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RULE. I. Of the terms composing each couplet form a ratio greater or less than 1, in the same manner as if the answer depended on those two and the third or odd term.

II. Multiply together the third or odd term and these ratios; the product will be the answer sought.

EXAMPLES FOR PRACTICE.

1. If 12 horses plow 11 acres in 5 days, how many horses would plow 33 acres in 18 days ?

Ans. 10. 2. If 480 bushels of oats will last 24 horses 40 days, how long will 300 bushels last 48 horses, at the same rate ?

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Ans. 121 days. 3. If 7 reaping machines can cut 1260 acres in 12 days, in how many days can 16 machines reap 4728 acres ?

354–47X Ans. 19.7 days. 4. If 144 men in 6 days of 12 hours each, build a walt 200 ft. long, 3 ft. high, and /2 'ft. thick, in how many days of 7 hours each can 30 men build a wall 350 ft. long, 6 ft. high, and 3 ft. thick?

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6 5. In how many days will 6 persons consume 5 bu. of potatoes, if 3 bu. 3 pk. last 9 persons

22 days ? 6. How many planks 103 ft. long and 1} in. thick, are equivalent to 3000 planks 12 ft. 8 in. long and 24 in. thick?

Ans. 65311. 7. If 300 bushels of wheat @ $1.25 will discharge a certain debt, how many bushels @ $.90 will discharge a debt 3 times as great ?

Ans. 1250 bu. 8. If 468 bricks, 8 inches long and 4 inches wide, are required for a walk 26 ft. long and 4 ft. wide, how many bricks will be required for a walk 120 ft. long and 6 ft. wide ?

3211 9. If a cistern 171 ft. long, 10} ft. wide, and 13 ft. deep, hold 546 barrels, how many barrels will a cistern hold that is 16 ft. long, 7 ft. wide, and 15 ft. deep?

Ans. 384 bbl. 10. If 11 men can cut 147 cords of wood in 7 days, when they work 14 hours per day, how many days will it take 5 men to cut 150 cords, working 10 hours each day?

1

PROMISCUOUS EXAMPLES IN PROPORTION. 1. If a staff 4 ft. long cast a shadow 7 ft. in length, what is the hight of a tower that casts a shadow of 198 ft. at the same time?

Ans. 113. ft. 2. A person failing in business owes $972, and his entire property is worth but $607.50; how much will a creditor receive on a debt of $11.33} ?

Ans. $7.08+. 3. If 3 cwt. can be carried 660 mi. for $4, how

many

cwt. can be carried 60 mi. for $12 ?

Ans. 99. 4. A man can perform a certain piece of work in 18 days by working 8 hours a day; in how many days can he do the same work by working 10 hours a day?

Ans. 143. 5. How much land worth $16.50 an acre, should be giv n in exchange for 140 acres, worth $24.75 an acre ?

6. If I gain $155.52 on $1728 in 1 yr. 6 mo., how much will I gain on $750 in 4 yr. 6-mo.?

Ans. $202.59.22 7. If 1 lb. 12 oz. of wool make 2; yd. of cloth 6 qr. wide, how many lb. of wool will it take for 150 yd. of cloth 4 qr.

wide ? 8, What number of men must be employed to finish a piece of work in 5 days, which 15 men could do in 20 days ? Ans. 60.

9. At 12s. 7d. per oz., N. Y. currency, what will be the cost of a service of silver plate weighing 15 lb. 11 oz. 13 pwt. 17 gr. ?

10. If a cistern 16 ft. long, 7 ft. wide, and 15 ft. deep, cost $36.72, how much, at the same rate per cubic foot, would another cistern cost that is 171 ft. long, 108 ft. wide, and 16 ft. deep?

11. A borrows $1200 and keeps it 2 yr. 5 mo. 5 da. ; what sum should he lend for 1 yr. 8 mo. to balance the favor ?

12. A farmer has hay worth $9 a ton, and a merchant has flour worth $5 per barrel. If in trading the former asks $10.50 for his hay, how much should the merchant ask for his flour?

13. If 12 men, working 9 hours a day for 155 days, were able to execute ş of a job, how many men may be withdrawn and the job be finished in 15 days more, if the laborers are employed only 7 hours a day?

Ans. 4. 14. If the use of $300 for 1 yr. 8 mo. is worth $30, how much is the use of $210.25 for 3 yr. 4 mo. 24 da. worth ?

15. What quantity of lining yd. wide, will it require to line 9. yd. of cloth, 1} yd. wide ?

Ans. 156 yd. 16. If it cost $95.60 to carpet a room 24 ft. by 18 ft., how much will it cost to carpet a room 38 ft. by 22 ft. with the same material ?

Ans. $185.00+. 17. If 1618 cords of wood last as long as 11,9 tons of coal, how many cords of wood will last as long as 157 tons of coal ?

