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Note to Teachers. In performing oral solutions which involve several operations, it will be found convenient, although not absolutely necessary, to use the terms plus and minus. These terms, however, should not be adopted until they are perfectly understood; and the duty of explaining them is here confided to the Teacher. It will not suffice, merely to tell the learner, that “plus means more, and minus means less,” for the idion of our language does not allow him to use more and less, as he is called upon to use plus and minus. The expressions, “7 more 5 is 12,” and, " 10 less 4 is 6," although true, are not very likely to meet the understanding of a young scholar. Perhaps it will be found necessary to resort to illustrations like the following.

Place 8 books in a pile before you, and say,“Here is a pile of 8 books, and I shall make the number of books in the pile 3 more.'

." T'hen, placing 3 additional books upon the pile, say,_"8 books plus 3 books are 11 books." Again proceed to say, “I shall now make the number 2 less." Then, taking off 2 books, say," 11 books, minus 2 books are 9 books."

SECTION 6. MISCELLANEOUS EXAMPLES. 1. How many days in the three Summer months; there being 30 in June, 31 in July, and 31 in August ?

Solution 30 days plus 31 days are 61 days; 61 days plus 31 days are 92 days.

2. There were 42 gallons of wine in a cask; but, the cask not being tight, 7 gallons have leaked out. How many gallons still remain in the cask ?

Solution. 42 minus 7 is 35. Answer. 35 gallons.

3. A boy that had 97 cents, paid 62 cents for a book, 18 cents for a morocco wallet, and 6 cents for a pencil. How many cents had he remaining ?

Solution. 62 cents (for book), plus 18 cents (for wallet), is 80 cents; 80 cents plus 6 cents (for pencil), is 86 cents. 97 cents minus 86 cents is 11 cents.

4. A black-smith bought 9 tons of coal, at 4 dollars per ton, and gave 3 dollars for having it drawn to his shop. How much did the coal cost him ?

Solution.” If the price of 1 ton was 4 dollars, the price of 9 tons was 9 times 4 dollars, or 36 dollars; 36 dollars plus 3 dollars (for having it drawn) is 39 dollars.

5. A schoolmaster laid out 96 cents in writing-books, at 8 cents apiece, and then gave away 5 of them. How many books had he remaining ?

Solution. He bought as many books, as 8 is contained times in 96, which is 12. Then, 12 books minus 5 books, (that he gave away), are 7 books.

6. A trader gave 16 dollars for a keg of tobacco, and after selling it, found he had gained 6 dollars. For how much did he sell it ?

7. A rich farmer in Vermont had a flock of 100 sheep; they went upon a mountain, and the wolves destroyed is of them. How many sheep had he renaining? 8. If a man spend 4 dollars in a week, how many

dol. lars will he spend in 9 weeks?

9. How many dozen of eggs can you buy for 64 cents, when the price of them is 8 cents per dozen?

10. A trader gave 48 dollars for 7 barrels of flour, and sold it for 6 dollars a barrel. What did he lose ?

11. How many weeks are there in 35 days ?

12. Four men made up a purse of 40 dollars, for a charitable purpose. The first man put in 9 dollars, the second 12 dollars, and the third 7 dollars;-how much did the fourth man put in ?

13. A sum of money was divided equally among 8 sailors; and Jack, who was one of the number, received for his share, 15 dollars. . What was the sum divided ?

14. How many days are there in 13 weeks and 5 days?

15. A trader bought 3 reams of paper, at 5 dollars per ream, and 7 maps, at 5 dollars apiece. How much did he give for the whole ?

16. If 49 bushels of corn should be divided equally among 7 men, how much would one man receive ?

Solution. As many times as 7 is contained in 49, so many bushels would one man receive.

17. If 45 dollars be divided equally between 5 men, how many

dollars does each man receive? 18. A man bought a turkey weighing 10 pounds, for 8 cents a pound, and then sold it for 3 cents a pound more than he gave. For how much did he sell it?

19. Charles had 25 cents; his father gave him 4 melons, which he sold for 6 cents apiece; he then paid 12 cents for a book. How many cents had he left? 20. If a man earn 6 dollars a week, how

many weeks will it take him to earn 48 dollars ?

21. Geographers consider the United States in four classes. There are 6 Eastern states, 4 Middle states,

How many

8 Southern states, and 6 Western states. states are there in the Union ?

22. A merchant paid 43 dollars for some iron, and sold it for 35 dollars. How many dollars did he lose?

23. A man paid 78 dollars for a piece of land, and 16 dollars for having it fenced; and he then sold it for 100 dollars. Did he gain or lose;—and how much?

24. A cabinet-maker sold 6 tables, at 14 dollars apiece. How many dollars did he receive ?

25. If I buy 10 yards of cloth, at 7 dollars a yard, how many five-dollar bills must I pay for it?

26. How many boxes of strawberries can you buy for 36 cents, when they are sold at 9 cents a box?

27. Suppose a trader, who has 12 barrels of flour on hand, should lay out 35 dollars in buying more flour, at 5 dollars a barrel; how many barrels would he have ?

