224. Important Per Cents. Certain per cents are used so frequently that their equivalent common fractions should be remembered. These are as follows:

To take 871% of 648 is, therefore, the same as to take 7 of 648. The similarity of these per cents to the corresponding decimal fractions given on page 87 should be noted.

17. How much is
18. How much is

19. How much is
20. How much is

of $2640? 12% of $2640?
of $3360? 371% of $3360?
of $4320? 621% of $4320?

of $5768? 87% of $5768?

21. An inch is what fraction of a foot? what per cent of a foot?

22. A pint is what fraction of a gallon? what per cent of a gallon?

23. Five cents is what fraction of a dollar? what per cent of a dollar?

24. If you wish to find 33% of a number, what fractional part of the number do you wish to find?

25. If a man spends one fifth of his income for rent, what per cent does he spend for this purpose?

26. What per cent of the perimeter is one side of a square? What per cent are two sides? three sides?

27. If there are 30 pupils in a class and 50% are boys, what fraction are boys? How many boys are there?

28. If there are 450 pupils in a school and 52% are boys, what decimal fraction of the pupils are boys? How many boys are there? How many girls are there?

29. If a city has a population of 18,400, and 22% are pupils in school, what decimal fraction of the population is in school? How many are in school?

30. If a shop employs 1680 workers, of whom 371% are men, 50% are women, and the rest are boys, 'how many are there of each ?

31. A merchant has $9600 invested in his business. The first year he made a profit of 61%, the second year 12%, and the third year 163%. How much did he make in the three years?

225. Terms used in Percentage. The number of which some per cent is to be taken is called the base.

The number of hundredths of the base is called the rate.

For example, in 25% of $300, $300 is the base and 25% is the rate. Sometimes 25 is called the rate per cent, 25% being called the rate, but these two terms are commonly used to mean the same thing.

The result found by taking a certain per cent of the base is called the percentage.

Therefore, the percentage is the product of the base and

the rate.

226. To find Some Per Cent of a Number. Required to find 233% of 275.

233% = 0.231.

Multiplying by 0.233, we have 65.311.

If we wish, we may write 23% as 0.2375 and then multiply. We may also, if we choose, write the product 65.3125.

Therefore, to find a required per cent of a number, multiply the number by the given rate.

275

.233

2061

825

550 65.31

16. In a school of 300 pupils 11% are in the sixth grade. How many pupils are in the sixth grade?

17. In a box of 192 oranges 61% have spoiled. How many have spoiled?

18. From a barrel of flour weighing 196 lb., 25% has been sold. How many pounds have been sold?

19. A contractor agreed to build a stone wall 72 ft. long. He has already built 20% of it. How many feet has he still to build?

20. A trolley car has a run of 56 mi. a day. When it has run 15% of this distance, how many miles has it run?

21. How much will 48% of a cubic foot of steel weigh if a cubic foot weighs 490 lb. ?

22. If a steel car when full carries 96,000 lb. of coal, how much does it carry when it is 62% full?

23. If out of 240 problems in arithmetic you solved 93% without any errors, how many did you solve correctly?

24. If a locomotive weighing 116 tons can exert a pull equal to 22% of its weight, how many tons of pull can it exert?

25. A ball team has played 32 games this season and has lost 37% of them. How many games has it won?

26. A cubic foot of water weighs 62 lb. Ice is 92% as heavy as water. What does 25 cu. ft. of ice weigh?

27. The diameter of a circle is about 31% as long as the circumference. What is the diameter of a circle whose circumference is 15 ft.?

28. A meter is 98% longer than a yard. How many inches in a meter?

29. A knot, used at sea, is 15% longer than a mile. How many feet are there in a knot?

30. A sidewalk 112 ft. long and 4 ft. 2 in. wide is to be made 12% longer and 20% wider. How many feet will it be extended? How much wider will it be? By how many square feet will its area be increased?

227. The Per Cent One Number is of Another. Because the percentage is the product of the base and the rate (§ 225),

therefore

The rate equals the percentage divided by the base.

For example, what per cent of 5 is 4?

Since 4 is the product of 5 by some per cent, therefore 4 ÷ 5, or 80%, equals the required per cent.

EXERCISE 131

Find what per cent the second number is of the first:

16. A man bought a horse for $150 and sold it for $175. How much did he gain? What per cent of the cost did he gain?

17. A man bought a farm for $6500 and sold it for $7150. How much did he gain? What per cent of the cost did he gain?

18. A boy weighed 75 lb. a year ago and he now weighs 82 lb. What per cent of 75 lb. has he gained?

19. A village had a population of 1200 five years ago. It now has a population of 1332. What has been the per cent of increase?

20. A poultry raiser has 231 chickens this year. Last year he had 220 chickens. What is the per cent of gain this year? The year before he had 200 chickens. What was the per cent of gain last year?