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9. A horse costing $120 was sold for $60; what per cent. of the cost did he sell for?

10. A man having $50 paid $10 for a coat; what per cent. of his money did the coat cost?

11. A farmer lost by decay 10 bushels of potatoes out of 40 bushels; what % did he lose?

12. Louis has half a dollar and John has 25 cents; what % of Louis's money is John's?

13. A man weighing 150 pounds lost 30 pounds through sickness; what % did he lose?

14. I have 10 cents, with which I buy a book, and sell it again for 15 cents; what % do I gain on my money?

15. I buy a watch for $10, and sell it for $15; what % do I gain on the money which I lay out?

WRITTEN EXERCISES. 1. A man owing $750 paid $624; what per cent did he pay?

PROOF. 750)624.000.83} or 831%

$750 6000

.831 2400

2250 2250

6000 150 1

150 750 5

$624.00 ANALYSIS.—624 is 634 of 750.624 changed to a decimal and carried to the hundredths place (per cent. being so many hundredths) =.837 or 831%.

RULE. Divide the percentage by the base, extending the division to hundredths.

2. What % of 1224 is 816?
3. What % of 17% is 65 ?

4. A clerk whose salary is $1500 pays $300 for rent; what % is that of his salary?

5. A city whose population was 45000 in 1860, had increased to 60000 in 1870; what was the increase, and what % is it of the population in 1860?

6. In a district school of 46 pupils, 12 are studying history; what % is that of the whole number?

7. A man sold a watch for $175, that had cost him $150; what did he gain, and what % of the original cost is the gain?

8: 4 of a barrel of flour was damaged by water; what % remained sound?

9. What % of 3 gal. 2 qt. 1 pt. is 1 gal. 3 qt. ?

10. A London merchant owing £198 9s. paid £66 3s.; what % did he pay?

11. What % of is $? is what % of 3?

12. A farmer's flock of sheep decreased from 480 to 320; what % did he lose ?

13. What % of the weight of a barrel of pork is the weight of a barrel of flour?

14. A merchant fails in business, owing $25000; what % can he pay, if his property is worth $8333.334?

15. If the standard for gold coin in the United States is 9 parts of gold to 1 part of alloy, what is the % of alloy in an eagle?

16. A farmer feeds his horses a mixture of oats and corn, in the proportion of 7 qt. of oats to 1 qt, of corn; what is the per cent. of oats in a peck of the mixture? In a bushel? In 100 bushels ?

17. What per cent. of 3.1416 is .7854?

CASE III. To find a number when any per cent. of it is given.

ORAL EXERCISES. 1. 12 is 3% of what number? ANALYSIS. If 12 is 3% of some number, 1% of that number is į of 12=4, and 100%, or the number, is 100 times 4= 400.

2. 20 is 10% of what number? 30 is 5% of what number?

3. 16 is 8% of what number? 4 is 20% of what number?

4. 25 is 25% of what number? 50% of what.number?

5. Charles has 12 dollars, which is 6% of what Robert has; how much has Robert?

6. A man buying a house made a payment of $400, which was 10% of its price; what was the price?

7. 80% of the pupils of a school were dismissed, while the remainder of the pupils, 40 in number, were detained; what was the entire number?

ANALYSIS.—100% or the entire number — 80%=20% detained. If 20% = 40 pupils, etc.

8. A man sold a horse for 20% more than he gave for him, receiving $240; what did he give for the horse ?

ANALYSIS.--100% or the cost of the horse + 20% gain= 120 % =$240, etc.

9. A man sold a horse for 20% less than he gave for him, receiving $160; what did he give for the horse? ANALYSIS.—100% - 20% = 80% = $160, etc. 10. 250 is 25% more than what number? 11. 250 is 25% less than what number?

WRITTEN EXERCISES. 1. $246 is 3% of what sum?

PROOF. .03)$246.00

$8200 $8200

.03

$246.00 ANALYSIS.—In this example we have the percentage and rate given, to find the base; now as the base multiplied by the rate gives the percentage, it is evident that the percentage divided by the rate must give the base.

RULE. Divide the percentage by the rate expressed as a decimal.

2. A man's taxes, at the rate of 21%, amount to $150; what is the valuation of his property?

3. A merchant failing in business pays 45 cents on the dollar; how much did he owe the man to whom he paid $1125?

4. An army lost 15% of its number in battle, 4% by desertion, and 11% by sickness, leaving but 14000 men fit for duty; what was the original number?

5. A man drew from bank $118.65, which was 15% of what he had deposited; what amount had he at first?

6. A man drew from bank $118.65, which was 15% of what he had left; what amount had he at first?

7. I expend 60% of my income, and save the balance, which is $1200; what is my income?

8. A farmer sold 450 bushels of corn, which was 331% of his entire crop; how much had he left?

9. A clerk's salary was increased 8%, making it $2700; what was his original salary?

10. $375 is 75% of the cost of my horse and carriage; what did they cost?

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11. A workman's wages were decreased 10%, leaving him but $1.35 per day; what did he receive before the reduction?

12. A man lost 20% of his weight through sickness, and then weighed 120 pounds; what was his original weight?

13. A merchant sold a barrel of flour for $9, which was 121% more than it cost him; what did it cost him?

14. What number increased by 331% of itself will equal 888?

REVIEW PROBLEMS.

ORAL EXERCISES. 1. What is 20% of 40? 40 is 20% of what number? What % of 40 is 20?

2. What % of 20 is 5? What is 5% of 20? 20 is 5% of what number?

3. What % of 5 cents is 1 cent? Of 50 cents is 10 cents ?

4. What % of 10 barrels is 2 barrels? Of 100 barrels is 20 barrels? Of 1000 barrels is 200 barrels?

5. 300 is 50% more than what number?
6. 300 is 50% less than what number?

7. What number increased by 10% of itself is equal to 220?

8. Sold a watch for $150, and thereby gained 50%; what did it cost me?

9. Sold a watch for $150, and thereby lost 50%; what did it cost me?

10. 25% of 80 is 20% of what number? 11. 331% of 90 is 3% of what number?

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