3.

TO FIND THE BASE.

1. 42 is 14% of what number?

ANALYSIS 1.-14% is 14, or. If 42 is of a number,

of

that number is of 42, or 6, and 50, or the number, is 50 times 6, or 300.

14

ANALYSIS 2.-If 14%, or 1%, of a number is 42, 10 is 14 of 42, or 3, and 188, or the number, is 100 times 3, or 300.

NOTE.-Either analysis may be used.

2. 16 is 4% of what?

3. 25 is 5% of what?

4. 40 is 32% of what?

5. 32 lbs. are 8% of what?

6. 20 bu. are 33% of what? 7. 8 qt. are 40% of what?

8. 6 is 13% of what?

9. 7 is 12% of what?

10. 10 quarts are 40% of how many gallons?

11. A farmer gained $6 on a horse, which was 3% of his value; what was the value?

12. $18 is 4 per cent. of my money; how much have I? 13. I rent a house at $120, which is 8% of the cost of the house; how much did it cost?

14. George spends $40 a year for cigars, which is 8% of his income; what is his income?

15. I paid $30 for a chain, which is 24% of the cost of watch; what is the cost of my watch?

my

16. My board costs me $310 a year, which is 40% of my salary; what is my salary?

17. A farmer sold 160 bushels of corn, which was 32% of his crop; what was the crop?

18. If by selling cloth at 20% gain I make 14 cents, what was the cost of the cloth?

19. Mr. Henry, owning of a ship, sold 30% of his share for $9000; what was the value of the whole ship?

20. 2 pk. 3 qt. was 25% of the nuts Harry gathered; how many did he gather?

REVIEW PROBLEMS.

1. A miller sold flour at $6, and thereby gained 20%; what was the cost of the flour?

SOLUTION.-20% equals ;, the cost, plus, the gain, equals £, or the selling price. If g of the cost of the flour is $6, is of $6, 01 $1, and, or the cost, is 5 times $1, or $5.

2. A horse was sold at $40 more than cost, which was at a gain of 50%; what was the cost?

3. A knife was sold at 30 cents less than cost, which was at a loss of 60%; what was the cost?

4. A miller sold some damaged flour at $6, and thereby lost 25%; what was the price of the flour?

5. A bookseller retails books at 75 cents each, and thereby gains 25% on cost; what did they cost him?

6. I bought a cow of my neighbor and sold her for $46, which was at a gain of 15%; how much did I pay for her?

7. If a merchant sells damaged cloth at $2 a yard, and thereby loses 20%, what was the cost of the cloth?

8. If a merchant make 8% by selling sheeting at 27 cents a yard, what did he pay for it?

9. What number, increased by 20% of itself, equals 48? 10. What number, increased by 75% of itself, equals 28? 11. 80 is 25% more than what number?

12. What number, diminished by 30% of itself, equals 28? 13. What number, diminished by 75% of itself, equals 16? 14. 63 is 30% less than what number?

15. What number, increased by the difference between 70% and 40% of itself, equals 52?

16. When cloth is sold at $1.65 a yard, at a gain of 10%, what is the cost?

17. I sold flour at $7.50 a barrel, at a gain of 20%; what was the cost of the flour?

18. Two boys have 110 marbles: one has 20% more than the other; how many has each?

19. What is the length of a ditch whose length, increased by 40% and 5 feet, equals 89 feet?

20. A horse and carriage cost $188: the horse cost 35% more than the carriage; how much did each cost?

21. In a school of 115 pupils the number of boys is 30% greater than the number of girls; how many are there of each?

22. What fraction, increased by 331% of itself, equals ? 23. Rudolph has 36 marbles, which is 25% less than William's number; how many has William ?

PROFIT AND LOSS.

