24. A boy wishing to distribute all his money among his companions gave to each 2 cents, and had 3 cents left; therefore, collecting it again, he began to give 3 cents to each, but found that in this case there was one who had received none, and another who had only 2 cents. How many companions, and how much money had he? Ans. 7 companions, and 17 cents. 25. What two numbers whose difference is 35 are to each other as 4: 5? 26. A man being asked the hour, answered that three times the number of hours before noon was equal to three fifths of the number since midnight. What was the time of day? SOLUTION Let x = the number of hours since midnight, i. e. the time; then 12 x the number of hours before noon. 27. A gains in trade $300; B gains one half as much as A, plus one third as much as C; and C gains as much as A and B. What is the gain of B and C ? Ans. B's, $375; C's, $675. 28. What number is to 28 increased by one third of the number as 2:3? Ans. 24. 29. What number is that whose fifth part exceeds its sixth by 15? 30. Divide $3740 into two parts which shall be in the ratio of 10: 7. 31. Divide a into two parts which shall be in the ratio of b: c. ab a c Ans. and b+c b+c 32. What number is that the sum of whose fourth part, fifth part, and sixth part is 37? 33. What quantity is that the sum of whose third part, fifth part, and seventh part is a? Ans. 105 a 71 34. A farmer sold 17 bushels of oats at a certain price, and afterward 12 bushels at the same rate; the second time he received 55 shillings less than the first. What was the price per bushel? 35. A certain number consists of two figures whose sum is 9; and if 27 is added to the number, the order of the figures will be inverted. What is the number? Let then SOLUTION. x the left-hand figure; 9 the right-hand figure. As figures increase from right to left in a tenfold ratio, 10 x + (9 — x) = =9x+9 the number; and when the order of the figures is inverted, 10 (9-x)+x=90-9x the resulting number. 36. A certain number consists of three figures whose sum is 6, and the middle figure is double the left-hand figure; and if 198 is added to the number, the order of the figures will be inverted. What is the number? Ans. 123. 37. Two men 90 miles apart travel towards each other till they meet. The first travels 5 miles an hour and the second 4. How many miles does each travel before they meet? G 38. A man hired six laborers, to the first of whom he paid 75 cents a week more than to the second; to the second, 80 cents more than to the third; to the third, 60 cents more than to the fourth; to the fourth, 50 cents more than to the fifth; to the fifth, 40 cents more than to the sixth; and to all he paid $68.15 a week. What did he pay to each a week? 39. What number is that to which if 20 is added two thirds of the sum will be 80? 40. What number is that to which if a is added the sum will be d? of с 41. A man spent one fourth of his life in Ireland, one fifth in England, and the rest, which was 33 years, in the United States. To what age did he live? 42. A post is one fifth in the mud, two sevenths in the water, and 18 feet above the water. How long is the post? 43. What number is that whose half is as much less than 40 as three times the number is greater than 156? Ans. 56. 44. Two workmen received the same sum for their labor; but if one had received $15 less and the other $15 more, one would have received just four times as much as the other. What did each receive? 45. Of the trees on a certain lot of land five sevenths are oak, one fifth are chestnut, and there are 32 less walnut trees than chestnut. How many trees are there? 46. Divide 474 into two parts such that, if the greater part is divided by 7 and the less by 3, the first quotient shall be greater than the second by 12. Ans. 357 and 117. 47. Two persons, A and B, have each an annual income of $1500. A spends every year $400 more than B, and at the end of five years the amount of their savings is $6000. What does each spend annually? Ans. A $1100, and B $700. 48. In a skirmish the number of men captured was 41 more, and the number killed 26 less than the number wounded; 45 men ran away; and the whole number engaged was four times the number wounded. How many men belonged to the skirmishing party? Ans. 240. 49. A and B have the same salary. A runs into debt every year a sum equal to one sixth of his salary, while B spends only three fourths of his; at the end of five years B has saved $1000 more than debt. What is the salary of each ? enough to pay A's Ans. $2400. 50. A man lived single one third of his life: after having been married two years more than one eighth of his life, he had a daughter who died ten years after him, and whose age at her death was one year less than two thirds the age of her father at his death. What was the father's age at his death? 51. Divide $864 among three persons so that A shall have as much as B and C together, and B $5 as often as C $11. 52. A father and son are aged respectively 32 and 8. How long will it be before the son will be just one half the age of the father? 53. A man's age was to that of his wife at the time of their marriage as 4: 3, and seven years after, their ages were as 5:4. What was the age of each at the time of their marriage? 28 21 54. One fifth of a certain number minus one fourth of a number 20 less is 2. What is the number? Ans. 60. 55. There are two numbers which are to each other as ; but if 9 is added to each, they will be as: . What are the numbers? Ans. 9 and 6. 56. A person having spent $150 more than one third of his income had $50 more than one half of it left. What was his income? 57. A merchant sold from a piece of cloth a number of yards, such that the number sold was to the number left as 45; then he cut off for his own use 15 yards, and found that the number of yards left in the piece was to the number sold as 1: 2. How many yards did the piece originally contain? Ans. 45. 58. Four places, A, B, C, and D, are in a straight line, and the distance from A to D is 126 miles. The distance from A to B is to the distance from B to C as 3: 4, and one third the distance from A to B added to three fourths the distance from B to C is twice the distance from C to D. What is the distance from A to B, from B to C, and from C to D? 59. A laborer was hired for 40 days; for each day he wrought he was to receive $2.50, and for each day he was idle he was to forfeit $1.25. At the end of the time he received $58.75. How many days did he work? Ans. 29. |