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?

OYSTER INDUSTRY

WRITTEN EXERCISE

Small "seed oysters" are taken from natural beds off the coast. They are "planted" in shallow water in "beds" rented from the state, and there are fattened. The large ones are called "box" oysters; the average or small ones, "cullings."

1. A man gathered 90 bu. of box oysters and 150 bu. of cullings. Each was what per cent of the other? of all?

$6.75 a thousand, which was 192% as much as he received per thousand for cullings. How much did he receive for all of his cullings?

4. He paid $66 rent for one oyster bed and 12% less for another. What did he pay for both?

5. The oyster man paid 15 a bushel for shifting his oysters to another bed, and 66% as much for freight. What was the cost for both items on 250 bu.? He also paid a man $2.50 a day for 12 days for dredging (gathering) and culling (sorting). What was the total of these three items of expense?

SIMPLE INTEREST REVIEWED

ORAL EXERCISE

Find the interest on the following sums for the times and at the rates specified:

1. $2 for 1 yr. at 5%; at 6%.

2. $25 for 1 yr. at 4%; at 2%.

3. $300, at 5%, for 1 yr.; for 2 yr.
4. $400, at 5%, for 1 yr.; for 3 yr.

5. $500, at 6%, for 1 yr.;

6. $700, at 6%, for 1 yr.;
7. $400, at 6%, for 2
8. $250, at 4%, for 1 yr.;

yr.;

9. $1000, at 5%, for 3 yr.;

10. $2500, at 4%, for 1 yr.;

yr.

for 6 mo.

for 11 yr.

for 2

yr. 6 mo.

for 1 yr. 6 mo.

for 3 yr. 6 mo.

for 2 yr.; for 21 yr.

11. $3000, at 6%, for 1 yr. 6 mo.; for 1 yr. 4 mo. 12. $2000, at 5%, for 1 6 mo.; for 2 yr. 6 mo. 13. $1500, at 3%, for 1 yr.; for 2 yr.; for 1 yr. 4 mo. for 3 yr.; for 6 mo.; for

14. $5000, at 6%, for 1 yr.; 3 mo.; for 1 mo.; for 15 da.

Find the amount of principal and interest together, given the following principals, rates, and times:

18. $500, at 4%, for 1 yr.; for 5 yr. 19. $1000, at 41%, for 1 yr.; for 2 yr. 20. $2000, at 5%, for 1 yr.; for 2 yr.

75. Illustrative problem. Find the interest on $500, at

6%, for 2 yr. 3 mo. 6 da.

1. The interest for one yr. is 6% of $500, or $30.

$68.00

3. Therefore the total interest is

76. How to find interest. Therefore, to find interest, Find the interest for one year, and multiply by the number of years or the part of a year.

WRITTEN EXERCISE

1. Find the interest on $275 for 3 yr. 6 mo. at 5%. 2. Find the interest on $1250 for 7 yr. 11 mo. at 6%. 3. Find the interest on $630 for 2 yr. 4 mo. 5 da. at 6%. 4. Find the interest on $345 for 2 yr. 3 mo. 3 da. at 5%. 5. Find the interest on $290 for 1 yr. 6 mo. 5 da. at 5%. 6. Find the interest on $350 for 1 yr. 9 mo. 15 da. at 4%. 7. Find the interest on $650 for 2 yr. 8 mo. 10 da. at 6%. 8. Find the interest on $1575 for 3 yr. 1 mo. 6 da. at 51%; at 41%; at 6%.

9. A man borrowed $250 on January 15, at 6%. He paid the principal and interest on October 15. How much did he pay?

10. A man borrowed $350 on January 27, at 6%. He paid the principal and interest on February 27 of the following year. How much did he pay?

11. A man bought 12 head of cattle on February 1, at $45 a head, giving his promissory note at 6%. He paid it on the 16th of the following April. What was the amount of principal and interest?