that each did. On trial they found that Mr. Presby could cut only 3 cords while Mr. Wheelock cut 5. What part of the whole would each man cut? How many dollars ought each man to receive? 34. Frederic and Benjamin gathered some nuts, of which Frederic gathered 4 quarts and Benjamin 2 quarts. They sold them for 39 cents. How many cents ought each to receive? 35. James, wishing to buy some drawing-pencils, asked his father for the money. His father replied, "5 good drawingpencils will cost as much as 7 writing-books at 7 cents apiece. Now, if you can tell me what six drawing-pencils will cost I will buy them for you." What should have been the answer? 36. Mr. Ames and Mr. Clapp bought the apples on 2 large trees, for 9 dollars, of which Mr. Ames paid 5 dollars and Mr. Clapp 4 dollars. There proved to be 87 pecks of apples. How many pecks ought each to have? 37. Waldo and George undertook to dig a large field of potatoes for 24 dollars. It turned out that Waldo could dig 3 bushels as often as George could dig 2. What part of the whole did each dig? They divided the money in proportion to the work each did. How many dollars did each receive? Partial explanation. Since Waldo dug 3 bushels as often as George dug 2, he would dig 3 bushels out of every 5 that were dug, and would, therefore, dig of the whole, while George would dig of the whole. 38. Mr. Bacon, Mr. Calrow and Mr. Hawley entered into a speculation together; Mr. Bacon put in 4 dollars as often as Mr. Calrow put in 3, and as often as Mr. Hawley put in 2. What part of the whole stock did each man put in? They gained 75 dollars. How many dollars ought Mr. Bacon to receive on his share? ought Mr. Calrow? ought Mr. Hawley? 39. A and B traded together; B put in twice as much money as A, and both put in 28 dollars. How much did each man put in? Partial solution. Since B put in twice as much as A, A and B together must have put in 3 times as much as A alone. Therefore, 28 dollars is 3 times what A put in. If 28 dollars is 3 times what A put in, A must have put in of 28 dollars, which is, &c. 40. Mr. Hooker and Mr. Phillips hired a pasture for 49 dollars; Mr. Hooker pastured 4 times as many animals as Mr. Phillips. How many dollars ought each to pay? 41. Mr. Bates and Mr. Conant received 33 dollars for doing a job of work, but Mr. Bates had done 3 times as much as Mr. Conant. How much ought each to receive? am. 42. William and Henry were talking about their ages. William said, "I am 8 years old." Then said Henry, "I am 7 years more than as old as you are, and my father is 10 as old as I Now, if you will tell me how old I am, I will give you f of 26 oranges, and if you will tell me how old my father is, will give you of 48 apples." What would you have called Henry's age, had you been in William's place? What would you have called his father's age? William gave both answers correctly, and Henry gave him the oranges and apples as he had promised him. How many oranges did William receive? How many apples? = of what number? of 7 times, which are 56, equal to 63. Therefore, of 63. = + Solution. be of 24, which is 8; and 7, or the number, must be 7 times 8, If 94 is of a number, or the number must be 8 times 94, which are 724-744. *This question is equivalent to, 8187= of what number? D. 1. of 42: = of what number? Solution. or 36. of 42 If 36 is = 6, and of 42 must equal 6 times 6, of some number, of that number must equal of 36, which is 9, and or the number must equal 9 times 9, or 81. Therefore, of 42 of 81. Remark. This question is equivalent to of 45 = § of what number? * 3 should not be reduced to an improper fraction. -- of = = 12 times what number? times what number? = 14 times what number? E. 1. If of a gallon of molasses cost 25 cents, what will 1 gallon cost? Solution. If of a gallon of molasses cost 25 cents, of a gallon will cost of 25 cents, which is 8 cents, and or 1 gallon will cost 4 times 8 cents, or 33 cents. Therefore, 1 gallon of molasses will cost 334 cents if of a gallon cost 25 cents. 2. If § of a yard of muslin cost 37 cents, what will 1 yard cost? 3. If of a yard of linen cost 53 cents, what will 1 yard cost? 4. If of a month's wages amount to 23 dollars, what will 1 month's wages amount to? 5. John is 17 years old, and his age is of his teacher's. How old is his teacher ? 6. Deborah says she has 41 cents. Then, says Lavinia, you have only as many as I have. How many cents did Lavinia have ? of his money would buy 51 7. David told George that pounds of raisins at 9 cents per pound. Then, replied George, you have 6 cents more than I have. How many cents had each of the boys? 8. Seth's father gave him a half dollar to buy a pound of tea with, saying to him, " of a pound of tea will cost 30 cents, and if you will tell me how much a pound will cost, you may have the money there will be left after paying for the tea." Seth answered correctly. What was his answer? How many cents did he have left after paying for the tea? 9. A farmer gave 7 dozen of eggs at 9 cents per dozen for of a gallon of oil. What was a gallon of the oil worth? 10. A butcher received 5g dollars for of a hundred weight of beef. What would he have received for a hundred weight at the same price? What would he have received for of a hundred weight? 11. A schoolmaster being asked his age replied, "§ of my life has been spent in teaching. I have taught in Boston 25 years, which is of all the time I have spent in teaching." What was his age? |