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EXERCISE 124

MISCELLANEOUS PROBLEMS

1. At 32¢ a gallon, what will 124 gal. of vinegar cost ? In each of the following examples estimate the approximate answer and write it down. After the problem is solved compare the approximate answer with the real answer. This is one of the best checks against absurd results. Thus 3] x 224 is a reasonable approximation for 32 x 224 in Ex. 2.

2. At 22¢ a pound, what will 33 lb. of steak cost ?
3. At 18¢ a gallon, what will 64 gal. of oil cost ?
4. At 26¢ a pound, what will 67 lb. of butter cost?
5. At 12}¢ a yard, what will 84 yd. of ribbon cost?
6. At $2.50 a yard, what will 73 yd. of velvet cost?
7. If 6 yd. of silk cost $6.75, what is the price per yard ?

8. If 8 doz. men's hose cost $55, what is the price per dozen ?

9. A man drives 39.6 mi. in 51 hr. What is the rate

per hour ?

10. If 48 doz. boys' hose cost $57.60, what is the price

per dozen ?

11. At 14¢ a gross, how many gross of buttons can be bought for $3.22 ?

12. A dealer buys 200 lb. of raisins for $19. How much do they cost a pound ?

13. A grocer pays $10.08 a gross for canned soup. How much does he pay per can ?

14. If 20 electric lights cost 10€ per hour, how long can we burn 4 such lights for 20¢ ?

15. A dealer pays $18.83 for 7 rocking chairs. How much does he pay for each ?

16. A dealer sells 17 pails of mackerel for $40.80. What is the price per pail ?

17. A man pays $1110 a year for the rent of a city house. How much does he pay a month ?

18. A grocer buys a 50-gallon barrel of Porto Rico molasses for $11.50. How much does it cost per gallon ?

19. A grocer sells a half chest of tea, 140 lb. to the chest, for $19.60. What is the price per pound ?

20. A merchant sold a 40-yard piece of cloth for $45, gaining 12}¢ a yard. How much did the piece cost him ?

21. A grocer buys 33} doz. 1-pound cans of cocoa at 43¢ each and sells them at 58% each. How much does he gain ?

22. A dry-goods dealer sold 75 yd. of cloth for $112.50, thereby gaining $28.50. How much did it cost him per yard ?

23. If a family uses 3 bbl. of flour in a year, and can buy the flour at $5.50 a barrel or at 3¢ a pound, how much will be saved by purchasing by the barrel ? (Allow 196 lb. to the barrel.)

24. If a family uses 14 gal. of kerosene in 5 weeks, and the kerosene costs 15¢ a gallon, how much will be used in 52 weeks, and how much will it all cost?

25. If gas costs $1 per 1000 cu. ft., and a family uses 2320 cu. ft. in October and 2475 cu. ft. in November, how much is the gas bill for the two months ?

26. At the beginning of the month the gas meter registers 14,260, and at the end of the month 17,140. How much is the gas bill for the month, at $1.25 per 1000 cu. ft.?

27. A grocer buys six 50-pound boxes of dried apples at 41% a pound and sells them at 6¢ a pound. How much does he gain in all? What fractional part of the cost does he gain ?

28. A salesman receives $15 a week. He works 49 weeks a year. His expenses are $396 a year. How much does he save a year? What fractional part of his income does he save?

29. I bought 6 lb. of prunes @ 1214,8 lb. of dried apricots @ 12}, 24 lb. of raisins @ 16¢, 14 lb. of figs @ 224, and } lb. of English walnuts @ 184, and gave the grocer a $5 bill. How much change should I receive ?

30. If 1 cu. ft. of water weighs 62 lb. 8 oz., what part of 1 oz. does 1 cu. in. of water weigh?

31. A gallon being 231 cu. in., what does 1 gal. of water weigh? 1 qt. of water ?

32. A certain kind of stone is 23 times as heavy as water. What does 21 cu. ft. of this stone weigh?

33. Another kind of stone is 3times as heavy as water. What does 3 cu. ft. of this stone weigh?

34. If good milk is 1.03 times as heavy as water, what is the weight of a can of such milk containing 3} cu. ft., the can itself weighing 6 lb. 4 oz. ?

