.218'.

14. A father dying left his son a fortune, of which he spent in 2 years, of the remainder lasted him 3 years longer, when he had only $3000 left. What fortune did his father bequeath him? Ans. $12000.

15. Three pipes will separately fill a cistern with water in 3 hours, 4 hours, and 5 hours. If the three pipes discharge into the cistern together, in what time will it be filled?

Ans. 11 hours.

16. If A could do a piece of work in 10 days, B in 12 days, and C in 15 days, in what time could A and B together do it? In what time the three together do it?

Ans. A and B in 5 days; A, B, and C in 4 days.

17. A merchant sold 4 yd. 3 qr. of cloth, at $5.25 per yard; 13 yd. 2 qr. of silk, at $1.12 per yard; and 7 yd. 24 gr. of linen, at $0.62 per yard. What did the whole amount to ? Ans. $44.890'.

18. How many yards of carpeting, which is of a yard wide, will be sufficient for a room 18 ft. 9 in. long, and 16 ft. wide ? Ans. 39 yards.

19. A grocer exchanged 12 cwt. 3 qr. 18 lb. sugar, at $7.184 per cut., for wheat at 81 cts. per bushel. How many bushels of wheat were required to pay for the sugar?

Ans. 113.505' bushels.

20. A gentleman has a flower garden 30 p. 3 yd. in length, and 17 p. 4 yd. in breadth. Without altering the area, he wishes to increase the breadth to 20 poles; how much must the length be diminished? Ans. 3 p. 2 yd.

21. If 5 yards of cloth which is 3 qr. wide, cost $10.50, what ought to be paid for 14 yards of cloth, of like quality, 5 gr. wide? Ans. $46.395'.

‘22. A and B barter as follows, viz., 4 T. 17 cwt. 3 qr. of hay, at $12 per ton, for corn at $1.87 per barrel. How many barrels of corn will be required as an equivalent for the hay? Ans. 31 barrels.

23. If the transportation of 15 cwt. 3 qr., 100 miles, costs $45.50; what ought to be charged for the conveyance of 37 T. 1 cwt., 400 miles? Ans. $8562.666'.

24. The sum of $500 is to be divided between A, B, and C, in such a manner that A's share shall be to B's as 5 to 3, and B's to C's as 3 to 7. What will be the share of each?

Ans. A's $166.666', B's $100, C's $233.333'.

25. If 5 laborers, working 8 hours a day, can dig a cellar 25 ft. long, 19 ft. wide, and 8 ft. deep, in 15 days, in what time ought 12 laborers, working 94 hours a day, to dig a cellar 201 ft. long, 17 ft. wide, and 84 ft. deep? Ans. 4.089' days.

26. A person failing in business, is indebted to A $300, to B $250, and to C $400. His assets amount to $550: what will be the proportional share of each creditor?

Ans. A's $173.684', B's $144.736', C's $231.578'.

27. A merchant has coffee at 12 cts., 16 cts., and 18 cts., a lb., and wishes to form, of the different kinds, a mixture worth 14 cents a pound. What must be the ratios of the mixture?

Ans. 6 lb. at 12 cts., 2 lb. at 16 cts., and 2lb. at 18 cts. 28. An estate consisting of 5000 acres of land, is to be divided among three persons, so that A's share shall be to B's as 2 to 5 and B's to C's as 3 to 8. Required the share of each. Ans. A's 491ff, B's 12298†, C's 327847.

29. Allowing 2 lb. of tea to be worth as much as 13 lb. of coffee; and 5 lb. of coffee, as much as 9 lb. of sugar; and 201 lb. sugar, as much as 50 lb. of rice; how many pounds of tea will be equivalent to 100 lb. of rice? Ans. 3,59 lb.

30. How many gallons of brandy at 25 cts. per gal., and how much water must be mixed with 5 gallons of brandy at 40 cts. per gal., that the adulterated compound may rate at 30 cts. per gal.? Ans. 1 gal. of each.

31. A, B, and C form a partnership for 12 months. A and B at once advance $2500 each as their portion of the capital stock. At the end of 3 months C advances $3000; and B withdraws $1000. The profits amount to $1500 what is the share of each? Ans. A's $576.923', B's $403.846', C's $519.230'.

