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Prob. 43. Upon measuring the corn produced by a field, being 48 bushels; it appeared that it yielded only one third part more than was sown. How much was that?
Aas. 36 bushels. Prob. 44. A Farmer sold 36 loads of hay to two persons. To the first one half, and to the second one fourth of what his stack contained. How many loads did that stack contain ?
Ans. 128 loads. Prob. 45. A Draper bought three pieces of cloth, which together measured 159 yards. The second piece was 15 yards longer than the first, and the third 24 yards longer than the second. What was the length of each ?
Ans. 35, 50, and 74 yards respectively. Prob. 46. A cask which held 146 gallons, was filled with a mixture of brandy, wine, and water. In it there were 15 gallons of wine more than there were of brandy, and as much water as both wine and brandy. What quantity was there of each?
Ans. 29, 44, and 73 gallons respectively. Prob. 47. A person employed 4 workmen, to the first of whom he gave 2 shillings more than to the second; to the second 3 shillings more than to the third ; and to the third 4 shillings more than to the fourth. Their wages amounted to 32 shillings. What did each receive ?
Ans. 12, 10, 7, and 3 shillings respectively. Prob. 48. A Father taking his four sons to school, divided a certain sum among them. Now the third had 9 shillings more than the younger; the second 12 shillings more than the third and the eldest 18 shillings more than the second ; and the whole sum was 6 shillings more than 7 times the sum which the youngest received. How much had each?
Ans. 21, 30, 42, and 60 shillings respectively.' Prob, 49. It is required to divide the number 99 into five such parts, that the first may exceed the
second by 3; be less than the third by 10; greater than the fourth by 9; and less than the fifth by 16.
Ans. 17, 14, 27, 8, and 33. Prob. 50. Two persons began to play with equal sums of money : the first lost 14 shillings, the other won 24 shillings, and then the second had twice as, many shillings as the first. What sum bad each at tirst ?
Ans. 52 shillings. Prob. 51. A Mercer having cut 19 yards from each of three equal pieces of silk, and 17 from another of the same length, found that the remants together were » 142 yards. What was the length of each piece ?
Ans. 54 yards. Prob. 52. A Farmer has two flocks of sheep, each containing the same number. From one of these he sells 39, and from the other 93; and finds just twice as many remaining in one às in the other. How many did each flock originally contain ?
Ans. 147. Prob. 53. A Courier, who travels 60 miles a day, had been despatched five days, when a second is sent to overtake him, in order to which he must travel 75 miles a day. In what time will he overtake the former?
Ans. 20 days. Prob. 54. A and B trade with equal stocks. In the first year A tripled his stock, and had $27 to spare; B doubled his stock, and had $153 to spare. Now the amount of both their gains was five times the stock of either. What was that?
Ans. 90 dollars. Prob. 55. A and B began to trade with equal sums of money. In the first year A gained 40 dollars, and B lost 40; but in the second A lost one-third of what he then had, and B gained a sum less by 40 dollars, than twice the sum that A had lost; when it appeared that B had twice as much money as A. What money did each begin with ?
Ans. 320 dollars.
Prob. 56. A and B being at play, severally củt packs of cards, so as to take off more than they left. Now it happened that A cut off twice as many as B left, and B cut off seven times as many as A left. How were the cards cut by each?
Ans. A cut off 48, and B cut off 28 cards. Prob. 57. What two numbers are as 2 to 3 ; to each of which if 4 be added, the sums will be as 5 to 7 ?
Ans. 16 and 24. Prob. 58. A sum of money was divided between two persons, A and B, so that the share of A was to that of B as 5 to 3 ; and exceeded five-ninths of the whole sum by 50 dollars. What was the share of each person?
Ans. 450, and 270 dollars. Prob. 59. The joint stock of two partners, whose particular shares differed by 40 dollars, was to the share of the lesser as 14 to 5. Required the shares.
Ans. the shares are 90 and 50 dollars respectively.
