XVIII. EQUATION OF PAYMENTS EQUATION OF PAYMENTS consists in finding a mean time for the payment at once of several debts, payable at different times, so that no loss of interest shall be sustained by either party. For instance, if A owes B one dollar, payable in 2 months, another dollar payable in 3 months, and a third dollar payable in 4 months, at what time may the three sums be paid at once, without injustice to either of them? It is evident, that the interest of 1 dollar for 2 months, is the same as the interest of 2 dollars for 1 month; and the interest of 1 dollar for 3 months, is the same as the interest of 3 dollars for 1 month; and the interest of 1 dollar for 4 months, is the same as the interest of 4 dollars for t month: 2 dollars, 3 dollars, and 4 dollars, added together, make 9 dollars for 1 month; but the three sums to be paid, when added together, make only 3 dollars, which sum being only a third part of 9 dollars, the term of credit must be three times as long, or 3 months, which is the equated time. This result is obtained by multiplying the sum, payable in 2 months, by 2; that payable in 3 months, by 3; and that payable in 4 months, by 4; and then adding the several products together, and dividing the sum of them by the sum of the debts. RULE. Multiply each debt by the time, in which it is payable, and divide the sum of the products by the sum of the debts: the quotient will be the equated time. 1. If I owe you 50 dollars payable in 4 months, 75 dollars payable in 6 months, and 100 dollars payable in 7 months, in what time may the three sums be paid at once, without loss to either of us ? 2. A owes B 200 dollars, 40 dollars of which is to be paid in 3 months, 60 dollars in 5 months, and the remainder in 10 months. At what time may the whole be paid at once, without injustice to either party? 3. Bought goods to the amount of 1552 dollars, payable at four different times, as follows; 225 dollars and 75 cents in 4 months, 250 dollars and 25 cents in 6 months, 425 dollars and 50 cents in 8 months, 650 dollars 50 cents in 10 months; but afterward agreed with my creditor to pay him all at once, at the equated time. What was the time ? 4. If I owe you three sums of money payable at different times, viz. 50 pounds in six months, 60 pounds in 7 months, and 80 pounds in 10 months, what is the equated time for paying the whole at once? 5. Bought goods to the amount of 1000 dollars, 200 dollars of which was to be paid down, 400 dollars in 5 months, and the remainder in 15 months; but it was afterward agreed, that the whole be paid at once. In what time ought the payment to be made? 6. A merchant has due to him a certain suin of money, to be paid as follows; Ž in 2 months, } in 3 months, and the rest in 6 months. What is the equated time for paying the whole ? 7. Sold goods amounting to 1296 dollars, of which 346 dollars was to be paid in 2 months, 323 dollars in 6 months, and the balance in 10 months; but the purchaser afterward agreed to make but one payment of the whole. What term of credit ought he to have? 8. Bought goods to the amount of 640 dollars 30 cents, payable down, 1 in 4 months, 1 in 8 months, and the balance in a year; but afterward made an agreement to pay the whole at one time. In what time ought I to pay for the goods? 9. A merchant has due to him $300 to be paid in 60 days, $500 to be paid in 120 days, and $ 750 to be paid in 120 days. What is the equated time for these dues ? 10. A owes B $ 1200, to be paid in 8 months; but A offers to pay $ 400 in 4 months, on condition that the remainder shall continue unpaid an adequate term of time. In what time ought the remainder to be paid ? 11: If a debt of $ 1000 be payable at the end of 7 months, and the debtor agree to pay $ 300 at present, what is the proper time for paying the rest ? XIX PROFIT AND LOSS. The ascertaining what is gained or lost in buying and selling, and the adjusting of the price of goods so as to gain or lose a certain sum, or a certain per cent., come under the head of Profit and Loss. 1. Bought a piece of broadcloth containing 28 yards for 112 dollars, and sold it at 5 dollars 25 cents a yard. How much, and what per cent. was my profit? (See Art. xiv, Example 45.). 2. Bought 3 pieces of broadcloth, containing 28 yards each, at 5 dollars 25 cents a yard. At what price per yard must I sell it, to gain 20 per cent.? 3. Bought cloth at 4 dollars 60 cents a yard, which, not proving so good as I expected, I sold at 3 dollars 91 cents a yard. What per cent. did I lose ? 