(hh) Find the sum of the three results. 37. Of 25 tons of meal at $25 per ton. 40. Of 23 yd. cloth at 27¢ a yard. (jj) Find the sum of the three results. 43. Of 3240 ft. lumber at $15 per M. (kk) Find the sum of the three results. 46. Of 99 lb. butter at 23¢ a pound. (11) Find the sum of the three results. 49. Paid $15.50 for ribbon at 163 a yard. How many yards did I buy? 50. Paid $24.75 for ribbon at 12 a yard. How many yards did I buy? (mm) Find the sum of the two results. EXAMINATION PROBLEMS. NOTE. Miscellaneous Problems. 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 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? (b) What per cent of the debt did he lose? 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 21 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 7 of 11. 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 $9.50: (a) What per cent did he make? (b) How much did the land cost him? (c) How much did he receive for it? 19. Purchased stock at a premium of 8 per cent. What rate of interest do I receive on the investment if it pays an annual dividend of 6% ? 20. Find the volume of a cube the area of whose surface is 100.86 square inches. 21. How many apples must a boy buy and sell to make a profit of $9.30, if he buys at the rate of 5 for 3 and sells at the rate of 4 for 3¢? 22. Find the cost of 1875 lb. hay at $ 6.50 per ton. 23. What is the interest on $1200 from Sept. 21, 1898, to May 5, 1899, at 7% per annum? 24. The area of a square field is 10 acres. distance diagonally across the field? 25. A "drummer" earns $2500 a year. dollars of this sum is a guaranteed salary. is his commission of 5% on his sales. of his annual sales? What is the One thousand The remainder What is the amount 26. The area of a triangle is 325 square inches. Its base is 25 inches. What is its altitude? 27. Gave 6 lb. butter worth 36 a pound for 3 gal. oil. What was the cost of the oil per gallon? 28. A can build a certain wall in 10 days; B can build it in 12 days, and C, in 15 days. In how many days can they build the wall working together? 29. A horse and a carriage together cost $550. The horse cost as much as the carriage. Find the cost of each. 30. A man willed of his property to his wife, of the remainder to his daughter, and the rest to his son. The difference between the wife's portion and the son's portion was $12480.333. How much was the man worth? 31. (a) How many loads, each containing a cubic yard, will be required to fill a street 150 feet long, 50 feet wide, and 21 feet deep? (b) How much will it cost at 18¢ per cubic yard? 32. A right-triangle has two equal sides. Its hypothenuse is 100 rods long. (a) Find one of its two equal sides. (b) Find its area. 33. What is the ratio of the area of a circle to the area of its circumscribed square? 34. What is the ratio of the square of the radius to the square of the diameter of the same circle? 35. A man's tax is $37.50. The rate of tax is 1%. Property is assessed at 30 % of its value. What is the man's property worth? 36. A field containing 160 acres is 40 rods wide. At 45¢ a rod, how much less would it cost to fence a square field containing the same number of acres? 37. My agent in Baltimore having sold a consignment of grain, after taking out his commission at 3%, and paying a freight bill of $1125.00, sent me a draft for the amount due $19536.00. For how much was the grain sold? me 38. How many pickets 4 inches wide, placed 3 inches apart, are required to fence a garden 21 rods long and 14 rods wide? 39. At $6.30 a cord what is the value of wood that can be piled under a shed 50 ft. long, 25 ft. wide, and 12 ft. high? 40. Find the curved surface of a cylinder 6 ft. in diameter and 12 ft. long. 41. (a) What is the bank discount and (b) what are the proceeds on a note for $125 payable in 90 days, the rate of discount being 8% ? 42. If sugar that cost 5¢ a pound is sold at 18 lb. for a dollar, what is the gain per cent? |