8. A bankrupt is indebted to B 844 dollars, to C 1200 dollars, and to D 1564 dolls. and his whole estate is worth only 2702 dollars, which he gives up to his creditors. How much must each have, in proportion to his debt? Ans. B must have 8632 5+ cts. 9. Three men rent a farm, containing 400 acres, for 600 dollars, for a certain time, of which B paid 120 dollars, C 240, and D the remainder; and they agree that the farm shall be divided in proportion to the sums paid by each. I demand each man's share? Ans. B's share 80 acres, C and D each 160 acres. 10. Three men have to share a legacy of 1500 dollars, of which A is to have 4, B, and C the remainder; but B relinquishes to A, and C leaving it to be divided between them, according to their shares in the whole. It is required to know how much of the legacy A and C receive respect. ively? Ans. A's part $1000, and C's $1500. 11. A father left an estate of 6000 dollars to three sons, in such a manner, that for every two dollars A got, B should have three, and C five. How much did each son receive? Ans. A $1200, B $1800, and C § 3000. 12. Two merchants have gained 1800 dollars, of which B is to have three times as much as C. How much is each to receive ? Ans. B receives $1350, and C § 450. 13. A, B and C, traded in company; A put in 140 dollars, B 250 dollars, and C put in 130 yards of cloth, at cash price. They gained 230 dollars, of which C took 100 dollars, for his share of the gain. How did C value his cloth what was A and B's part per yard, in common stock, and of the gain ? Ans. C valued his cloth at $2 5049 cts. a yard. COMPOUND FELLOWSHIP, Or Fellowship with time, is occasioned by several partners being continued in trade an unequal term of time. RULE. Multiply each man's time by his stock in trade, and add the several products together, and say, as the sum of the several products is to the whole gain or loss, so is each man's product to his particular share of the gain or loss. EXAMPLES. 1. A, B and C, hold a pasture in common, for which they A put in 8 horses for 6 weeks, B 12 for 8 pay 76 dollars. weeks, and C 12 for 12 weeks. X 12 = 144 288 2. B and C traded in company; B put in $800 dollars for 5 months, and C 3140 dollars for 6 months, and they gained 1103 dollars 66 cents. What is each man's share of the profit? Ans. B's $554 163 cts. and C's $549 50 cts. 3. B put in a stock of 1800 dollars, and C, at the end of six months, put in a stock that entitled him, at the end of the year, to an equal share of the gain. How much did C put in ? Ans. 3600 dollars. 4. Three persons had received 665 dollars interest. B put in 4000 dollars for a year, C 3000 for 15 months, and D 5000 for 8 months. How much is each man's part of the interest? Ans. B's $240, C's $225, and D's $200. 5. Three merchants enter into partnership for 16 months. B put into stock at first 600 dollars, and at the end of six months 200 dollars more. C put in at first 1200 dollars; but at the end of 12 months, was obliged to take out 600 dollars. D put in at first 1000 dollars, and at the end of 12 months, put in 800 dollars more. With this stock they gained 2500 dolls. What is each man's share of the gain? Ans. B's $560,0, C's $8119, D's $92718175. 6. B and C got into partnership; B put in, first January, a thousand dollars; and C put in, first of May following, a sum which entitled him to an equal share of the gain with B, at the year's end. How much did he put in? Ans. 1500 dollars. 7. Two merchants hired a sleigh, in the winter, to go to Pittsburgh from Washington, (G. C. Ohio,) and back, for 40 dollars, the distance 100 miles between both places, with conditions, that they might take in two other passengers. Now, when at Wheeling, they took in C, and when at Pittsburgh, on their return, they took in D to Wheeling, where they also left C. Now, the distance from here, (Washington.) to Wheeling, is 40 miles. It is required to divide the sleigh-ride among them, in proportion to the miles they travelled? The two merchants each paid $13 79 cts. D paid 4 132 EQUATION OF PAYMENTS Is finding the supposed equated time, to pay at once several debts, due at different periods of time, so that no loss shall be sustained by either party. RULE, Multiply each payment by its time, and divide the sum of the several products by the whole debt, and the quotient will be the equated time. The correct Rule is, to find the present worth of each particular sum; then find on what time these present worths will be increased to the total of the particular sums, payable at the particular times to come, and that is the true equated time for the payment of the whole debt. EXAMPLES. 1. Bowes C 380 dollars, to be paid as follows, viz. 100 dollars in six months, 120 in eight months, and 160 in twelve months. What is the equated time for the payment of the whole debt? Ans. 9 months 4+ days, 2. B is indebted to C 480 dollars, whereof is to be paid in three months, 4 in six months, and the remainder in nine months. Required the equated time for the payment of the whole debt? Ans. 5 months 7 days. 3. M owes N 1000 dollars, whereof 200 dollars is to be paid at present, 400 dollars at five months, and the rest at fifteen months; but they agree to make one equated payment of the whole debt. Required the time? Ans. 8 months. 4. Cowes D 1400 dollars, to be paid in three months; but D being in want of money, C pays him 1000 dollars at the expiration of two months. How long then, after three months, may he in justice defer the payment of the rest? Ans. 2 months. NOTE. This question is solved by inverse proportion; for C paid 1000 dollars one month before the debt was due: therefore D allows C to keep the remaining 400 dollars so long, as will requite him for the 1000 dollars he received one month before due. Thus, As 1000 : 1 :: 400 : 2 months. 5. A merchant has due to him a certain sum of money, to be paid at two months, at three months, and the rest at six months. What is the equated time for the payment Ans. 4 months. of the debt? POSITION Is a Rule which, by false or supposed numbers, taken at pleasure, discovers the true ones required. It is divided into two parts, Single and Double. SINGLE POSITION Is when one number is required, the properties of which are given in the question. RULE. Take any number, and set it down, and proceed as the question directs; then say, as the result of the operation is to the given sum in the question, so is the supposed number to the true one required. PROOF. Substitute the answer in the place of the sup posed number, and proceed as before. EXAMPLES. 1. A man, driving his hogs to market, was asked by another how many he had. He answered he could not tell, but said, that the and of them, added together, made 70. 13 本 How many had he? Ans. 120. 2. A schoolmaster being asked how many scholars he had, said, if I had as many more as I have now, half as many, one-third, and one-fourth as many, I should then have 148. How many scholars had he? Ans. 48 scholars. 3. What sum is that, the,, and of which, will make 308 ? Ans. 240. 4. A man, after spending and of his money, had 60 dollars left; how many had he at first? 5. A gentleman a chaise did buy, Ans. $144. They cost two hundred and forty dollars, The harness came to half of the horse, The horse twice of the chaise. If you find the price of them, Take them, if you please. Ans. Harness $60, chaise $60, horse $120. 6. A person left his son a sum of money, for which he is to receive interest, when he comes of age, at 6 per cent. per annum, simple interest. Now, at the expiration of 5 years, he received, for principal and interest, 644 dollars 80 cents. What was the sum left his son ? Ans. $496. 7. Three persons discoursing together concerning their ages, says B, I am 20 years of age; says C, I am as old as B, and half D; and says D, I am as old as you both. I demand the age of each person? Ans. B 20, C 60, and D 80 years. 8. A vessel has three cocks, B, C and D. B can fill it in one hour, C in two hours, and D in four hours. In what time will they all fill it together? Ans. In 34 min. 174 sec. 60 :: 40: 34 min. 174 sec. Ans. C D min. As 1 : 60 :: 1 : |