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 enough to pay A's debt. What is the salary of each? 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? Transposing and uniting, — — — — 9 x72, the father's age. 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? 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. A 60. A cask which held 44 gallons was filled with a mixture of brandy, wine, and water. There were 10 gallons more than one half as much wine as brandy, and as much water as brandy and wine. How many gallons were there of each? 61. Two persons, A and B, travelling each with $80, meet with robbers who take from A $5 more than twice what they take from B; then B finds he has $26 more than twice what A has. How much is taken from each ? Ans. From A, $69; from B, $32. 62. Four persons, A, B, C, and D, entered into partnership with a capital of $84816; of which B put in twice as much as A, C as much as A and B, and D as much as A, B, and C. How much did each put in? 63. In three cities, A, B, and C, 1188 soldiers are to be raised. The number of enrolled men in A is to that in B as 3:5; and the number in B to that in C as 8: 7. How many soldiers ought each city to furnish? Ans. A, 288; B, 480; C, 420. 64. Divide $65 among five boys, so that the fourth may have $2 more than the fifth and $3 less than the third, and the second $4 more than the third and $5 less than the first. 65. A merchant bought two pieces of cloth, one at the rate of $5 for 7 yards, and the other $2 for 3 yards; the second piece contained as many times 3 yards as the first times 4 yards. He sold each piece at the rate of $6 for 7 yards, and gained $24 by the bargain. How many yards were there in each piece? Ans. First, 84; second, 63. 66. A drover had the same number of cows and sheep. Having sold 17 cows and one third of his sheep, he finds he has three and a half times as many sheep as cows left. How many of each did he have at first? ⠀⠀⠀⠀67. A four dealer sold one fourth of all the flour he had and one fourth of a barrel; afterward he sold one third of what he had left and one third of a barrel; and then one half of the remainder and one half of a barrel; and had 15 barrels left. How many had he at first? 68. A merchant bought a barrel of oil for $50; at the same rate per gallon as he paid, he sold to one man 15 gallons; then to another at the same rate two fifths of the remainder for $14. How many gallons did he buy in the barrel ? 69. Two pieces of cloth of the same length but different prices per yard were sold, one for $5 and the other for $7.50. If there had been 5 more yards in each, at the same rate per yard as before, they would have come to $15.47. How many yards were there in Ans. 21. each? 70 A and B began trade with equal sums of money. The first year A lost one third of his money, and B gained $750. The second year A doubled what he had at the end of the first year, and B lost $150, when the two had again an equal sum. What did each have at first? 71. A man distributed among his laborers $2.50 apičce, and had $25 left. If he had given each $3 as long as his money lasted, three would have received nothing. How many laborers were there, and how much money did he have? Ans. 68 laborers, and $195. 72. A man who owned two horses bought a saddle for $35. When the saddle was put on one horse, their value together was double the value of the other horse; but when the saddle was put on the other horse, their value together was four fifths of the value of the first horse. What was the value of each horse? 73. From a cask two thirds full 18 gallons were taken, when it was found to be five ninths full. How many gallons will the cask hold? 74. A farmer had two flocks of sheep, and sold one flock for $60. Now a sheep of the flock sold was worth 4 of those left, and the whole value of those left was $8 more than the price of 8 sheep of those sold, and the flock left contained 40 sheep. How many sheep did the farmer sell, and what was the value of a sheep of each flock? Ans. Number sold, 15; value, $4 and $1. 75. A man has seven sons with 2 years between the ages of any two successive ones, and the sum of all their ages is ten times the age of the youngest. What is the age of each? 76. Divide 75 into two parts such that the greater increased by 9 shall be to the less diminished by 4 as 3:1. 77. Divide a into two parts such that the greater increased by b shall be to the less diminished by c as m: n. 78. What two numbers are as 3 4, while if 8 be added to each the sums will be as 5: 6? 79. Divide 127 into two parts, such that the difference between the greater and 130 shall be equal to five times the difference between the less and 63. |