75. 1. If 6 cords of wood cost $15, what will 4 cords cost?

ANALYSIS. Four cords are, or of 6 cords. If 6 cords of wood cost $15, 4 cords will cost of $15; of $15 is $5, and of $15 is 2 times $5, or $10. Therefore, &c.

Or, the pupil may use the form of analysis used in section 22, on page 41.

2. If 9 pounds of sugar cost 75 cents, what will 12 pounds cost?

3. If 6 men can cut 45 cords of wood in 3 days, how many cords can 8 men cut in the same time? 4. If 31 yards of cloth cost $101, how much will 7 yards cost?

5. If 43 pounds of butter cost 66 cents, what will 23 pounds cost?

6. If a mechanic earn 13 shillings in 14 days, how much can he earn in a week?

7. If $71 will buy 3 cords of wood, how many cords can be bought for $101?

8. If barrel of flour cost $43, what will of a barrel cost?

=

ANALYSIS. What part of is? }=}, and } = 1; the ratio of to is the same as of 3 to 4, Then, since barrel of flour cost $41, of a barrel will cost of $4}; 1 of £= 36= $6. Therefore, &c.

9. If a man can run 6 miles in of an hour, how far can he run in 3 hours?

10. How many yards of carpeting of a yard wide are equal to 12 yards of a yard wide? 11. If a staff 3 feet long cast a shadow 5 feet in length, what would be the length of the shadow cast by a pole 13 feet long?

12. If the sawing of of a cord of wood cost 61 shillings, what would the sawing of 3 cords cost?

13. John earns 9 cents as often as James earns 15 cents; when John has earned 63 cents, how much has James earned?

14. Two persons start from different points and travel towards each other; the first one travels 7 miles while the other travels 5 miles, and when they meet the first one has traveled 70 miles; how far apart were they when they started?

15. If 4 men can build a wall 60 feet long in 6 days, in what time can 3 men build a wall 90 feet in length?

ANALYSIS. In 3 of 88 of 6 days, which are 12 days. Or thus if it will take 4 men 6 days to build a wall 60 feet long, it will take 1 man 4 times 6 days, or 24 days, and 3 men can do it in of 24, or 8 days; to build a wall 1 foot long will require of 8, or 3 days, and to build a wall 90 feet long will require 90 times as many days, or 90 times o, equal to 12 days. Therefore, &c.

16. If 5 men can do a piece of work in 10 days, how many men will do a piece of work 4 times as large in 20 days?

17. If a man perform a journey in 8 days, by traveling 9 hours a day, how many days will he require to perform the same journey, if he travel 12 hours a day?

18. If 5 horses eat 1 tons of hay in 1 month, how many tons will 6 horses eat in 23 months?

19. How many days will it take 5 men to earn $113, if 3 men earn $ in of a day?

20. If 1 horse eat 1 bushels of oats in 3 days, in how many days will 4 horses eat 49 bushels?

21. If a barrel of flour will supply a family of 4 persons 5 weeks, how much will supply a family of 3 persons 2 weeks?

22. If 3 furnaces consume 121 tons of coal in 7 days, how long will 17 tons last 5 furnaces?

76.

CHAPTER VIII.

PERCENTAGE.

THE terms, percentage and per cent.,signify by the hundred, or hundredths, that is, a certain number of parts of each one hundred parts, of whatever denomination. Thus, by 5 per cent. is meant 5 cents of every 100 cents, $5 of every $100, 5 bushels of every 100 bushels, &c. Therefore, 5 per cent. equals 5 hundredths, (150,) or 2b. 8 per cent., 8 hundredths, (180,) or of the given number or quantity.

1. A man, having $40, lost 3 per cent. of it; how many dollars did he lose?

ANALYSIS. Since he lost 3 per cent., or 180, on $1, on $40 he lost 40 times 13, or 138 of $1, equal to $14. Therefore, &c.

