PERCENTAGE.

273. 1. A merchant lost $4 out of every $100 worth of goods sold on account of bad debts. What part of his sales did he lose?

2. A man spent $5 out of every $10 that he earned. How many hundredths of his earnings did he spend?

3. A company of soldiers engaged in battle lost 1 out of every 10 men. How many was that per hundred or per cent?

4. In a school 6 out of every 10 pupils are girls. How many hundredths of the number are girls? What per cent?

5. What is 15, or 5 per cent, of $500? $2000? Of $3000? Of $5000 ?

Of $1000? Of

6. What is, or 2 per cent, of $400? Of $600? Of $1000? Of $1200? Of $1600 ?

7. What is 6 per cent of $600 ? Of $800? Of $1000?

274. The expression Per Cent means by the hundred. It is a contraction of the Latin per centum, by the hundred.

275. The commercial Sign of Per Cent is %.

Thus, 8% is read 8 per cent.

276. That part of arithmetic which treats of processes involving per cent is termed Percentage.

277. Since per cent is a number of hundredths, it is usually expressed as a decimal.

It may also be expressed as a common fraction. Thus,

10 per cent is written 10%, 10, 1%.

121 per cent is written 121%, .12, .125,

12.

100

279. Express by common fractions in their lowest terms:

Problems in percentage involve the following elements: 281. The number of which the per cent is to be found, or the Base.

282. The number of hundredths taken, or the Rate.

283. The number which is a certain number of hundredths of the base, or the Percentage.

284. The sum of the base and percentage, or the Amount.

285. The base less the percentage, or the Difference.

In the formulas, B represents the base; R, the rate; P, the percentage; A, the amount; and D, the difference.

286. To find the percentage when the base and rate are given.

EXPLANATION. Since 121% of a number is .12 of it, 12% of $864.80

$864.80x.12 $108.10, is .123 of $864.80, or $108.10.

or

of $864.80=$108.10.

FORMULA,

Or,

Since 12% of a number is

of it, 12% of $864.80 is of $864.80, which is $108.10.

BX R=P.

8. A man bought 350 cows, and then sold 60% of them. How many cows had he left?

9. A farmer had 375 acres of land, and sold 33% of it. How much remained?

10. B bought 3480 barrels of flour, and then sold 16% of it. How many barrels remained ?

11. C, having a flock of 575 sheep, sold 64% of them. How many had he left?

12. A man's income is $900 a year, and he spends 67% of it. How much does he spend?

13. D bought 1320 acres of land, and sold 371% of it. How much had he left?

14. In a school of 400 pupils, 621% are boys. How many boys are there in the school?

15. How much metal will be obtained from 375 tons of ore if the metal is 101% of the ore?

16. A farm cost $4750, but since it was purchased the farm has decreased 161% in value. What is the present value of the farm?

17. If cloth will shrink 51% of its length in sponging, what will be the shrinkage of a piece of cloth containing 42 yards before sponging?

18. If a man's salary is $1350 a year, and his expenses are 871% of that sum, how much can he save yearly?

19. A man having $27,000, invested 18% in bank stock, 121% in bonds and mortgages, 34% in town property, and the rest in a farm. How much did the farm cost?

20. Mr. B receives a salary of $1800 a year. He pays 15% of it for board, 81% for clothing, and 16% for other expenses. What are his yearly expenses, and how much does he save?

21. A man bequeathed 15% of his estate to a college, 10% to an asylum, 10% to a church, 5% to a public library, and the remainder he divided equally among his 7 children. What did each child receive, the estate being worth $150,000?

287. To find the rate when the base and percentage are given. 1. What part of 25 is 5? How many hundredths of 25 is 5? What per cent?

2. What part of 40 is 4? How many hundredths? What per cent?