32. How many ounces of gold 18 carats fine, must be compounded with 5 oz. 23 carats fine, and 8 oz. 22 carats fine, that the compound may be 20 carats fine? Ans. 15 ounces.

33. In a joint speculation, A had 4 of the capital for 6 months, B of it for 9 months, and C the remainder for 12 months. The loss amounted to $500: what loss should be sustained by each ?

Ans. $80.645' by A, $193.548' by B, $225.806' by C. 34. A merchant has four kinds of coffee, worth, respectively, 8 cts., 12 cts., 14 cts., and 20 cts. per lb. What quantity of each kind must be taken to form a mixture of 100 pounds, which shall rate at 15 cts. per pound?

Ans. 42 lb. at 20 cts., 19 lb. at each of the other rates. 35. The sum of $3000 is to be divided between A, B, C, and D in such a manner that A's share shall be to B's as 21⁄2 to 3; B's to C's as 3 to 4, and C's to D's as 5 to 6. What will be the share of each? Ans. A's $524.475', B's $629.370', C's $839.160', D's $1006.993'.

36. If 20 bushels of wheat be worth 37 bu. of rye, and 3 bu. of rye be worth 1 barrel of corn, and 2 barrels of corn be worth 9 bu. of oats, and 25 bu. of oats be worth 1 ton of hay; how many tons of hay should be exchanged for 100 bushels of wheat? tons.

Ans. 9

CHAPTER X.

PERCENTAGE, AND ITS APPLICATIONS.

PERCENTAGE.

$244. Percentage is an allowance at a certain rate for every hundred.

The Latin per centum, or its contraction, per cent., signifies by the hundred.

One per cent. on any number is one for every hundred; two per cent. is two for every hundred; and so on.

One per cent. on any sum of money is $1 for every $100; two per cent. is $2 for every $100; and so on.

§ 245. The ratio of percentage is the rate per cent. divided by 100. It is usually expressed decimally, by making two integral figures decimals in the rate per cent.-prefixing Os when necessary.

Thus 1 per cent. on any number is ro, or .01, of that number; the fraction Too, or .01, being the ratio of percentage for 1 per cent.

What is the ratio for 2 per cent.? For 3 per cent.? For 4 per cent.? For 5 per cent.? For 6 per cent.? For 10 per cent.?

§ 246. When the rate per cent. is a mixed number, or a proper fraction, the ratio of percentage will be a mixed fraction, which may be reduced to a simple fraction.

Thus the ratio for 2 per cent. is

2

100

ratio for per cent., that is, of 1 per cent. is

What is the ratio for per cent.? For 14 per cent.? For 23 per cent.

=.02}=.025; and the

=.0075.

100

247. The ratio of percentage multiplied by 100 produces the rate per cent. Thus the ratio being .03, the rate per cent. is .03X100 3.

The rate per cent. is readily found from the decimal ratio, by making two decimal figures in the ratio integral.

Thus the ratio being .0125, the rate per cent. is 1.25=14.

If the ratio is .01, what is the rate per cent? If the ratio is .02? If the ratio is .015? If the ratio is .0225? If the ratio is .0375?

Basis of Percentage.

§ 248. The sum or number on which percentage is computed, at any given rate, may be called, for convenience, the basis of percentage.

Thus when we say, 2 per cent. on $300, the basis of percentage is $300.

If the rate per cent. is 2, and the amount of percentage $4, what is the basis of percentage? If the rate per cent. is 3, and the amount of percentage $9? If the rate per cent. is 4, and the amount of percentage $12? If the rate per cent. is 5, and the amount of percentage $20? If the rate per cent. is 6, and the amount of percentage $30 ?

§ 249. To find an AMOUNT OF PERCENTAGE on a given number. Multiply the given number, or basis of percentage, by the ratio of percentage; the product will be the amount of percentage.

EXAMPLE.

To find 5 per cent. on $150.

The ratio of percentage is 18.05.

(§ 245).

100

Then $150X.05= $7.50, the amount of percentage. Observe that 5 per cent. on $150, is Too of $150, and multiplying by a fraction finds such a part of the multiplicand as is expressed by the multiplier.

By PROPORTION. $100: $150::$5: Amount of percentage.

From a given Amount of Percentage, to find the Basis of Percentage.

From the preceding Rule it follows, that

§ 250. The amount of percentage divided by the ratio of percentage, gives the basis of percentage.