2. What is 5 per cent. of $25? of $30? of $45? 3. What is 7 per cent. of $15? of $40? of $200 ? 4. What is 6 per cent. of $18? of $37? of $54? 5. What is 3 per cent. of 50 bushels of corn? 6. What is 10 per cent. of 160 tons of plaster? 7. What is 25 per cent. of 96 gallons of wine? 8. What is 12 per cent. of 33 pounds of sugar? 9. What is 15 per cent. of 110 barrels of flour? 10. What is 8 per cent. of 28 yards of cloth? 11. What is per cent. of $45 ?

ANALYSIS. Since 1 per cent of $45 is 45, of 1 per cent. is of, or, equal to $. Therefore, &c. per cent. of $28? of $44? of $56? per cent. of $63? of $120? per cent. of 30 barrels of cider ? per cent of 70 sheep? of 35 cows? per cent. of 34 hundred weight?

12. What is

13. What is

14. What is

15. What is 3

16. What is 21

17. A man bought 75 barrels of apples, and on opening them, found 8 per cent. of them spoiled; how many barrels did he lose?

18. If I have $200 deposited in the bank, and draw out 15 per cent. of it, how much remains?

19. A farmer, having 176 sheep, sold 75 per cent. of them, and kept the remainder; how many did he keep?

20. A young man, having $104, lost 121 per cent. of it in gambling; how many dollars did he lose, and what per cent. of the whole had he left?

77. 1. What fraction of a number is 8 of it?

per cent.

ANALYSIS. Since 1 per cent. is To, 8 per cent. is 8 times do, or 185,25. Therefore 8 per cent. equals of any number or thing.

=

2. What fraction of a number is 6 per cent.? 7 per cent.? 10 per cent.? 12 per cent.?

3. What fraction of a number is 6 per cent.? 163 per cent.? 20 per cent.? 371 per cent.? 40 per cent.?

4. If you have $120, and lose 33 per cent. of it, what part of it will you lose?

5. James, having 250 marbles, lost 40 per cent. of them at play; what part of the whole had he left, and how many did he lose?

6. What per cent. of a barrel of flour is of it? ANALYSIS. Since the whole of any number or thing is equal to 100 per cent., & of one barrel of flour is equal to of 100 per cent., or 40 per cent. Therefore, &c.

7. If a man save § of his income, what per cent. does he spend?

of his money in dry

8. If a merchant invest goods, what per cent, does he invest?

78. 1. A farmer, having 20 sheep, lost 5 of them by disease; what per cent. did he lose?

of 100

ANALYSIS. Since 20 sheep are 100 per cent., or all that he had, 5 sheep are, or, of all he had; and per cent. is 25 per cent. Therefore, &c.

2. What per cent. of 21 is 7?

3. What per cent. of 50 is 5? 10? 20? 25 ? 4. What per cent. of $40 is $5? $8? $25? $30 ? 5. What per cent. of 18 pounds is 3 pounds? 12 pounds?

6. What per cent. of 42 miles is 6 miles? 7 miles ? 7. What per cent. of 12 is 21?

8. What per cent. of 30 is 12? 15? 20?

9. What per cent. of 18 is 9? 12? 15? 10. 1 is what per cent. of 9? of 15? of 21? 11. 24 is what per cent. of 71? of 121? of 10? 12. is what per cent. of 31? of 163? of 20? 13. 12 is what per cent. of 8? of 12? of 20? 14. If from a hogshead of molasses a grocer draw 42 gallons, what per cent. of the whole will remain ?

15. From a box of tea containing 60 pounds, 15 pounds were sold at one time, and 25 pounds at another; what per cent. of the whole remained unsold?

16. In a heap of potatoes containing 150 bushels, 3 bushels of every 5 are bad; what per cent. are bad, and how many bushels are good?

17. A gambler, having $250, lost $80 at play ; what per cent. of his money did he lose, and what per cent. had he left?

18. James, having 62 cents, gave 37 for a book; what per cent. of his money had he left?

19. A grocer, having a barrel of sugar containing 200 pounds, sold of it at one time, and of the remainder at another time; what per cent. remained unsold?