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3. In this graph, Figure 82, the solid black columns represent the average yearly wage of 584 persons who left school at 14 years of age. The hatched columns represent the average wage received by 215 persons who remained in

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technical schools till 18 years of age. Find the average amount received by a person in each group from the age of 14 to the age of 25 inclusive. The figures in this graph were taken from a report of a Commission on Industrial and Technical Education in Massachusetts.

4. From a study of a group of distinguished Americans it was found that of 5,000,000 American men with no schooling, 31 had attained distinction; of 33,000,000 with elementary education only, 808 had attained distinction; of 2,000,000 with high school education, 1245 had attained distinction; of 1,000,000 with college education, 5768 had attained dis

tinction. We may say then that a man with no schooling has 31 chances out of 5,000,000 of attaining distinction, or a chance of .0000062. Find the chance of attaining distinction of a man in each of the other classes. Express the answers as decimals. The chance of the college graduate to attain distinction is how many times as great as the chance of each of the other classes?

5. This table gives a comparison of the wages of persons who left New York City schools at 14 years of age with those who left at 18 years of

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CHAPTER IX

APPLICATIONS OF PERCENTAGE

63. Use of percentage in business. The principles of percentage which the pupil has already learned are applied to many difficult problems of business, some of which the pupil is now ready to understand.

All of us will have business with banks and should understand how their problems are solved. We shall have to pay taxes and shall want to know how they are computed. We shall want to send money to distant places, shall want our property insured, and shall meet many other problems to which the principles of percentage must be applied.

The pupil will find no new principles of percentage involved in these problems. Their difficulty consists in the business conditions involved, with which the pupil has had little experience. To understand clearly the problems of this chapter the pupil should be given experiences as nearly like those in real business transactions as possible. He should write checks, give and receive notes, buy drafts, compute taxes and go through the forms of paying them. His class can organize a stock company to buy a farm or manage a bank, and each member of the class can have a part in the various business transactions involved.

64. The percentage formulas. The problems which follow require the pupil to know the percentage formulas. Find 334% of 360. Name the base, rate, and percentage. Give the formula for finding the percentage when base and rate are known; the rate when percentage and base are known; the base when percentage and rate are known.

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2. Express as per cents: .12, .08, 5.67, 1.00, 10.00, 9, .06, .009, .3468.

3. State a rule for changing decimals to per cents.

4. Express as decimals: 6%, 75%, 3.6%, .08%, 346%, 100%, 842.9%, %, 3%.

5. State a rule for changing per cents to decimals.

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6. Express as per cents:,, t, t, b, b, b, c, 2, . 7. Express as common fractions in their lowest terms: 5%, 25%, 60%, 75%, 12%, 16%, 331%, 140%, 65%, 48%, 66%, 1371%.

8. The enrollment in a school was 550 pupils in a certain year. The following year the enrollment decreased 18%. What was the enrollment the second year?

9. A teacher's salary is increased from $75 a month to $80 a month. What is the per cent of increase?

10. Find a number that is 10% more than 960.

11. Find a number that is 6% less than 75. 12. 165 is 10% more than what number? 13. 380 is 5% less than what number?

14. The corn crop of the United States in a certain year was 2,566,927,000 bu., and in the following year 3,159,494,000 bu. What was the per cent of increase?

15. At the same time the wheat crop increased from 636,318,000 bu. to 650,828,000 bu. What was the per cent of increase in the wheat crop?

16. On a certain day the price of wheat in the Chicago market ranged from $2.14 a bushel to $2.46 a bushel. The second price is what per cent of the first? The first price is what per cent of the second? What profit would have been made by a man who bought 10,000 bu. at the lower price and sold it at the higher? What per cent of the cost?

17. A dairyman sold 2500 lb. of milk which averaged 2.8% butter fat. That was how many pounds of butter fat? What was the butter fat worth at 24¢ a pound?

18. In 1917 the price of silver advanced from 78¢ to $1.08 an ounce. What was the per cent of increase in price?

19. A farmer invests $24,000 in a farm. The first year it pays him 44% profits. Find the amount of profits.

65. Useful equivalents. Much use is made in percentage of the following equivalents. The pupil should practice until these equivalents can be given in 60 seconds or less.

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1. Find these per cents of the numbers in the first column:

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