16. What part of 2721 square feet is 9 square feet? 17. The material for a cloak cost $121, the making $114. What part of the entire cost was the cost of making? 18. If a man can do a piece of work in 25 days, what part of it can he do in 64 days? 19. A can lay a hall floor in 6 days, B can do it in 8 days. What part of the work can each do in one day? What part can both together do in one day? 20. Three men working at the same rate per day did a piece of work for $90. A worked 5 days, B 6 days, and C 8 days. How much did each receive per day? How much did each receive for his work? 21. In a rectangular lot 100 ft. long and 80 ft. wide there is an asparagus bed, also rectangular, 50 ft. long and 12 ft. wide. What part of the lot does the bed occupy? 22. What part of his earnings does a man spend who works 6 days a week, receiving $1.75 per day, and paying for his board $4 a week, and for all other expenses $32.50 a quarter (13 weeks)? 235. To find the whole when a part is given. a. In of a ream of many quires are there in paper there are 8 quires. How of a ream? In a whole ream? b. 8 is of what number? SOLUTION. Since 8 is of a number, 1 half of 8, or 4, is of the number, and g of the number is 5 times 4 or 20. c. If the weight of of a bushel of potatoes is 45 pounds, what is the weight of 1 bushel? d. 6 hours equal of what number of hours? e. 12 days equal of what number of days? of a comforter. f. of a mile equals of what part of a mile? g. Mrs. Pratt has been 6 hours tacking At the same rate, how long will it take her to finish it? h. If I sell grapes for 60 cents and thereby lose a sum equal to of the cost, what was the cost? NOTE. If was lost, remained. i. A vessel having lost of her cable, has 200 feet remaining. How many feet had she at first? j. Carl is 14 years old, which is 1 times the age of Alfred. How old is Alfred? NOTE. - Carl's age is 7 of the age of Alfred. k. What was the cost of mutton per pound which sells for 8, at a gain of of the cost? Of yearlings which sell for 10%, at a gain of of the cost? Of lamb which sells for 12¢, at a gain of of the cost? 7. By reason of large importations from Vera Cruz, hard asphalt sold at $9 per ton. If this was a falling off of from the former price, what was the former price? m. A and B are to share $100. B is to have as much as A. What is each one's part? NOTE. A's part must be of itself, and B's part with A's part will equal of A's part. But the two together have $100; then $100 is of A's part. n. A mother and her son together have $ 45; the son's part is as great as the mother's. What is each one's part? o. When $6 received for the use of money is sum loaned, what is the sum loaned? of the p. Of what sum of money is 4 cents ? is 6 cents 100 236. Examples for Written Work. 23. lb. of what? = 26. 61 of what? = 29. If of a barrel of flour weighs 73 pounds, what is the weight of a barrel? 30. A farmer received in one year $3575 as a royalty for oil produced on his farm. If this was of the value produced, what is the value produced? What is the cost per pound 31. Of veal when 5 pounds can be bought for 92 cents? 32. Of butter when 41 pounds can be bought for $1.65? 33. Of sugar when 12 pounds can be bought for a dollar? 34. Of tea when a box of 13 pounds costs $10? 35. What is the cost per gross of pencils when 5 gross can be bought for $77? 36. When 7 gallons of molasses costs $3.15, what is the price per gallon? 37. If 4 pounds of halibut costs $1.19, what is the cost per pound? 38. After losing of his property a man had $2400 left. How much money had he at first? 39. A sold of his farm and had 412 acres left. How many acres had he at first? 40. Mr. White owning of a yacht sold of his share for $550. What was the value of the yacht at the same rate? 41. What number is that which increased by of itself equals 2914? 42. What number is that which diminished by of itself equals 2914? 43. Water in changing from the temperature of ice to that of boiling, increases its bulk about 1 cubic foot in every 24. At this rate of increase, how many cubic feet of boiling water will equal the weight of 1000 cubic feet of ice water? 44. From a hogshead of molasses 311 gallons were taken, after which of the original quantity remained. How many gallons did the hogshead contain at first? 45. When of of a vessel is worth $980, how much is the whole vessel worth? 46. In a college of 342 students there were as many women as men. What was the number of each? 47. A dealer sold an umbrella for $5.20, which was 1g times what he paid for it. How much did he pay for it, and what was his gain? 48. A man failing in business paid only of the value of his bills. If Mr. Taft lost $2050 by him, what was the amount of Mr. Taft's bill? 49. Four children picked cranberries which they sold for $2.60. One picked 5 quarts, another 7 quarts, another 6 quarts, another 8 quarts. How much did they receive per quart? How much should each receive for all he had? ALIQUOT PARTS OF NUMBERS. 237. What is one of the four equal parts of 8? of 9? One of the equal parts of a number is an aliquot part of the number. Thus, 24 is an aliquot part of 9. Oral Exercises. a. Of the number 10 find; 1; 1; 1; 2; 4. b. Of the number 30 find ; ; 4 3 4 5 5 3 e. Of the number 100 find f. Of the number 100 find ; 4; 3; 4; 6; 8; ; ; 16. g. Of the number 144 find; 1; 1; b; b; b; 12; 1; + Tz; }; 2. h. Of the number 200 find; 1; 1; 7; 1; 1; 1; 12; 1. ;;;;;古;ㄨˇ By using the aliquot parts of numbers, especially of 10, 100, and 1000, the work of multiplying and dividing can often be materially shortened. 238. Illustrative Example. What is the cost of 26,500 shingles at $2 per thousand? WRITTEN WORK. 4)265.00 26,500 shingles at $1 a thousand would cost $26.50; 26,500 shingles at $10 per thousand would cost ten times as much, or $265.00; at $21 per thousand, they would cost of $265.00, or $66.25. Ans. $66.25. i. Give the shortest way of multiplying by 25; 12; 37; 621; 87; 3; 331; 66. j. Give the shortest way of dividing by 25; 12; 3; 331, etc. Examples for Written Work. 239. What is the amount of the following purchases: 50. 2 tubs of butter, each containing 35 pounds at 25¢, and 1 tub of 45 pounds at 37? 51. 2 boxes of cheese, each containing 75 pounds at 121, and 1 box of 82 pounds at 163¢? 52. 1 quarter of beef weighing 190 pounds at 61, and 1 quarter weighing 210 pounds at 81¢? 53. 60 yards of cashmere at 621; 54 yards at 75; 36 yards at 87? 54. 19 yards of velvet at $1.331; 25 yards at $1.50; 22 yards at $1.663? 55. 3 yards of crash at 134; 7 yards at 114; 5 yards of broadcloth at $4.50. NOTE. First find the cost of 10 yards. 56. 12 yards of silk at 794; 33 yards at 854; 37 yards at $2.66. 57. How many pounds of cocoa at 331 per pound, can be bought for $1? For $25? 58. 428 × 163 = ? 60. 521÷12 =? 62. 186÷ 61 = ? 59. 262 × 621=? 61. 482 × 37 = ? 63. 216 ÷ 33} = ? |