18. A company of 9 men bought 6 tracts of land, each containing 24 acres. How many acres belonged to each man?

19. A divisor is 25 and the quotient is 7. If the divisor were 35, what would the quotient be?

20. If a man can walk 216 miles in 8 days, how far can he walk in 5 days?

21. How many times can a vessel holding 12 gallons be filled from 10 barrels, each holding 18 gallons?

22. 40 cabbages were planted in each of 9 rows. Had they been planted in 8 rows, how many would have been in each row?

23. 15 men completed a piece of work in 30 days. Had it been necessary to complete it in 10 days, how many men should have been employed?

24. Paid 220 dollars for cows, at 20 dollars apiece. If I sold them at 25 dollars apiece, how much did I receive for them?

25. A dividend is 480, and a divisor 12. If the quotient were divided by 2, what would the divisor be?

26. An express train made a trip in 8 hours, at the rate of 45 miles an hour. What distance per hour should it have run to make the trip in 10 hours?

27. A trader sold 24 hogs at 9 dollars apiece, and spent the money for sheep, at 6 dollars each. How many sheep did he buy?

28. A farmer sold his hay for 360 dollars, at 12 dollars a ton. If he had sold it at 15 dollars a ton, how much would he have received?

29. A bolt of cloth was made into 5 suits, each containing 7 yards, and the lot was sold for 140 dollars. At what price per yard was it sold?

30. 480 pounds of beef were consumed by 24 men in Io days. What was the daily allowance of each man?

I.

LESSON XVI.

Which will cost the more, and how much more18 tons of straw, at 4 dollars a ton, or 15 cords of wood, at 5 dollars a cord?

2. A and B are traveling on the same road, and in the same direction, A being 30 miles ahead, but B travels 8 miles an hour, and A only 5 miles. In how many hours will B overtake him?

3. In the above question, if they had traveled in opposite directions, how far apart would they have been at the end of 10 hours?

4. A clerk's salary is 15 dollars a week, and his 'expenses 7 dollars a week? How much will he save in 12 weeks?

5. If an apple is worth 12 plums, and I orange is worth 5 apples, how many plums should be given for 5 oranges?

6. Two men bought a horse for 80 dollars. After paying 20 dollars for his board, and receiving 40 dollars for his use, they sold him for 100 dollars. How much money did each gain?

7.

Robert had 36 marbles, and Henry had 45. Each gave one-third of his marbles to the other. How many

had each then?

8. If 15 barrels of flour are worth 75 dollars, and 18 barrels are given for 9 tons of hay, what is the hay worth per ton?

9. How many dozen eggs, at 16 cents a dozen, should be exchanged for 4 pecks of beans, each containing 8 quarts, at 5 cents a quart?

IO. 9 rows of sweet potatoes were planted, with 20 hills to each row. Had the same number of hills been planted in 12 rows, how many hills would have been in each row?

II.

Sold 12 barrels of pears for 42 dollars, thereby losing 6 dollars. For how much per barrel should they have been sold to gain 12 dollars?

12. A hogshead of molasses contained 63 gallons. A part was drawn off, and sold for 50 cents a gallon. If 350 cents were received for it, how many gallons remained unsold?

13. Paid 96 dollars for flour at 4 dollars a barrel. Sold 8 barrels at 6 dollars a barrel, and the remainder at 5 dollars a barrel. Find my gain.

14. The product of three numbers is 180. Two of them are 4 and 5. What is the third?

15. The sum of two numbers is 28. If 19 is one of them, what is their product?

16. The difference of two numbers is 15. less number, what is 10 times their sum?

If 5 is the

17. The quotient of two numbers is 9. If 45 is one of them, what is their difference?

18. A lady bought an equal number of oranges and apples for 108 cents. If she paid 3 cents for an apple, and 6 cents for an orange, how many of each did she receive?

19. A cistern will hold 360 barrels of water. If it receives 36 barrels an hour by one pipe, and discharges 21 barrels an hour by another, in what time will it be filled?

20. If a certain number be divided by 8, the quotient will be 13, with a remainder of 7. What is the number? If a certain number be multiplied by 6, the product will be 16 less than 166. What is the number?

21.

22. Sold 12 cows for 150 dollars, thereby losing 30 dollars. For how much per head should I have sold them to gain 60 dollars?

23. Sold 8 acres of land for 400 dollars, thereby gaining 80 dollars. Had I sold the land for 300 dollars, how much would I have lost?

24. Two men are 144 miles apart, and travel toward each other, one going 5 miles an hour, the other 4 In how many hours will they meet?

miles.

25. 25 men have provisions for 12 days. How many men could consume the provisions in 15 days?

26. A man walked 140 miles in 4 days. how far could he walk in 12 days?

At that rate

27. A merchant sold a certain number of barrels of flour for 150 dollars, thereby gaining 25 dollars. If he received 6 dollars a barrel, what was the cost per barrel?

28. If 25 sheep cost 125 dollars, for how much per head must they be sold to gain 75 dollars?

29. If 20 hogs cost 120 dollars, for how much must they be sold to gain 2 dollars per head?

30. Paid 180 dollars for hay, at 12 dollars a ton, and sold it at 10 dollars a ton. Find my loss.

31. Sold 16 cords of wood for 100 dollars, thereby gaining 20 dollars. If I had sold it for 4 dollars a cord, how much would I have lost?

32. Paid 240 dollars for cows, at 15 dollars each, but 4 having died, at what price per head must I sell the remainder to sustain no loss?

33. A can husk 9 bushels of corn while B husks 12 bushels. When A has husked 108 bushels, how many has B husked?

34.

A man can earn 25 cents in an hour, and his son How much will they together have earned when the boy has earned 150 cents?

15 cents.

35. Two men built a wall for 200 dollars. One worked 30 days, and received 3 dollars a day. The other received 2 dollars a day. How many days did he work?

36. 8 men were employed to do a piece of work in 15 days, but 2 of them failed to come. the others employed?

How long were

37. Sold 6 horses at 50 dollars each, and then borrowed enough money to enable me to buy 5 lots at 80 dollars apiece. How much did I borrow?

38. Having paid 500 dollars for 20 acres of prairie land, I sold part of it for 360 dollars, thereby gaining 60 dollars. How many acres did I sell?

39. A has 18 sheep. B has twice as many, less 4. C has as many as A and B together. How many sheep have all?

40. A girl is 15 years old, which is 12 years less than the age of her brother. Her father is 32 years older than her brother, and her mother is 7 years younger than the father. How old are the brother, father, and mother?

PRINCIPLES.

To Teachers.

Much difficulty has heretofore arisen in regard to the proper understanding and interpretation of the use of the signs,, X, and; and, until recently, standard authorities have differed in respect to their meaning when employed in the statement of abstract problems. The ambiguity attendant upon the solution of certain problems involving the use of the signs X and ÷, in connection with the other signs, has led some authors to omit all such problems from their works. It is true, however, that in the primary grades it is almost impossible to impress their real meaning upon the minds of the pupils, and it is therefore not considered wise to undertake it. But as the student progresses, it is evident that the time must come when a thorough knowledge of the meaning of all the signs is imperatively necessary; and it is the au