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IV. Divide 56 x 35 = 1960 by 15 x 8 = 120.
Operation No. 1.

Operation No. 2.
120)1960 (164

7 7

49

$6 x 85 120

1

16

X5 x 8 3 3 760

3 720

Observe that in the above the factor 40 1

5 is stricken out of 15 and 35, and the 120 3

factor 8 is stricken out of the divisor and out of the 56 of the dividend.

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MISCELLANEOUS PROBLEMS.

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NOTE.-Employ “Short Methods” in the solution of the followiug problems.

How many cords of wood-
1. In a pile 32 feet by 8 feet by 4 feet? *
2. In a pile 40 feet by 16 feet by 6 feet?
3. In a pile 32 feet by 30 feet by 10 feet?

(aa) Find the sum of the three results.

How many acres of land

4. In a piece 180 rods by 28 rods? +
5. In a piece 64 rods by 96 rods?
6. In a piece 136 rods by 32 rods?
(bb) Find the sum of the three results.

7. Multiply 64 by 96 and divide the product hy 16 24 x 2.

8. Multiply 250 by 72 and divide the product by 161 x 3 x 24.

(cc) Find the sum of the two results.

* Think of a cord as 8 feet by 4 feet by 4 feet. + Think of an acre as 40 rods hy 4 rods.

Find the cost

9. Of 346 acres of land at $50 per acre. .10. Of 346 acres of land at $51 per acre. 11. Of 346 acres of land at $52 per acre. 12. Of 346 acres of land at $49 per acre. 13. Of 254 acres of land at $51 per acre.

(dd) Find the sum of the five results.

14. Of 243 ft. iron pipe at 333$ a foot. 15. Of 243 ft. iron pipe at 343¢ a foot. 16. Of 243 ft. iron pipe at 353¢ a foot. 17. Of 243 ft. iron pipe at 323¢ a foot. 18. Of 156 ft. iron pipe at 35}¢ a foot.

(ee) Find the sum of the five results.

19. Of 260 lb. butter at 25° a pound.
20. Of 260 lb. butter at 26¢ a pound.
21. Of 260 lb. butter at 274 a pound.
22. Of 260 lb. butter at 24¢ a pound.
23. Of 184 lb. butter at 274 a pound.

(ff) Find the sum of the five results.

24. Of 350 lb. coffee at 124¢ a pound. 25. Of 350 lb. coffee at 131¢ a pound. 26. Of 350 lb. coffee at 1414 a pound. 27. Of 350 lb. coffee at 1134 a pound. 28. Of 330 lb. coffee at 163 a pound. 29. Of 330 lb. coffee at 1734 a pound. 30. Of 330 lb. coffee at 15%¢ a pound. 31. Of 240 lb. coffee at 254 a pound. 32. Of 240 lb, coffee at 264 a pound. 33. Of 240 lb. coffee at 27¢ a pound.

(gg) Find the sum of the ten results.

Find the cost

34. Of 24 tons coal at $24 per ton.
35. Of 34 tons coal at $3} per ton.
36. Of 44 tons coal at $44 per ton.

(hh) Find the sum of the three results.

37. Of 25 tons of meal at $25 per ton.
38. Of 35 acres of land at $35 per acre.
39. Of 45 M. ft. of lumber at $45 per M.

(ii) Find the sum of the three results.

40. Of 23 yd. cloth at 27¢ a yard.
41. Of 36 yd. cloth at 34¢ a yard.
42. Of 42 yd. cloth at 48¢ a yard.

(jj) Find the sum of the three results.

43. Of 3240 ft. lumber at $15 per M.
44. Of 2460 ft. lumber at $15 per M.
45. Of 1620 ft. lumber at $16 per M.

(kk) Find the sum of the three results.

46. Of 99 lb, butter at 234 a pound.
47. Of 99 lb. butter at 28¢ a pound.
48. Of 98 lb. butter at 24¢ a pound.

(11) Find the sum of the three results.

49. Paid $15.50 for ribbon at 1634 a yard. How many yards did I buy?

50. Paid $24.75 for ribbon at 1234 a yard. · How many yards did I buy?

(mm) Find the sum of the two results.

EXAMINATION PROBLEMS,

Miscellaneous Problems.

NOTE.—The following problems are selected mainly from sets of examination questions supplied to the author for this purpose by one hundred school principals and superintendents.

1. Each edge of a cube is diminished by 1o of its length: (a) By what fraction of itself is the volume diminished ? (b) By what fraction of itself is the surface diminished?

2. How many cubical blocks, each edge of which is ft., are equivalent to a block 8 ft. long, 4 ft. wide, and 2 ft. thick?

3. A ladder 78 ft. long stands perpendicularly against a building. How far must it be pulled out at the foot that the top may be lowered 6 ft.?

4. A merchant sold of a quantity of cloth at a gain of 20% and the remainder at cost:

(a) His gain was what per cent of the cost ? (b) If he gained $7.29 what was the cost of the goods?

5. What must I pay for 4% stock to get 5% on the investment?

6. The cubical content of one cube is eight times that of another:

(a) How does an edge of the first compare with an edge of the second ?

(b) How does the surface of the first compare with the surface of the second ?

7. A creditor receives $1.50 for every $4.00 that is due him and thereby loses $301.05:

(a) What was the sum due him? the debt did he lose ?

(b) What per cent of

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8. At $20 per M., board measure, what is the cost of the following: A stick of timber 30 feet long and 14 inches square, and a plank 18 feet long, 8 inches wide, and 22 inches thick?

9. A and B hire a pasture for $85; A puts in 8 cows and B puts in 12 cows. How much should each pay?

10. Simplify the following: of of 13.

11. Seven times John's property, plus $32200, equals 21 times his property. How much is he worth?

12. Two men engage in business with a joint capital of $5000. The first year's gain was $1760, of which one received $1056. How much capital did each furnish?

13. Thirty-five per cent of the men in a regiment being sick, only 637 men were able to enter battle. How many men were there in the regiment ?

14. A lawyer collected 80% of a debt of $2360 and charged 5% commission on the sum collected. How much did the creditor receive?

15. Write a negotiable note for $500, making yourself the payee and James J. Rogers the maker. Interest at the legal rate.

16. A speculator bought stock at 25% below par and sold it at 20% above par. He gained $1035. How much did he invest?

17. What is the rate per cent per annum, if $712 gains $142.40 in 3

yr.

4 mo.? 18. A person asked for a lot of land, 40% more than it cost him, but finally reduced his price 15% of his asking price and sold it making 89.50:

(a) What per cent did he make? (b) How much did the land cost him? (c) How much did he receive for it?

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