20. Henry is as old as his father, and the sum of their ages is 70 years; how old is each?

21. If to my age you add its , its, and 16 years, the sum will be 3 times my age; how old am I?

22. Saul is 16 years older than John, and of Saul's age equals of John's; how old is each?

23. Mr. Rambo and Mr. Kerr own two farms: Mr. Rambo owns as much land as Mr. Kerr, and Mr. Kerr owns 25 acres more than Mr. Rambo; how many acres does each own?

24. Mr. S and Mr. T own a number of sheep: Mr. S's number is 1 times Mr. T's number, and Mr. T's number is 40 less than Mr. S's; how many has each?

1. In a school of 50 pupils there are 3 boys to every 2 girls; how many boys must leave that there may be an equal number of boys and girls?

2. In the same school how many girls should be admitted that the number of boys and girls may be equal?

3. In a school of 45 pupils the number of boys is to the number of girls as 3 to 2; how many boys must leave that the number of boys may be to the number of girls as 2 to 3? 4. In the same school how many girls must be admitted to make the proportion of girls to boys as 3 to 2?

5. In a school of 40 pupils, if the proportion of boys to girls is as 5 to 3, how many girls must be admitted to make the proportion of boys to girls as 5 to 6?

6. In an alloy of 40 pounds there are 30 pounds of copper and 10 pounds of tin; how much tin must be added that there may be 2 pounds of tin to every 3 of copper?

7. In an alloy of copper and silver there are 4 pounds of copper and 6 of silver; how much copper must be added that there may be 2 pounds of copper to 1 of silver?

8. A pole 124 feet in length was broken so that of the

longer piece equaled

from the longer that

of the shorter; how much must be cut

of its length may be of the shorter?

9. If an alloy contain 30 oz. of gold and 2 oz. of silver, how much silver must be added that 24 oz. of the alloy may contain 20 oz. of gold?

SUG. Since 24 oz. of the alloy contain 4 oz. of silver, 30 oz. will contain 1 times 4 oz. of silver, or 5 oz. of silver; there must therefore be added 5 oz. minus 2 oz., or 3 oz., of silver.

10. If an alloy contain 18 pounds of silver and 1 pound of copper, how much copper must be added that 10 pounds of the alloy may contain 9 parts silver and 1 part copper?

11. If alcohol is 90% strong, how much water may be added to a gallon so that the alcohol may remain 75% strong?

12. For every cow a farmer keeps he allows 2 acres of pasturage and 1 acre of corn; how many cows can he keep on 12 acres?

SUG.-Each cow requires 3 acres.

13. If a farmer can pasture 2 cows on 4 acres, and 2 cows will eat the produce of 1 acre of roots, how many cows can he keep on 15 acres?

14. If a man allow 2 acres of roots for every 5 cows he keeps and 4 acres of pasturage for every 2 cows, how many cows can he keep on 36 acres, and how much land must he have in pasture, and how much in roots?

15. If a farmer allow one acre of corn for every 6 sheep and an acre of grass for every 4 sheep, how many sheep can he keep on 20 acres?

16. Mr. A has 36 sheep: he allows 1 acre of corn for every 6 sheep and 1 acre of grass for every 4 sheep; how many acres does he use?

17. A farmer allows 6 acres of pasturage for every 3 cows and 1 acre of roots for every 3 cows; he also allows 1 acre

of corn for every 6 sheep and 2 acres of grass for every 8 sheep; how many acres does it require to keep 12 cows and 24 sheep?

18. How far may a person ride in the cars at the rate of 20 miles an hour and return by carriage at the rate of 8 miles an hour, if he is gone hours?

SOLUTION.-If he goes 20 miles an hour, he travels 1 mile in 2 of an hour; if he returns at the rate of 8 miles an hour, he travels 1 mile in § of an hour; hence to go one mile and return requires +}, or, of an hour. He therefore can go and return as many miles as is contained times in 7, or 40 miles.

19. How far may a person ride in a coach going 6 miles an hour and be gone 9 hours, returning on foot at the rate of 3 miles an hour?

20. I drive to the city at the rate of 6 miles an hour and return by rail at the rate of 30 miles an hour; how far is it if I traveled the distance in 6 hours?

21. If I travel to the city by steamer at the rate of 15 miles an hour and return by rail at the rate of 30 miles an hour, how far is it if I spend 24 hours in the city and return in 8 hours?

22. A boat that sails at the rate of 10 miles an hour goes down a stream whose current is 2 miles an hour; it returns in 5 hours; how far did it travel?

23. A steamer goes up a river at the rate of 12 miles an hour and returns at the rate of 16 miles an hour; it is gone 7 hours; how far did it travel, and what is the rate of the current?

24. A dinner was engaged for 20 persons, but 4 were absent, whereby the expense of each of the others was increased 50 cents; what was the total cost of the dinner?

SOLUTION. Since the expense of each of the remaining 16 was increased $, the total increased expense was 16 times $2, or $8, which

should have been paid by the 4 absentees: the expense to each was therefore of $8, or $2, and to the 20, 20 times $2, or $40.

25. Eight men hire a coach, but by taking in 4 others the expense of each was reduced 25 cents; how much did they pay for the coach?

26. Four men buy a store, but by taking in an equal partner the amount to be paid by each was reduced $2000; what was the cost of the store?

27. Six men buy a boat, but afterward take in 2 partners, and thereby reduce the amount paid by each $5000; what was the amount paid for the boat?

28. An excursion party of 50 hire a boat, but 10 having failed to pay, the expense of each of the others was increased 50 cents; what was the charge for the boat?

29. Three boys, A, B, and C, camped together: A furnished 4 loaves of bread, and B 5 loaves, while C paid 30 cents; how should this money be divided?

30. Silas, Wilson, and Milton lunched together: Silas furnished 3 eggs, and Milton 6, while Wilson paid 10 cents; to whom should the money be paid?

31. Four men camped together: A furnished 4 loaves of bread, B 5 loaves, and C 7 loaves, while D contributed 40 cents; how should the money be divided?

1. What is the time of day if of the time past midnight equals the time to noon?

SOLUTION. Since of the time past midnight equals the time to noon,, or the time past midnight, plus of the time past midnight, or the time to noon, equals of the time past midnight, or the time from midnight to noon, 12 hours. If of the time past midnight equals 12 hours, of the time equals of 12 hours, or 3 hours, and §, or the time past midnight, equals 3 times 3 hours, or 9 hours; hence it is 9 o'clock A. M.

NOTE.—It will be helpful to the pupil first to draw a diagram in solving these questions, as follows, in which P represents the present time:

2. What is the time of day if the time past midnight equals the time to noon?

3. What is the time of day if the time past noon equals of the time to midnight?

4. What is the time of day if the time past midnight equals the time to noon?

5. What is the time of day if the time past midnight equals the time to noon?

6. What is the time of day if the time past midnight equals the time to midnight again?

7. What is the time of day if of the time past noon equals the time to noon again?

8. What is the time of day if the time past noon equals the time to midnight?

9. What is the time of day if the time past midnight is the time past noon?

10. What is the time of day if of the time to midnight is the time past noon?

11. What is the time of day if the time past midnight equals the time past noon?

12. How many more spaces does the minute-hand of a clock pass over in an hour, than does the hour-hand?

13. How many spaces does the minute-hand gain on the hour-hand in 1 hour? In 2 hours? In 4 hours?

14. How long does it take the minute-hand to gain one space on the hour-hand? 3 spaces? 6 spaces?

15. At what time after one o'clock are the hour-hand and the minute-hand together?

REMARK.-The minute-hand gains one space.