Prob. 60. A Bankrupt owed to two creditors 1400 dollars ; the difference of the debts was to the greater as 4 to 9. What were the debts?
Ans. 900, and 500 dollars. Prob. 61. Four places are situated in the order of the four letters A, B, C, D. The distance from A to Dis 34 miles, the distance from A to B : distance from C to D :: 2:3, and one-fourth of the distance from A to B added to half the distance from C to D, is three times the distance from B to C. What are the respective distances ?
Ans. AB=12, BC=4, and CD=18 miles. Prob. 62. A General having lost a battle, found that he had only half his army plus 3600 men left, fit for action; one-eighth of his men plus 600 being wounded, and the rest, which were one-fifth of the whole army, either slain, taken prisoners, or missing, Of how many men did his army consist ?
Ans. 24000. · Prob. 63. It is required to divide the number 9!
into two such parts that the greater being divided by their difference, the quotient may be 7.
Ans. 49 and 42. Prob. 64. A person being asked the hour, answered that it was between five and six; and the hour and minute hands were together. What was the time?
Ans. 5 hours 27 minutes 164 seconds. Prob. 65. Divide the number 49 into two such parts, that the greater increased by 6 may be to the less diminished by 11 as 9 to 2.
Ans. 30 and 19. Prob. 66. It is required to divide the number 34 into two such parts that the difference between the greater and 18, shall be to the difference between 18 and the less :: 2 : 3.
Ans. 22, and 12. Prob. 67. What number is that to which if 1, 5, and 13, be severally added, the first sum shall be to the second, as the second is to the third.
Ans. 3. Prob. 68. It is required to divide the number 36 into three such parts, that one-half of the first, one third of the second, and one-fourth of the third, shall be equal to each other,
Ans. 8, 12, and 16. Prob. 69. Divide the number 116 into four such parts, that if the first be increased by 5, the second diminished by 4, the third multiplied by 3, and the fourth divided by 2, the result in each case shall be the same.
Ans. 22, 31, 9, and 51. Prob. 70. A Shepherd, in time of war, was plundered by a party of soldiers, who took of his flock, and of a sheep; another party took from him of what he had left, and of a sheep; then a third party took į of what now remained, and į of a sheep. After which he had but 25 sheep left. How many had he at first ?
Ans. 103. Prob. 71. A Trader maintained himself for 3 years at the expense of 501 a year; and in each of those
years augmented that part of his stock which was not so expended by 1 thereof. At the end of the third year his original stock was doubled. What was that stock ?
Ans. 7401. Prob. 72. In a naval engagement, the number of ships taken was 7 more, and the number burnt two fewer, than the number sunk. Fifteen escaped, and the fleet consisted of 8 times the number sunk. Of how many did the fleet consist ?
Ans. 32, Prob. 73. A cistern is filled in twenty minutes by three pipes, one of which conveys 10 gallons more, and the other 4 gallons less, than the third, per minute. The cistern holds 820 gallons. How much flows through each pipe in a minute ?
Ans. 22, 7, and 12 gallons. Prob. 74. A sets outs from a certain place, and travels at the rate of 7 miles in five hours ; and eight hours afterwards B sets out from the same place, and travels the same road at the rate of five miles in three hours. How long, and how far, must A travel before he is overtaken by B ?
Ans. 50 hours, and 70 miles. Prob. 75. There are two places, 154 miles distant, from which two persons set out at the same time to to meet, one travelling at the rate of 3 miles in two hours, and the other at the rate of 5 miles in four hours. How long, and how far did each travel before they met ?
Ans. 56 hours; and 84, and 70 miles.
§ II. SOLUTION OF PROBLEMS PRODUCING SIMPLE
Involving more than one unknown Quantity. 266. The usual method of solving determinate problems of the first degree, is, to assume as many unknown letters, namely, x, y, z, &c., as there are unknown numbers to be found; then, having properly