39. To find what per cent one number is of another.

1. If your school had a team in a baseball league with 7 other teams, could you tell which team has the best standing after several games have been played? Do you know how a big league computes the percentages of its teams?

2. Suppose your team has played 20 games and has won 11 of them, what part of the games played has it won? What per cent of them has it won?

3. Team B has played 25 games and has won 14 of them. What part of its games has it won? What per cent of them?

4. Team C has played 30 games and has won 16 of them. What per cent of its games has it won?

5. Team D has played 27 games and has won 15. What per cent has it won?

6. Team E has played 28 games and has won 14 of them. What per cent has it won?

7. Which team has won the largest per cent of the games played? Which is second?

8. Beginning with the best team, name them in the order of their standing.

Notice that the standing of a team is a per cent of the number of games played. The number of games played is therefore the base.

In the above problems you have been required to find what per cent the number of games won is of the number of games played.

In finding what per cent one number is of another the second number, of which the per cent is taken, is the base. The first number, which is a certain per cent of the second, is the percentage, and it is required to find the rate per cent.

The rate per cent is found by dividing the percentage by the base, expressing the quotient as hundredths, then as per cent.

1. 3 is what part of 5? What per cent of 5?

2. 18 is what per cent of 72?

3. What per cent of 96 is 30?

4. 2 is what per cent of 15?

5. 125 is what per cent of 625? Of 125? Of 25?

6. There are 15 boys in a room of 35 pupils. What per cent of the pupils are girls?

7. .3 is what per cent of 30? Of .03?

8. 2 is what per cent of 200?

9. 200 is what per cent of 2? 10. What per cent of 50 is 1000? 11. What per cent of 1000 is 50? 12. 1000 is what per cent of 1? 13. 1 is what per cent of 1000? 14. What per cent of 250 is 30?

15. 19.2 is what per cent of 600?

16. 85 is what per cent of 412, correct to .1%?

17. What per cent of 732 is 935, correct to .1%?

18. What per cent of 5432 is 1763, correct to .01%?

19. In a certain test 10 questions were given. John answered 8 correctly. What per cent did he make on the examination?

20. In the same examination Mary gave 81⁄2 correct answers. What per cent did she make?

21. Compute the per cent of games won by each team in

22. In a rifle match each contestant fired 25 shots. A made 18 hits, B made 22, C 24, and D 21. What per cent of each man's shots hit the target?

23. A superintendent of schools wanted to know which room had the best attendance on a certain circus day. Room A had 3 pupils absent out of 40; room B had 7 absent out of 52; room C had 4 absent out of 32; room D, 5 out of 42; room E, 3 out of 36; room F, 6 out of 45; room G, 2 out of 25; room H, 4 out of 45; room I, 8 out of 40. What per cent of the pupils of each room were present? Name the rooms in the order of their attendance rank, the one having the best attendance coming first.

24. In 100 pounds of garden soil there are 14.41 pounds of water. What per cent of the wet soil is water? After the water has been taken out, its weight is what per cent of that of the dry soil?

25. An acre of soil 7 inches deep weighs about 2,000,000 pounds. If it contains 328.8 barrels of water, what per cent of the weight of the soil is water? Assume that a barrel

contains 4 cubic feet. A cubic foot of water weighs 62 pounds.

40. To find a number of which a certain per cent is known. 1. The product of two numbers is 15. One of the numbers is 3. What is the other?

2. The product of two numbers is 85. One of the numbers is 5. Find the other.

3. One of the two factors of 117 is 13. Find the other factor.

4. What number multiplied by 2 gives 5 as a product? 5. What number multiplied by 5 gives 2 as a product? 6. If the product of two numbers is 22 and one of the numbers is 7, what is the other number?

7. The product of two numbers is 36. One of the numbers is .03. What is the other?

8. What number multiplied by .25 will give 284.3 as a product?

9. What number multiplied by 5% will give 24 as a product?

10. If the product of two numbers is given and one of the numbers is known, how may the other be found?

11. The formula p=rXb tells that the percentage is the product of the base and the rate per cent.

If the percentage and the base are known, how may the rate be found?

12. If the percentage and the rate are known, how may the base be found?

These answers give us these two rules :

The base equals the percentage divided by the rate per cent. The rate per cent equals the percentage divided by the base. We now have the three formulas :

(1) p=bXr, (2) b=2, and (3) r=2.

The pupil should notice that in all computations with r, r is expressed as a common or a decimal fraction.

Exercise 40

Use the formulas in solving the following exercises :

1. r=32%, p=4. Find b.

SOLUTION. Here b is desired, so formula (2) must be used.

9. Two inches is what per cent of 6 inches? 10. Six inches is what per cent of 2 inches? 11. A foot is what per cent of a yard? 12. An inch is what per cent of a foot?

13. A quart is what per cent of a gallon?

14. A pound Troy is 5760 grains and a pound avoirdupois is 7000 grains. A pound Troy is what per cent of a pound avoirdupois?

15. A centimeter is what per cent of an inch?

16. An inch is what per cent of a centimeter?

17. A liter is 1.0567 liquid quarts. A liter is what per cent of a liquid quart?

18. A square meter is 1.196 sq. yd. It is what per cent of a square yard? A square yard is what per cent of a square meter?

19. A square mile is 2.59 square kilometers. It is what per cent of a square kilometer? A square kilometer is what per cent of a square mile?