The number of which a per cent is taken is called the base. The per cent taken is called the rate or the rate per cent. The result of taking the per cent of the base is called the percentage.

Exercise 36

1. Representing the base by b, the rate by r, and the percentage by p, make a formula for finding the percentage when the base and rate are given.

2. Use the formula p=rb to find p when, a. r=8% and b=20.

HINT. Express r as a decimal. Here r = .08. b. r=25% and b=144.

c. r=43% and b=2.5.

d. r 2.5% and b = $14,720.

e. r=163% and b=7243 acres.

f. r=371% and b= $146,738.

3. A family spends 20% of its income for rent, 30% for food, 25% for clothing, 10% for incidentals, and saves the balance. The family income is $1200 a year. How much does it pay for rent? How much does it save?

4. If a family saves 83% of its yearly income of $1575, how much does it save in a year?

5. The per cents of waste in the different cuts of beef are given in the following table :

How much waste is there in a 12-pound cut of each of

these kinds of beef?

in a 12-pound cut?

What is the average per cent of waste

6. In a certain room 333% of the pupils made a grade of exactly 75% on a test. There were 42 pupils in the room and there were 12 questions on the test. How many correct answers were given by all the pupils making 75% on the test?

7. How much water in 5 bushels of potatoes weighing 60 pounds to the bushel, if 78% of their weight is water?

8. A chicken is 44% water. How much water do we buy when we buy a five-pound chicken?

9. A student in a summer sold $1500 of aluminum ware. For his pay he received 40% of the selling price of the aluminum sold. How much was he paid?

10. A certain kind of tire for automobiles formerly sold for $24. The price has been advanced 121%. What is the price now?

11. A bushel of corn plants eight acres. field 15% of the corn did not germinate. failed to germinate?

In an eighty-acre How many bushels

12. A workman receives $3.50 a day. His wages are increased 10%. How much does that increase his income in a year of 300 working days?

13. If a grocer buys berries at 40¢ a gallon and sells them at an advance of 100% how much does he make on 34 gallons?

14. A pupil has a garden 25 ft. X42 ft. He plants 8% of his ground in lettuce, 9% in radishes, 163% in beans, 331% in tomatoes, and the remainder in potatoes. The lettuce and radishes yield $1 for each 7 square feet, the beans $1 for each 25 square feet, the potatoes $1 for each 30 square feet, and the tomatoes $1 for each 35 square feet. He has spent for fertilizer and labor 8% of the returns from his crops. How much does he clear for his own work?

A PER CENT MORE OR LESS THAN A NUMBER 71

37. A per cent more or less than a number. When we speak of more than a number we mean the result of adding of that number to the number. One-half more than 10 is

of 10+10, or 15.

If Mr. Smith raised 33% more apples than Mr. Brown, who raised 360 bu., then Mr. Smith raised 331% of 360 bu. more than 360 bu., or 480 bu.

One-fourth less than a certain number means the result of subtracting of the number from the number. Twentyfive per cent less than 80 means 80-25% of 80, which is 60.

Exercise 37

1. Find more than 60; less than 45.

2. Find 33% less than 384; 7% more than $256. 3. The population of Indianapolis in 1910 was 233,650. What was the population after it had increased 5%?

4. Fred and Robert each get a salary of $85 a month. Fred's salary is first raised 10% and then lowered 10%. Robert's salary is first lowered 10% and then raised 10%. Which now gets the better salary? Estimate the answer and then compute it.

5. A merchant found that his sales for a certain month amounted to $8750. The following month they increased 4%, the next they increased 7%, the next they decreased 3%, the next they increased 1%, the next they decreased 4%. What was the amount of the sales for the last month? What were the average monthly sales for the six months?

6. The cost of a certain article was 83% less than the selling price, which was $150. What was the cost?

7. A boy put $50 in the savings bank with the understanding that the bank would increase it by 2% every six months. How much did he have in the bank at the end of the first six months? At the end of 2 years?

8. John finds that in his sixteenth year his height increased 61%. At the beginning of the year his height was 5 feet. What was it at the end of the year?

9. The taxes in a certain city increased .3% over last year's taxes. If a man paid $245 last year, what were his taxes this year?

10. A stalk of corn 20 in. high increased in height 45% in two weeks. The height of the corn after the increase was what per cent of its height before the increase?

11. A quantity of salt is dried until it loses 10% in weight. Its weight after the drying is what per cent of its weight before?

12. A hog loses 19% of its weight in being killed and dressed. If a hog weighs 280 pounds on foot, how much does it weigh dressed?

13. If new corn loses 3% of its weight in drying, is it better to pay 75 cents a bushel for new corn or 80 cents for old corn? A bushel of corn weighs 56 lb.

14. A city lot worth $475 five years ago has increased in value 12% in the five years. How much is it worth now?

15. Make a formula for finding the weight, W, of an object which has increased in weight at the rate, r, from the weight,

w.

16. Make a formula for finding the value, V, of an article which has decreased in value the per cent, r, from the value, v.

17. Can you give the answers to the first two exercises in Exercise 34 in the time stated there?

18. Give orally 121% of each of the following: 80, 120, 1000, 6.4, 20, .56.

19. Give orally 33% of each of the following: 18, .018, 200, $5.70, 3 in.

38. To reduce any common fraction to per cent.

To change any common fraction to a decimal you have learned to divide the numerator by the denominator.

EXAMPLE 1. Reduce to a decimal.

SOLUTION. .375 Therefore = .375.

1. to tenths; to hundredths; to thousandths. 2. to tenths; to hundredths; to thousandths. 3.to per cent.

4.to per cent.

5. to thousandths.

6. 3 to tenths; to thousandths.

7. 23 to hundredths; to tenths; to thousandths.

8. 1 to per cent.

9. .3 to per cent.

10. .2 to thousandths; to hundredths; to per cent.

11. 0 to per cent; to thousandths.

12. .003 to per cent.

13., 12, 31, .001 to per cents.

14. Make a rule for changing a common fraction to a per cent.

15. Repeat the rule for changing a per cent to a decimal. 16. Make a rule for changing a decimal to a per cent.

17. Change to per cents: .75, .18, .018, .003, 400, 2000.

18. What per cent of anything is of it? ? ? ? ? 음? ? ?