1. I bought corn at 40 cents a bushel and sold it at a gain of 12%; how much did I get for it?

ANALYSIS 1.-If I gain 121%, I gain

121

100'

or, the cost, plus,

of 40 cents is 45 cents.

the gain, equals, or the selling price. ANALYSIS 2.—121% equals }; } of 40 cents is 5 cents; hence I sold the corn for 40 cents plus 5 cents, or 45 cents.

2. If I buy a cow for $40, how must I sell her to gain 20%?

3. How must I sell eggs for which I pay 20 cents a dozen, so as to gain 30% ?

4. If a boy pay 30 cents a dozen for oranges, how must he sell them apiece so as to gain 60% ?

5. If I buy 10 barrels of apples for $25, how must I sell them per barrel to gain 20% ?

6. A merchant paid 80 cents a yard for silk; how must he sell it to gain 12% ?

7. A house cost $2000, and was sold at a gain of 51%; at what price was it sold?

1. If a sheep is bought for $4 and sold for $6, what is the gain per cent.?

ANALYSIS.-If a sheep is bought for $4 and sold for $6, the gain is $6 minus $4, or $2. $2 is of $4, or of 100%, which is 50%.

2. If I buy a cow at $30 and sell her at $36, what is the gain per cent.?

3. When a dealer buys melons at $12 a hundred and sells them at $16 a hundred, what is his gain per cent.?

4. What is the gain per cent. on a book that is bought at 40 cents and sold at 50 cents?

5. A produce dealer buys eggs at 25 cents a dozen and sells them at 30 cents a dozen; what is his gain per cent.? 6. A merchant buys potatoes at 60 cents a bushel and retails them at 25 cents a peck; what is his gain per cent.?

7. A butcher buys beef at 6 cents a pound and retails it at 10 cents a pound; what is his gain per cent.?

8. A huckster buys oranges at 25 cents a dozen and retails them at 5 cents apiece; what is his gain per cent.?

9. When a bushel of chestnuts costs $2 and is retailed at 10 cents a quart, what is the gain per cent.?

10. I sold of a farm for what the whole farm cost me; what was the gain per cent.?

11. What is the loss per cent. when of an article is sold for the value of of it?

12. A piano was bought for $250, and after several years' use was sold for $150; what was the loss per cent.?

13. A dealer bought flour at $6 a barrel and sold it at 90 cents a sack (of a barrel); what was his gain per cent.?

14. How must goods costing $3 be marked so that the seller may drop 10% in his price and still make 20% ?

1. A boy sold a book for 15 cents more than cost, and gained 10%; what was the cost?

ANALYSIS.-10%, or the gain, is of the cost. If of the cost is 15 cents, 10, or the cost, is 10 times 15 cents, or $1.50.

2. If a farmer sell a horse at $30 more than cost, and thereby gain 15%, what was the cost?

3. A miller sold damaged flour at $1.50 less than its actual value, and thereby lost 25%; what was the real value of the flour?

4. A piano was sold at $30 less than cost, which was at a loss of 15%; what was the cost?

5. If I lose 40 cents by selling an article at 12% below its value, what is the value?

6. A man's property having increased 30% in value, he sold it for $600 more than cost; what did it cost him?

7. Property having depreciated in value, I sold my house for $2500 less than cost, and thereby lost 50%; what was the cost of the house?

1. If by selling eggs at 30 cents a dozen I make 20%, what did the eggs cost me?

ANALYSIS. Since I gained 20%, or of the cost, I sold the eggs at +, or, of the cost. If g of the cost is 30 cents, of the cost is of 30 cents, or 5 cents, and, or the cost, is 5 times 5 cents, or 25

cents.

2. A jeweler sold a watch for $75, thereby gaining 25%; what did he pay for the watch?

3. If by selling coffee at 28 cents I make 12%, what was the cost of the coffee?

4. A boy sold his knife for 40 cents, which was 20% less than cost; at what price must he have sold it to gain 10%? 5. A gentleman sold a horse for $168 and a carriage for $84; he gained on each 12%; what was the cost of each?