28. If I pay 19 dollars to one man, 13 to another, and 31 to another, how many dollars do I pay out ?

29. If a laborer can earn 7 dollars in a week, how many weeks will he be in earning 42 dollars ?

.30. How many hats, that are sold at 6 dollars apiece, can a man who has 50 dollars pay for;—and how many

31. If you should perform 19 examples in arithmetic, every day, how many would you perform in 6 days?

32. Samuel Moderate earns 7 dollars a month, and John Smart earns 15 dollars a month. How much more will John earn than Samuel, in 6 months ?

33. If 1 man do 1 day's work in 1 day, how many will it take to perform 7 days' work, in 1 day?

34. If 4 men will perform 4 days' work in 1 day, how many days' work will 4 men perform in 9 days ?

35. How many days will it take 4 men to dig a cellar, that 1 man would be 36 days in digging ?

36. How many days will it take 7 men to clear a piece of wood-land, that 28 men can clear in one day?

37. How many men will it take to perform as much work in 1 day, as 11 men can perform in 6 days?

38. How many days will it take 4 men to perform the same work, that 12 men can perform in 3 days?

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39 A trader has three bundles of bank notes;23 dollars in one bundle, 15 dollars in another, and 34 dollars in another; but in one of the bundles there is a note of 5 dollars, which is counterfeit. How many dollars of good money has he?

40. Stephen has lost 30 cents, and has found 10 cents; he now has 18 cents. How much had he at first?

41. A farmer went to the city with 8 barrels of cider, which he sold at 4 dollars a barrel. He then purchased 3 hogsheads of salt, at 3 dollars per hogshead, and paid an old debt of 12 dollars. How many dollars had he to

carry home?

42. If I pay 3 dollars apiece for 7 umbrellas, and 6 dollars apiece for 6 hats, for how many dollars must I sell the whole, in order to gain 7 dollars ?

43. A nian borrowed 75 dollars, and the next day paid all but 14 dollars of it. How much did he

pay

: ? 44. A. spent 5 dollars as often as B. spent 3 dollars. How much did A. spend, while B. spent 27 dollars ?

Solution. As many times as 3 dollars are contained in 27 dollars, so many times 5 dollars did A. spend. 3 dollars are contained in 27 dollars 9 times; therefore A. spent 9 times 5 dollars.

45. A man and a boy were gathering corn;—the man gathered 7 rows, in the same time that the boy gathered 4 rows. How many rows would the man gather, while the boy was gathering 32 rows ?

46. A man and a boy were digging potatoes; the man dug 11 bushels in the same time that the boy dug 6 bushels. How many busbels would the boy dig, while the man was digging 55 bushels ?

47. Suppose butter to be worth 12 cents a pound, and tea 42 cents a pound;-how many pounds of butter must be given for 2 pounds of tea?

48. A farmer sold 2 cows at 23 dollars apiece, and 9 sheep at 5 dollars apiece; he received in payment, 3 ploughs at 8 dollars apiece, and the rest in money. How much money did he receive ?

49. 4 boys found a purse containing 29 dollars. They paid 2 dollars for advertising it; and, as no owner appeared, they agreed to take 6 dollars apiece io themselves, and give the remainder to a poor woman. How much was there remaining for the woman? 50. What sum of money must be divided among

16 men, in order that one man shall receive 4 dollars ?

51. Two classes are studying arithmetic. The first class is 81 examples in advance of the second; the second performs 40 examples in a day, and the first, 31. In how many days will the second overtake the first ?

52. A lady paid 6 dollars for silk, 9 dollars for cambric, 7 dollars for linen, and then had 13 dollars remaining. How many dollars had she at first ?

53. How many barrels of flour, at 6 dollars per barrel, can the baker who has 45 dollars, purchase; and how many dollars will he have remaining

54. A trader, that has 48 dollars, wishes to buy all the boots he can pay for, at 5 dollars a pair, and then lay out the remainder of his money in shoes, at 1 dollar a pair. How many pairs of boots, and of shoes, must he buy?

55. What sum of money must be divided among 18 men, in order that one man shall receive a dollars ?

56. Three inen made up a purse of 40 dollars. The first man put in 6 dollars, and the second 3 times as much as the first. How much did the third put in ?

57. Eliza gave a poor woman 4 cents, Augusta gave her 3 times as much as Eliza, and Lucy 3 times as much as Augusta. How much did the woman receive ?

58. If a man dig 30 bushels of potatoes in a day, and a boy 13 bushels, how many bushels will they both dig in a day? How many will they both dig in 3 days ?

59. A farmer purchased 15 sheep;-he sold 8 of them at 4 dollars apiece, and the remainder at 3 dollars apiece; and then found that he had gained 7 dollars. How much did he give for the sheep?

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