3 If 40 of silver, worth 5s. the ourice, be melted wit 8oz. at 4. what is one ounce of this mixture worth? answer 45 4d. 4 A wine merchant mixes 13 gallons of wine at 4s 100 the gallon, with 24 gallons, at 55 6d, and 16 at 6s 3d.4= what is a gallon of this mixture worth? answer 55 76 5 A goldsmith melted together Son. of gold of 22 carats fine, 1b. 8oz. of 21 carats fine, and 10 oz. of 18 carats fine; what is the quality or fineness of the composition? 8 answer 20 carats fine. 6 A refiner melted 5lb. of silver bullion of 80%. fine, with 10lb. of 70%, and 15lb. of 60%. fine; of what fineness is 1lb. of this mass! answer Gaz. 13dwt, 8gr, fine. CASE 2, When the prices of several simples are given, to find how much of each, at their respective rates, must be taken, to make a compound at any proposed price RULE. Write the rates of the simples under each other; link each rate, which is less than the mean rate, with one or more that is greater; the difference or sum of the differences, between each rate and the mean price, placed opposite the respective rate or rates, with which it is linked, will be the several quantities required. Note I. If all the given prices be greater, or lefs than the mean rate, they must be linked to a cipher. Different modes of linking will produce different answers. EXAMPLE S. 1 How much rye at 4s. the bushel, barley at 3s. and oats at 23. will make a mixture worth 25 6d. the bushel? 48 6 at 4 Mean rate 30 367 24. 2 Canary at 25. a quart, Sherry at 16d. and Malaga at Is. how much of each must be taken, that the mixture may be worth is 6d. the quart? 3 A druggist has several sorts of tea, viz, at 12s. per lb. at 11s. at gs. and at 8s. how much of each sort must be taken, to be sold at 10s. per lb. lb. s.p.lb. 2 at 12 II 16. s.p.lb. 16. s.p.lb. 1 at 12 3 ans. 9 4 How much sugar at 4d. at 6d. and at 11d. per pound, must be mixed together, so that the composition may be worth 7d. per lb. answer 1lb. or 1 C.wt. of each, or any other weight of equal quantity. an 5 It is required to mix several sorts of wine, at 35. 55 and 75. per gallon, with water, that the mixture may beworth 4s. per gallon; how much of each sort must the mix-ture consist of? answer 1 gal. wine at 3s. . ditto at 5s. 4 ditto at 757 and 3 gals. water. CASE 3. When the rate of all the simples, the quantity of one of them, and the compound rate of the whole mixture are given, to find the several quantities of the rest; RULE. Place the mean rate, and the several prices, and take their differences, as in case 2; then, As the differences of the same name with the quantity given, Is to rest of the differences respectively; So is the quantity given, To the several quantities required. EXAMPLE $ 02 EXAMPLES. A merchant has 40lb. of tea, at 6s. per 16. which he would mix with some at 55 8d. at 5s 2d. and 4s 6d. per b. how much of each sort must he take, to mix with the 40lb. that he may sell the raixture at 55 5d. per lb. 3+7=100 3+7=10 11+3=14 11+3=14 against the price of the quantity As 14:10:40: 40: } [ 28 at 4s. 6d. and 55.2d. per lb. } ans. per lb. S 2 How much barley at 2s 6d rye at 3s. and wheat at 4s. per bushel, must be mixed with 12 bushels of oats, at 18d. per bushel, that the whole may rate at is 1od. per bushel ? answer bushel of each. 3 How much gold of 16, 20, and 24 carats fine, and how much alloy, must be mixed with roo. of 18 carats fine, that the composition may be 22 carats fine? answer 100%. of 16 carats fine, 10 of 20, 170 of 24 and ro of alloy. 4 Ten bushels of wheat, at 4s. per bushel, with rye at 3s. barley at zs. and oats at 1s. what quantity of these must be mixed with the wheat to rate at 2s 4d. per bushel? 2bu. 20. of rye, S4obu. of rye, 50 barley, oats. Lobu of rye, 3 ans. barley, 4 ans. 14 barley, 14 oats. (14 oats. 12bu. 2p. of rye, 2bu. of rye, barley, barley sobu. of rye, jans. 70 barley, oats. CASE 4. When the rates of the several simples, the quantity to be compounded, and the mean rate thereof are given, to find the quantity of each simple; RULE RULE. Link the several prices, and place their differences as be fore; then, As the sum of the differences, Is to the quantity to be compounded;" EXAMPLES. - 1 A brewer had 3 sorts of beer, viz. at 10d. Sd. and 6d. per gallon; how much of each sort must he take, to make 30 gallons, worth 74. per gallon? 1 As 6 30::1 to 5 gals. at 10d.&8d. 1 6. 30::4 to 20 at 6d. 3+1=4 11/0 6 answer. 2 A druggist compounds medicines, at 4s. 55. and 8s. per lb. to make two parcels, one of 21lb. at 6s. the other of 35lb. at 7s. per lb. what quantity of each must be taken? answer { 6lb. at 4s. } 21/b. at 6s. & { 5lb. at 4s. 5 25 5 8 35lb. at 7s. per lb. 3 A merchant had 4 sorts of coffee, at 8d. 12d. 18d. and 22d. per lb. the worst would not sell, and the best was too dear, he therefore concluded to mix 120/6. what quantity of each must he take, so as to sell at 16d. per lb? answer 36lb. at 8d. 12 at 12d. 24 at 18d. and 48 at 22d. 4 How many gallons of water must be mixed with wine, at 4s. per gallon, so as to fill a vessel of 80 gallons, that may be afforded at 2s 9d. per gallon? answer 25 gallons of water with 55 of wine. 5 A goldsmith has gold of 15, 17, 20 and 22 carats fme, and would melt together of each of these so much, as to make a mass of 40oz. of 18 carats fine; how much of each sort is necessary? answer 16oz. of 15, 4 of 17, 8 of 20 & 12 of 22 carats fine POSITION. POSITION. Po OSITION is a rule for finding an unknown number, by one or more supposed numbers; and is either single or double. SINGLE POSITION. Single position teaches to resolve such questions as require only one supposed number. RULE. Work with a supposed number according to the tenor of the question; then, As the result of that operation, Is to the supposed number; To that required.. PROOF. Work with the answer according to the tenor of the ques tion, and the result must equal the given number. Note. If the refults of two or more fuppofed numbers be in the fame pro portion as the number fuppofed; or If upon working with two fuppofed numbers, and multiplying each of them by the result of the other, the produs be equal, then the quef tion may be folved by fingle pofition, otherwise not. 60 Proof. Result 10 2 B's age is 1 A's; C's twice B's; both with A's make 132 years; how old is each of them? answer A 24, B 36, and C 72 years. |