EXERCISE 106.

1. There were 125 pupils at school on Monday, 130 on Tuesday, 128 on Wednesday, 132 on Thursday, and 125 on Friday. What was the average daily attendance?

2. A spring of water that yields 250 gal. an hour supplies a town containing 360 families.

What is the

average daily supply of water for each family?

3. A wine merchant put into an empty cask 15 qt. of brandy costing $1.10 a quart, 66 qt. costing $1.20 a quart, and 43 qt. costing $1.40 a quart. At what price per quart must he sell the brandy to gain one fifth of the cost?

4. A grocer mixed 120 lb. of tea costing 50 cents a pound with 180 lb. costing 40 cents a pound. At what price per pound must he sell the mixture to make a profit of $30 on the whole ?

5. A grocer buys two kinds of tea at 40 cents a pound and 56 cents a pound, respectively, and mixes them in the ratio of 5 to 3. What is his profit, if he sells 56 lb. of the mixture at 84 cents a pound?

6. The average length of ten sticks is 2 ft. 10 in.; one stick is 27 in. long, another 37 in. long, and the remaining eight are of the same length. What is the length of one of the remaining eight?

7. The average age of the boys in the four classes of a school is 18.4 yr., 17.9 yr., 16.8 yr., and 15.7 yr. The classes contain 29, 33, 34, and 33 boys, respectively. What is the average age of the boys in the school?

8. Seven boys weigh respectively 119.7 lb., 105 lb., 178.3 lb., 165.3 lb., 142.8 lb., 109 lb., 154.2 lb. What is their average weight?

9. In what proportion should tea costing 60 cents a pound be mixed with tea costing 45 cents a pound that the cost of the mixture should be 54 cents a pound?

10. A merchant has teas that cost 80 cents, 60 cents, and 40 cents a pound, respectively. How many pounds of each kind shall he take to make a mixture of 1000 lb., so that in selling it at 70 cents a pound he may make a profit of 8 cents a pound?

11. A grocer mixed black tea that cost him 28 cents a pound with green tea that cost him 42 cents, and by selling the mixture at 35 cents a pound he gained of its cost. What was the actual cost of the mixture a pound?

In what ratio were the teas mixed?

12. A dealer has an order for 1000 bu. of wheat at 70 cents a bushel. In what proportion shall he mix three kinds of wheat at 66, 69, and 72 cents a bushel to fill the order?

13. A wine merchant mixes wines that cost $0.95, $1.05, $1.10, and $1.20 a gallon to make a mixture costing $1.00 per gallon. How many gallons of each kind of wine does he take?

14. A merchant wishes to fill a barrel that will hold 240 lb. of sugar with sugar costing 44, 44, and 5 cents a pound, respectively, so that the mixture may cost 4 cents a pound. How many pounds of each kind shall he take?

15. A grocer wishes to mix 12 lb. of coffee at 40 cents a pound and 20 lb. at 35 cents a pound with coffee at 28 cents a pound, so that the mixture may be worth 30 cents a pound. How many pounds at 28 cents must he use ?

16. A grocer mixed 14 lb. of coffee costing 32 cents a pound, 18 lb. costing 35 cents a pound, 22 lb. costing 38 cents a pound, and 40 lb. costing 30 cents a pound. What is the cost of the mixture per pound, and at what price must he sell it to gain 0.25 of the cost?

17. In what proportion may oils costing $1.20, $0.80, and $0.60 a gallon be mixed that the mixture may cost $0.70 a gallon?

CHAPTER XII.

PERCENTAGE.

409. A percentage of a number is the result obtained by taking a stated number of hundredths of it.

One hundredth of a number is called one per cent of it; two hundredths, two per cent; and so on.

410. A rate per cent is a fraction whose denominator is 100, and whose numerator is the given number of hundredths. The methods of common fractions or of decimals are used in the solution of all examples in Percentage. The shortest method is the best method.

411. The symbol % stands for the words per cent. Thus, 13% is 0.13; 21% is 0.02; 867% is 8.67.

412. Example. Express 37% as a common fraction.

SOLUTION.

371% =

371 3
100 8

Hence,

413. To Express a Rate Per Cent as a Common Fraction, Write the rate for the numerator and 100 for the denomi nator, and reduce this fraction to its lowest terms.

414. Example. Express as a rate per cent.

415. To Express a Common Fraction as a Rate Per Cent,

Divide 100 by the denominator of the fraction and multiply the quotient by the numerator.

416. Examples.

1. Express 0.4 as a rate per cent.

SOLUTION. 0.4 = 0.40, or 40%.

2. Express 0.4575 as a rate per cent. SOLUTION. 0.4575 = 0.45,75% = 0.453, or 453%.

3. Express 0.00375 as a rate per cent.

SOLUTION. 0.00375 0.00 3
375 = = 0.003 = 3%. Hence,

1000

417. To Express a Decimal as a Rate Per Cent, Write the decimal as hundredths, and the number that expresses the hundredths is the rate per cent required.

NOTE.

If the decimal has more than two places, the figures that follow the hundredths' place signify a fraction of 1%.

418. Problems in Percentage are conveniently divided into three classes, as follows:

Class I. To find a certain fraction of a number.

Class II. To find the fraction that one number is of another.

Class III. To find a number when a fraction of it is given.

The following examples illustrate the three classes :

Class I. What number is of 300?

Class II. What fraction of 300 is 200 ?

Class III. What is the number, if 200 is of it?

The fraction in each class is expressed in hundredths for the sake of a uniform standard; the phrase per cent is used for the word hundredths, and the symbol % is written for the phrase per cent.

Thus, in common fractions 8 is of 16; in decimals 8 is 0.5 of 16; in percentage 8 is 50% of 16.

In common fractions 5 is of 40; in decimals 5 is 0.125 of 40; in percentage 5 is 12% of 40.

419. One hundred per cent of a number is the number itself.

421. To Find a Percentage of a Number,

Multiply the number by the given rate per cent, expressed

as a common fraction or as a decimal.