35. Ice is 0.92 as heavy as water. How much does 1 cu. ft. weigh? How much will a block of ice weigh that is 34 ft. long, 24 ft. wide, and 14 in. thick ?

36. A water tank for fire purposes is placed on top of a factory. It is 16£ ft. long, 81 ft. wide, and 48 ft. deep. When filled within 2 in. of the top, what is the weight of the water ?

37. I bought 8 cans of peaches @ $3.75 a dozen, 15 cans of tomatoes @ $1.37} a dozen, 9 cans of soup @ $1.50 a dozen, 3} lb. of raisins @ 18¢ a pound, 2} lb. of nuts @ 17% a pound, 1} gal. of sirup @ 60¢ a gallon, 1} doz. cakes of soap @ 42¢ a dozen. How much was my bill ? Write the bill.

38. If a boy rides 233 mi. on a bicycle in 24 hr., what is his rate per hour ?

39. In buying 2doz. cans of peaches, how much is gained by buying @ $3.74 a dozen over buying at the rate of 3 cans for a dollar ?

40. What is the cost of 64 lb. of mackerel @ 16¢, 3} lb. of codfish @ 124, and 4 cans of salmon at the rate of 2 cans for a quarter ?

41. I bought } gal. of olive oil @ $3.30 a gallon, but i of what I bought leaked out. What rate per gallon do I pay for what is left ?

42. In buying 48 cans of tomatoes, how much is gained by buying two cases of 2 doz. each, @ $2.89 a case, over buying at the rate of 3 cans for 40¢ ?

43. I bought 3 gal, of best maple sirup @ $1.12} a gallon, and 2} gal. of New Orleans molasses @ 62¢ a gallon, and gave the grocer a $5 bill. How much change did I receive ? (Neglect fractions less than 1%, although in a bill a fraction of a cent is usually called a cent.)

44. I bought 8 lb. of prunes @ 12}\, 4 lb. of figs @ 194, 2} lb. of candles @ 12}, 12 lb. of sugar @ 6}f, and 24 lb. of English walnuts @ 184, and gave the grocer a $5 bill. How much change did I receive ?

45. I bought 10 lb. of white beans @ 616,3} lb. of split peas @ 74,3 cans of soup @ 12%, and 2} lb. of paraffin candles @ 121¢. How much was my bill ?

46. If we buy 12 lb. of sugar at 524, 3} lb. of tea at 60%, and 12 lb. of coffee at 371!, how much is the bill ?

47. If 12 cups of flour make 4 loaves of bread, how many loaves will a barrel of flour make ? Allow 3 cups of flour to the pound, and 196 lb. of flour to the barrel.

48. If a recipe will provide enough for 5 persons, and you wish to provide for 8 persons, what part must you add to the recipe? Instead of 10 teaspoons you would need how many ?

49. Providing 1} potatoes for each person at a meal, how many potatoes would you need for 8 persons ?

50. If there are 40 potatoes in a peck, and you use 12 of them, what fractional part of a peck do you use?

51. If a family uses of a peck of potatoes in one day, how many pecks will it use in a month of 30 days ?

52. Allowing 4 cups to the quart, a quart of cranberries divided among 16 pupils in a class would allow what part of a cup to each member?

53. Cranberries are cooked with half as many cups of sugar as of berries, and half as many cups of water as of sugar. If you wish to cook 3 pt. of cranberries, how much sugar will you use? How much water ?

54. If flour costs $6.25 a barrel (196 lb.), or 31% a pound when bought by the pound, how much is saved on 196 lb. of flour in buying by the barrel ?

55. If a family uses 12 cups of flour in each baking of bread, and there are 2 bakings a week, and we allow { lb. to the cup, how many pounds of flour would be used in a year?

56. If we pay 25¢ for a box of domino sugar weighing 3} lb., how much do we pay per pound ?

57. A gallon of water contains 231 cu. in., and 1 cu. ft. of water weighs 621 lb. If the water in a tank weighs 14,437} lb., how many gallons are there?

On pages 226-230 many industrial problems are included, requiring the use of denominate numbers and fractions, as suggested by the New York State Syllabus. If further work of this nature is needed at this time, pages 99–142 may be reviewed in whole or in part.

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