1. 25 is 2. 40 is

ORAL EXERCISE

of what number? 50% of what number? of what number? 33% of what number?

3. Of what number is 50 one half? one third? two thirds? 10%? 25%? 50%? 100%? 125%? 200%?

The following numbers are the given per cents of what other numbers?

Think of the rate as a common fraction. If 7 is 10% of a number, it is of the number. Hence the number is 70. If 20 is 66% of a number, it is of the number, and is 10. Hence the number is 30.

25. If $6 is 3% of a number, what is 1% of the num ber?

What is the number?

26. If $9.12 is the interest on a certain sum for 1 yr. at 3%, what is the sum ?

27. If $4.50 is 5% of a certain sum, what is the sum? If it is 21%, what is the sum?

28. If a piece of cloth shrinks 2 yd., the shrinkage being 5%, what was the original length?

29. A kettle of water loses 25% of its contents in boiling, and then contains 2 qt. less than it did at first. How much did it contain at first?

What is the number which, if decreased by 25% of itself, becomes the following?

If 150 is of a number, what is ? ?

Also, if decreased by 331% of itself, becomes the

Also, if decreased by 20% of itself, becomes the fol

Also, if increased by 163% of itself, becomes the fol

Also, if increased by 12% of itself, becomes the fol

Also, if increased by 66% of itself, becomes the fol

72. Illustrative problem. $13.80 is 6% of what amount?

Or we may think that since $13.80 is 6% of some number, 1% is of $13.80, or $2.30, and 100% is 100 times $2.30, or $230.

73. The percentage (part) divided by the rate equals the base (whole).

1. $0.85 is 2%

2. $1.43 is 4%

3. $1.75 is 6%

WRITTEN EXERCISE

of what sum? 5% of what sum ? of what sum? 5% of what sum? of what sum? 10% of what sum? 4. $22.68 is 7% of what sum? 20% of what sum? 5. On what sum is $7 the interest for 1 yr. at 4%? 6. If $13.50 is the interest on a certain sum for 2 yr. at what is the interest for 1 yr.? What is the principal? 7. A class measuring a certain distance on a wall made an error of 0.28 ft., which was 0.07% of the total distance. What was the distance?

8. A certain city has increased 4230 in population in ten years, which is 15% of the population ten years ago. What was the population then?

9. A merchant gained $4375 last year, which was 17% of his capital. This year he has lost $2750. What per cent of his capital has he lost this year?

10. A man lost $247.50 in business last year, or 15% of his capital at the beginning of the year. How much was his capital at the beginning of the year?

74. Illustrative problems. 1. A man gained 163% on his capital of $18,000. How much did he then have?

1. His capital +163% of his capital = 1163% of his capital. 2. 1163% of $18,000 = $21,000, the amount after the increase. 2. A village having a population of 1900 ten years ago has since lost 13%. What is its present population?

1. Population - 13% of the population = 87% of the population. 2. 87% of 1900 = 1653, the present population.

In the first of these examples we might, of course, find 16%, or, and add, and in the second we might find 13% and subtract.

WRITTEN EXERCISE

1. Increase $2750 by 15% of itself; by 12% of itself. 2. Decrease $3500 by 12% of itself; by 8% of itself. 3. What is the amount of $350 and a year's interest at 6%? at 5%? at 31%? at 41%?

4. A school had 204 pupils last year and has 163% more this year. How many has it now?

5. What is the amount of $825 and two years' interest, the annual rate being 4%? 5%? 6%? 41%?

6. A merchant starts the year with $15,500, and loses 15% in his business. What does he then have?

7. Decrease $750 by 50% of itself; that result by 50% of itself; and that result by 50% of itself. The result is what per cent of the $750?

8. A man started in business with $8500. The first year he gained 15%, and the next year he lost 15% of what he then had. How much had he then?

9. Write out a rule for finding the base increased or decreased by a certain per cent of itself, given the base and rate.

THE CATTLE INDUSTRY

WRITTEN EXERCISE

1. A ranchman owned 960 head of cattle in the fall, but the losses by storms and disease brought the number down to 928 in the spring. What was his per cent of loss?

2. In a certain year cattle on the range in the Southwest were worth $8.40 a head; a few years later they were worth $13.44 a head. What was the rate of increase in value?

3. In another year cattle in the same locality were selling for $22.50 a head, an increase of 80% in their value of five years before. What was their value then?

4. On the upland pastures in the Southwest it averages about 20 acres per head to pasture a steer through the winter. How many square miles for 1000 head?

5. A western farmer bought in November of one year 30 steers at $48.14 each, and fed them six months, or exactly 183 days. The corn cost him $9 a day for all the steers, and the hay 10 a day for each. He sold them for $121.06 each. How much did he lose on the lot, not considering the interest on his investment?