5. If of an acre of land is worth $37.50, how much are 35 acres worth at the same rate?

6. Three men, A, B, and C, engage in partnership. A has $2000 in the business 5 months, B $3000 4 months, and C$4000 2 months. The profits of the business amount to $3600. What is each man's share?

7. The estimated increase of the real and personal property of the United States from 1880 to 1890 was nearly 50%. At the same rate of increase the value of the total property of the country at the end of the century would be about $100,000,000,000. What was the total amount of the property in 1890 ?

8. What was it in 1880 ?

9. The population of the country at the end of the century was about 76,000,000. How much property was there per capita?

10. In the first years of Washington's administration it cost about $7,000,000 a year to carry on the government. The population was about 4,000,000. What was the ratio of expense to the population?

11. The annual expense of the government is now about $685,000,000. If we reckon the population at 76,000,000, what is the present ratio of expense?

1. Divide .000024 by .032.

2. Multiply $568 by .151.

3. Change 1.45 sq. yd. to the fraction of a square rod. 4. Change of a pint to the decimal of a gallon.

5. What part of a mile is of a rod?

6. What part of a ton is 621 lb.?

7. At $4 a barrel, how many barrels of flour can be bought for $80% ?

8. At a yard, what will be the cost of 158 yards of. cloth?

10. If 4 is added to both terms of the fraction, how much will the fraction be increased or diminished?

11. If 5 is subtracted from both terms of the fraction 11, how much will the fraction be increased or diminished? 12. What will be the cost of 20 shares of bank stock, whose par value is $100 each, at 80?

13. What will be the cost of 10 shares of railroad stock, whose par value is $100 each, at 1123, including brokerage at 1% ?

14. A man sold $10,000 of 4% railroad stock at 734, paying brokerage of %. How much did he receive?

15. If I receive an annual dividend of $400 on 5% bank stock, how many shares of $50 each do I own?

16. If I have sufficient 4% government bonds of $500 each to yield quarterly interest to the amount of $260, how many bonds have I?

17. How many 3% bonds of $100 each will it take to yield a semi-annual income of $450?

Proportion

In some cases in the comparison of quantities, the corresponding terms are not directly proportional, but are inversely proportional.

1. If 2 men can do a piece of work in 7 days, how long would it take 4 men to do the same work?

In this case the greater the number of men the less the number of days. The days are not directly proportional to the men, but inversely proportional. The proportion is not 2:4 = 7: x but 4 : 2 = 7: x.

2. If 8 men can do a piece of work in 10 days, how long will it take 3 men to do an equal piece of work?

3. If a certain number of men can build 20 rods of fence in 3 days, how many rods can they build in 7 days? Are the rods and the days directly proportional or inversely proportional?

4. How many men will it take to do a piece of work in 12 days that 4 men can do in 9 days?

5. If 13 horses eat 42 bu. 3 pk. 3 qt. of oats in 18 days, how many oats will they eat in the month of May?

6. If a quantity of oats will last 8 horses 5 days, how long would the same quantity last 12 horses?

7. If one rectangle is 8 ft. long and 5 ft. wide, and another containing the same number of square feet is 4 feet wide, how long is it?

8. How many yards of cloth of a yard wide will it take to line 12 yards of cloth of a yard wide?

9. If 12 acres are sufficient pasture for 4 cows, how many acres will be sufficient for 25 cows?

10. The area of one end of a square prism is 36 square feet, and its length is 12 feet. The length of a second prism which contains the same volume is 10 feet. What is the area of one end of the second?

The base of a regular pyramid is a regular polygon, and the vertex is directly over the center of the base. Pyramids are triangular, square, pentagonal, hexagonal, etc., according to the forms of their bases. The volume of a pyramid is of the volume of a prism having an equal base and altitude, or of the product of the area of the base and altitude.

1. What is the volume of a prism whose base has an area of 24 sq. ft. and whose altitude is 6 ft. ?

2. What is the volume of a pyramid whose base has an area of 24 sq. ft. and whose altitude is 6 feet?

3. What is the volume of a pyramid whose base is 9 feet square and whose altitude is 12 ft. 4 in. ?

4. Find the difference between the volume of this pyramid and that of a prism having the same dimensions.

5. In a triangular pyramid one side of the triangle forming the base is 4 ft. 6 in. The perpendicular distance from this side to the opposite vertex is 3 ft. 4 in. Find the area of the base.

6. The altitude of the pyramid is 5 ft. 3 in. Find the volume.

7. What is the volume of a square pyramid one side of whose base is 18 in. and whose altitude is 24 in.?

Problems for Arithmetic or Algebra

See pp. 94, 152.

1. What interest will $1 gain in 2 years at 5%?

2. How many dollars will gain 50 cents in 2 years at 5%?

3. What is the amount of $1 for 1 yr. 6 mo. at 6%? 4. How many dollars will it take to amount to $3.27 in the same time and at the same rate?

5. How much will $5 gain in 4 yr. at 1%?

6. At what per cent would $5 gain 80 cents in the same time?

7. What interest will $100 gain in 1 yr. at 4%?

8. In how many years will $100 gain $20 at 4%? 9. What principal will gain $12 in 6 months at 6%? 10. What principal will amount to $275 in 1 yr. 3 mo. at 8% ?

11. At what rate will $75 gain $9.45 in 4 yr. 2 mo. 12 da.?

12. In what time will $140 gain $18.20 at 4%?

13. What sum at 6% will amount to $718.21 in 2 yr.? 14. What sum invested at 6% will produce a semiannual income of $3150?

15. At what rate will $3750 produce $225 of interest in 1 yr. 6 mo.?

16. In what time will $1500 yield $116.92 of interest at 3%?

17. If I pay $31.75 for the use of $1500 for 4 mo. 7 da., what is the rate?

18. Find how long it will take for a sum of money to double itself at simple interest at 31%.