4. Bought 1250 barrels of flour for 6250 dollars. At what price per barrel must I sell it, to make a profit of 12 per cent.? 5. Bought 30 hogsheads of molasses, at 20 dollars a hogshead, in Havana; paid duties 20 dollars 66 cents; freight 40 dollars 78 cents; porterage 6 dollars 5 cents; insurance 30 dollars 84 cents. What per cent. shall I gain by selling at 26 dollars per hogshead ? 6. Bought wheat at 75 cents a bushel; at what price per bushel must I sell it, to gain 20 per 7. A merchant received from Lisbon 180 casks of raisins, containing 80 lb. each, which cost himn 2 dollarg 18 cents a cask. At what price per cwt. must he sell them, to gain 25 per cent.? 8. If I sell sugar at 8 dollars per cwt., and thereby lose 12 per cent., what per cent. do I gain or lose, by selling the same at 9 dollars per cwt.? 9. If I purchase 6 pipes of wine for 316 dollars, and Sell it at 59 dollars 50 cents a hhd. do I gain or lose, and what per cent. ? cent. ? 10. If you purchase 5cwt. lqr. 12lb. of rice, at 2 dollars 80 cents per cwt., at what price per pound must you sell it, to make 6 dollars on the whole ? 11. If I purchase 13cwt. of coffee at 12į cents per pound, at what price per lb. must I sell it, to gain 80 dollars 8 cents on the whole ? 2. A miller sold a quantity of corn at 1 dollar a bushel, and gained 20 per cent.; soon after, he sold of the same, to the amount of $37.50, and gained 50 per cent. How many bushels were there in the last parcel, and at what did he sell it per bushel ? XX. PARTNERSHIP. PARTNERSHIP is the union of two or more individuals in trade. The company thus associated is called a firm: and the amount of property, which each partner puts into the firm, is called his stock in trade. The profit or loss is shared among the partners, when the stock of each is employed an equal length of time, in proportion to each partner's stock in trade; but, when the stock of the several partners is employed in the firm unequal terms of time, in proportion to each one's stock and the time it was employed. 1. A, B, and C entered into partnership, and the stock of each was employed in the firm one year. A put in 240 dollars, B 360 dollars, and C 120 dollars. They gained 350 dollars. What was each partner's share of the gain? We find in this example, that the whole capital of the firm · was 720 dollars. A's stock was 240 dollars, and he must have 40 of the gain. B's stock was 360 dollars, and he must have 20 of the gain. C's stock was 120 dollars, and he must have 420 of the gain. Observe the following statement. 240 720 360 720 120 720 and 2 of $350. is 116 dollars, A's share, ; and Ž of $350. is 175 dollars, B's share. and of $ 350. is 58} dollars, C's share. $ 350 Proof. 2. Messrs. Ralph Wheeler, Samuel Slade, and James Libbey forined a connexion in business under the firm of Wheeler, Slade, and Libbey. Wheeler pui into the firm 2500 dollars; Slade 2000 dollars; and Libbey 1500 dollars. The stock of the several partners was in trade the same term of time, and they gained 1500 dollars. What was each partner's share of the profit ? 3. Messrs. Joel Haven, Israel Varnam, Tyler Penniman, and James Conant formed a partnership under the firm of Haven, Varnun), and Co. Haven put into the firm 4000 dollars, Varnum 2500 dollars, Penniman 1500 dollars, and Conant 750 dollars. They traded in partnership 3 years, and gained 1750 dollars. How much was each partner's share of gain? 4. A, B, C, and D traded together one year. A put in 800 dollars, B 500 dollars, C 300 dollars, and D 150 dollars; but by misfortune they lost 350 dollars. What loss did each partner sustain ? 5. A gentleman dying, left two sons and a daughter, to whom he bequeathed the following sums; viz. to the elder son 1200 dollars, to the younger, 1000 dollars, and to the daughter 800 dollars; but it was found that his whole estate amounted only to 750 dollars. How much did each child receive from the estate ? 6. Three merchants bought a ship, for which they gave 8000 dollars. A paid 2850 dollars, B 1980 dollars, and C the rest: in her first voyage she cleared 6400 dollars. How much of the profit had each partner? 7. A and B traded together. A put into the firm 540 dollars, and B the rest: they gained 387 dollars, of which B's share was 225 dollars. What was A's gain, and what was B's stock ? 8. The capital stock in the firm of Farmer, Turner and Hancock, was 18477 dollars 60 cents. Farmer's stock was 9238 dollars 80 cents; Turner's 6929 dollars 10 cents; and Hancock's the remainder. The stock |