18. A miller has a bin 8 ft. long, 4} ft. wide, and 21 ft. deep, and its capacity is 75 bu.; how deep must he make another bin which is to be 18 ft. long and 38 feet wide, that its capacity may be 450 bu.?

Ans. 733 ft. 19. If 4 men in 21 days, mow 63 acres of grass, by working 81 hours a day, how many acres will 15 men mow in 3 days, by working 9 hours a day?

Ans. 40.11 acres. 20. If an army of 600 men have provisions for 5 weeks, allowing each man 12 oz. a day, how many men may be maintained 10 weeks with the same provisions, allowing each man 8 oz. a day? 8 017

21. A cistern holding 20 barrels has two pipes, by one of which it receives 120 gallons in an hour, and by the other discharges 80 gallons in the same time; in how many hours will it be filled ?

22. A merchant in selling groceries sells 14/& oz. for a pound; how much does he cheat a customer who buys of him to the amount of $38.40 ?

Ans. $3,45. * 23. If 5 lb. of sugar costs $.621, and 8 lb. of sugar are worth 5 lb. of coffee, how much will 75 lb. of coffee cost? /?,

24. B and C have each a farm; B's farm is worth $32.50 an acre, and C's $28.75; but in trading B values his at $10 an acre. What value should C put upon

his? 25. If it require 3593 reams of paper to print 12000 copies of an 8vo. book containing 550 pages, how many reams will be required to print 3000 copies of a 12mo. book containing 320 pages ? ?

26. If 248 men, in 5 days of 12 hours each, dig a ditch of 7 degrees of hardness, 232; yd. long, 3ydwide, and 24 yd. deep; in how many days of 9 hours each, will 24 men dig a ditch of 4 degrees of hardness, 387 yd. long, 54 yd. wide, and 31 yd deep?

Ans. 155

PERCENTAGE.

440. Per Cent. is a contraction of the Latin phrase per centum, and significs by the hundred; that is, a certain part of every hundred, of any denomination whatever. Thus, 4 per cent means 4 of every hundred, and may signify 4 cents of every 100 cents, 4 dollars of every 100 dollars, 4 pounds of every 100 pounds, etc.

NOTATION. 441. The character, %, is generally employed in business transactions to represent the words per cent.; thus 6 % signifies 6 per cent.

442. Since any per cent. is some number of hundredths, it is properly expressed by a decimal fraction ; 'thus 5 per cent. = 5 % = .05. Per cent. may always be expressed, however, either by a decimal or a common fraction, as shown in the following

TABLE.

Words.

Symbols.

Decimals.

Common fractions.

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.01 .02 .04 .05 .06 .07 .08 .10 .20 .25 .50 1.00 1.25 .00 .00 .12

20 100 25 100 50 100 100 100 ? 5

per cent.

1

5

1 200

* per cent.

i per cent. 12; per cent.

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10
12

12 %

EXAMPLES FOR PRACTICE.

1. Express decimally 3 per cent. ; 9 per cent.; 12 per cent. ; 16 per cent.;

23 per cent. ; 37 per cent.; 75 per cent.; 125 per cent. ; 184 per cent. ; 205 per cent.

2. Express decimally 15 %; 11 %; 41 %; 53 %; 81%; 203 % ; 25% %; 353 % ; 24% %; 130} %.

3. Express decimally per cent.; # per cent. ; $ per cent. ; 3 per cent. ; $ per cent.; 2 per cent.; i per cent. ; 1 per cent.; 10 per cent.

4. Express by common fractions, in their lowest terms, 4 % ; 373 %; 164 %; 113 %; 429 %; 45 1 %; 43.17 %. 5. What per cent. is .0725 ? ANALYSIS. .0725 .071

7} %, Ans. 6. What per cent. is .065 ?

Ans. 64 %. 7. What per cent. is .14375 ?

Ans. 143 %. 8. What per cent. is .0975?

93% 9. What per cent. is .014 ? 10. What per cent. is .1025? 11. What per cent. is .004 ? 12. What per cent. is .028 ? 13. What % is .1324? 14. What % is .0843 ? 15. What % is .004-4 ?

Ans. Í % 16. What % is .003.13?

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GENERAL PROBLEMS IN PERCENTAGE.

443. In the operations of Percentage there are five parts or elements, namely: Rate per cent., Percentage, Base, Amount, and Difference.

444. Rate per Cent., or Rate, is the decimal which denotes how many hundredths of a number are to be taken.

Notes.-1. Such expressions as 6 per cent., and 5 %, are essentially decimals, the words per cent., or the character %, indicating the decimal denominator.

2. If the decimal be reduced to a common fraction in its lowest terms, this fraction will still be the equivalent rate, though not the rate per cent.

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