Therefore, that is, or, x+2x+4x+5x=14,400; x= 1200, from which the shares of the other three are easily obtained. Prob. 39. A draper has four pieces of cloth whose united value is 224 dollars. The value of the second piece is double that of the first; the value of the third is five times that of the first; and the value of the fourth is six times that of the first. What is the value of each? Let x represent the value of the first; then 2x will represent the value of the second, 5x the third, 6x the fourth. Hence, that is, or, x+2x+5x+6x=224, 14x=224, x= 16, the value of the first piece, from which the value of the other pieces is readily obtained. Prob. 40. A grocer has four casks, which together will contain 144 gallons. The capacity of the second is twice that of the first; the capacity of the third is six times that of the first; and the capacity of the fourth is seven times that of the first. What is the capacity of each? Let x= the capacity of the first cask; then 2x the capacity of the second, 6x the third, and 7x the fourth. Therefore, that is, x+2x+6x+7x=144; Prob. 41. Four persons purchased a farm in company for 4680 dollars, of which B paid three times as much as A, C paid four times as much as A, and D paid five times as much as A. Let What did each pay ? x= the sum A paid; 3x the sum B paid; 4x= the sum C paid; Therefore, that is, or, 5x= the sum D paid. x+3x+4x+5x=4680; 13x=4680, x= 360, 3x=, etc. Prob. 42. Four persons, A, B, C, and D, drew prizes in a lottery to the amount of 2250 dollars. B drew three times as much as A, C drew five times as much as A, and D drew six times as much as A. What did each person draw? Prob. 43. An estate of 5440 dollars is to be divided between four heirs, A, B, C, and D. B is to receive three times as much as A, C is to receive six times as much as A, and D is to receive seven times as much as A. How much did each receive? Prob. 44. A farmer has 144 fruit-trees in his orchard, consisting of plum, cherry, peach, and appletrees. The number of cherry-trees is four times the number of plum-trees; the number of peach-trees is five times the number of plum-trees; and the number of apple-trees is six times the number of plum-trees. What is the number of each sort? Prob. 45. Four gentlemen entered into a speculation, for which they subscribed 5850 dollars, of which B paid four times as much as A, C paid six times as much as A, and D paid seven times as much as A What did each pay? Therefore, that is, or, x+4x+6x+7x=5850; 18x=5850, x= 325, 4x=, etc. Prob. 46. The number of days that four workmen were employed were severally as the numbers 1, 2, 3, and 4, and the number of days' work performed by them all was 250. How many days was each workman employed? Ans. The first was employed 25 days, Prob. 47. The estate of a bankrupt, valued at 33,600 dollars, is to be divided among four creditors according to their respective claims. The debts due to B are double those due to A; those due to C are four times those due to A; and those due to D are five times those due to A. What sum must each receive? Ans. A receives 2,800 dollars; C receives 11,200 dollars; D receives 14,000 dollars. Prob. 48. A draper has four pieces of cloth, whose united value is 168 dollars. The value of the second piece is double that of the first; the value of the third is five times that of the first; and the value of the fourth is six times that of the first. What is the value of each? Ans. The value of the first is 12 dollars; the second is 24 dollars; the third is 60 dollars; the fourth is 72 dollars, Prob. 49. A grocer has four casks, which together will contain 256 gallons. The capacity of the second is twice that of the first; the capacity of the third is six times that of the first; and the capacity of the fourth is seven times that of the first. capacity of each ? What is the Prob. 50. Four persons purchased a farm in company for 8840 dollars, of which B paid three times as much as A, C paid four times as much as A, and D paid five times as much as A. What did each pay? A paid 680 dollars; B paid 2040 dollars; Ans. C paid 2720 dollars, D paid 3400 dollars. Prob. 51. Four persons, A, B, C, and D, drew prizes in a lottery to the amount of 4875 dollars. B drew three times as much as A, C drew five times as much as A, and D drew six times as much as A. What did each person draw? Ans. A drew 325 dollars; B drew 975 dollars; C drew 1625 dollars; D drew 1950 dollars. Prob. 52. An estate of 9775 dollars is to be divided between four heirs, A, B, C, and D. B is to receive three times as much as A, C is to receive six times as much as A, and D is to receive seven times as much as A How much did each receive? |