standing debts, and to advance his stock, on being allowed a discount of 17 per cent, to which C assents. Required a state of their respective accounts. 10. A father, ignorant of numbers, ordered £311. 15s. to be divided among his five children, thus: give A (says he), B , C, D, and E. It is required to divide the sum among them, according to the father's intention. 11. Divide 739 acres, 1 rood, among A, B, C, and D, according to their rents, which are: A's £200.; B's £133. 6s. Sd.; C's £113. 7s. 9d.; and D's £78. 11s. 2d. per annum. 12. A, B, and C, pay money into one common stock.-A pays £150, which lies 6 months; B, £160, which lies 8 months; and C, £800, which lies 5 months. They gained £510. 15s.; required each man's share of the gain. 13. Three merchants, A, B, and C, pay money into a common stock. A pays £100, which remains 8 months; B £70, which remains 6 months; and C £50, which remains 10 months. The profits come to £45. Required each partner's share, according to his stock, and the time it was in trade. 14. If a bankrupt's debts amount to £1850. 10s. and his effects to £971. 10s. 3d. Required how much his composition should be per pound. 15. A bankrupt owed £2850, and paid his creditors with £1068. 15s. Required how much he paid per pound. 16. A bankrupt who pays his creditors 10s. 6d., pays in all £1081. 10s. What was the amount of his debts? 17. A merchant, failing in business, offers his creditors 15s. per pound, in 6 months; or equal security, to pay 20s. per pound, at the end of 5 years, without interest. Which of these offers should the creditors accept? ALLIGATION. THIS rule is chiefly employed to resolve questions relating to the mixture of several ingredients together*. CASE I. WHEN THE QUANTITIES AND PRICES OF SEVERAL INGREDIENTS, MIXED TOGETHER, OR GOODS, AT DIFFERENT PRICES, ARE GIVEN, TO FIND THE MEAN PRICE OF ANY PROPOSED QUANTITY. RULE. Divide the whole value by the whole quantity, which will quote the mean price. Or, as the whole quantity is to the whole value, so is any pro posed part to its price. EXAMPLE I. If 35 lb. of tea, at 7s. 6d., 28 lb. at 7s., and 17 lb. at 6s. 8d., were mixed together, what would 1 lb. of the composition be worth? * By this rule the mean or average price of goods sold in different quantities, and at different prices, may also be found. EXAMPLE II. What is the average price, per cwt. of the following quantities of sugar, sold at the following prices? cwt. qr. lb. 30 hhds. weighing, net 451 2 17 at 63s. Od. per cwt. 150 ditto 40 ditto cwt. qr. Ib. S. 451 2 17 at 63 2270 3 14 at 67 2270 3 14 at 67s. 6d. per cwt. 623 1 25 at 74 4 3346 cwt. is 46344 10 3346)258083 0 mean price is 68s. 2d. EXERCISES. 1. If 81 gallons of rum at 18s. 6d.; 47 gallons at 17s. 6d.; and 16 gallons at 15s. were mixed together; what would a gallon of the mixture be worth? 2. If 10 oz. of silver at 5s. 6d.; 9 oz. at 5s. 4d.; and 8 oz. at 5s. 3d. were melted down together; what would an ounce of the composition be worth? 3. If 8 oz. of gold, at 76s. 8d.; 9 oz. at 77s.; 10 oz. at 77s. 6d.; 5 oz. at 77s. 7d.; and 8 oz. at 77s. 8d. per oz. were melted down together; what would an ounce of the composition be worth? 4. Required the average price, per quarter, of the following quantities of wheat; 351 quarters at 63s. per quarter; 333 ditto at 67s. per ditto. CASE II. WHEN THE PRICES OF THE INGREDIENTS ARE GIVEN, TO FIND WHAT QUANTITY OF EACH MUST BE TAKEN TO COMPOSE A MIXTURE, AT A GIVEN PRICE, NONE OF THE QUANTITIES BEING LIMITED. RULE. Place the prices under each other, and the mean price on their left. Link the prices together, so that one greater than the mean price may always be coupled with one less; then place the difference between each price, and the mean on the right of that price with which it is connected. These differences are the respective quantities at the prices on their left. EXAMPLE. A person wishes to mix gold of 18 carats fine, with gold of 19, of 21, and of 23 carats fine; what quantity of each must he take, that the composition may be 22 carats fine? 1. One would mix tea at 8s. per lb. with other kinds at 7s. 6d.; 78.; 6s. 8d.; and 6s. per lb., what quantity of each kind must he take, that the mixture may be worth 7s. 4d. per lb.? 2. One would mix brandy at 8s. 6d. per gallon, with other kinds at 9s.; 9s. 6d.; and 10s.; so that the composition may be worth 9s. 3d. per gallon. What quantity of each must he take? 3. How much alloy must be mixed with bullion, 11 oz. fine, to render the composition only 9 oz. fine? 4. How much sugar at 7d., at 8d., and at 11d., per lb., must be mixed together, to form a composition worth 9d. per lb. ? CASE III. WHEN THE MEAN PRICE, THE PARTICULAR PRICE OF EACH INGREDIENT, AND THE QUANTITY OF ONE OF THE INGREDIENTS ARE GIVEN TO FIND THE QUANTITY OF EACH OF THE OTHERS. RULE. Find the quantities by last case, as if none of them were given; then say, as the difference on the right of the price, whose quantity is given, is to each of the other differences; so is the given quantity to the several quantities sought. EXAMPLE. A goldsmith has 18 oz. of gold, worth 77s. 9d. per oz., and other kinds at 77s. 6d., at 77s. and at 76s. 9d. per oz., of which he wishes to form a mass worth 77s. 4d. per ounce; what quantity of each kind must he take? then, 74: 18: 10 oz. at 77s. 6d. 7 S. d. : 5 :: 18: 129 oz. at 76s 9d. = Proof 463 oz. at 77s. 4d. = 3579 54 EXERCISES. 1. How much sugar, at 8d., at 9d., and at 10d. per lb., must be mixed with 28 lb. at 7d., that the mixture may be worth 94d. per lb.? 2. A goldsmith mixes 16 oz. of silver, at 5s. 8d. per oz., with other kinds, at 5s. 6d. and 5s. 3d, and as much alloy as reduces the mass to 5s. 2d. per oz. Required the weight of the mass. 3. A vintner mixes 8 gallons rum at 16s., and other kinds at 15s. 5d., at 15s., and at 14s. 6d. a gallon, with as much water as reduces the mixture to 12s. per gallon. Required the quantity of each ingredient in the mixture. CASE IV. WHEN THE WHOLE QUANTITY OF THE MIXTURE IS GIVEN, TO FIND THE QUANTITY OF EACH INGREDIENT. |