4s 6d. another at 4s. and another at 3s. 6d. per bushel; and he would mix an equal quantity of each together; I demand the price of a bushel of this mixture? Ans. 4s. 10. A brewer had several sorts of ale, viz. one sort at 208 per barrel, another at 25s. a third at 30s, and a fourth at 35s per barrel: and he would mix an equal quantity of each together: I demand the price of a barrel. and also of a gallon of this mixture? Ans. 27s 6d per barrel, and 10d Iqr. per gallon. 8 OF ALLIGATION ALTERNATE. Q. What is Alligation Alternate ? A. Alligation Alternate is, when the rate of several things are given to find such quantities of them as are necessary to make a mixture, which may bear a certain rate propounded. Q. How are the rates of prices of the given things to be ordered? A. They must be placed one over mean the other, and the propounded price of rate 7 the composition against them: thus, 4 Prices 5 of the 6 Sim 8 ples. 2 Link the several rates together, in such sort, that one greater than the mean rate may be coupled to another which is less. 3. Take the differences between the mean rate, and the several prices, and place them each against his yoke-fellow and for the rest, observe the following cases. : CASE 1. Q. What do you observe in this first case? A. When the prices of the several things, together with the mean rate of the mixture are given, without any quantity to find how much of each ingredient is required to compose the mixture: take the difference between each price, and the mean rate, and set them alternately, and they will be the quantities required. Q. How are the operations in this and the following cases proved? A. They are all proved by Alligation Medial. EXAMPLES. 1. How much rye at is per bushel. barley at 3s per bushel. and oats at 2s per bushel, will make a mixture warth 2s 6d per bushel? Ans. 6 bushels of rye, ó bels of barley, and 24 bushels o oats 2. How many raisins of the sun at 7d per ib. and Màlaga raisins at 4d per lb. may be mixed together for 6d per Ib? Ans. 2lb. of raisins of the Sun, and lib. Malaga raisins. Note. Questions in this rule do frequently admit of an infinite variety of answers, and all in whole numbers as in this last example, where 2 and 1 do answer the question, yet any other 2 numbers will as truly do the like, that are in the same proportion. [ 4 : 2 3. A grocer would mix three sorts of sugar together, viz. one sort of 100. per lb. another at 7d. and another at 6d. how much of each sort must he take, that the whole mixture may be sold for 8d per lb. lb. d. lb. d lb. d. Ans. 3 at 10: 2 at 7 and 2 at 6 per lb. 4. A malster hath several sorts of malt, viz. one sort at 4s per bushel, another at 3s. 6d. a third at 3s and a fourth at 2s per bushel, and he is desirous to mix so much of each sort together, that the whole may be sold at 2s 6d per bushel; I demand how much he must take of each sort? Bush. s. B. d. B. s. B. 6. Ans. 6 at 4; 6 at 3 6; 6 at 3 and 36 at 2 per bushel. 5. A druggist hath several sorts of tea, viz. one sort at 12s per lb. another at 11s. a third at 9s and a fourth at 8s per lb. I demand how much of each sort he must mix together, that the whole quantity may be afforded at 10s per ib? lb. s.p.lb. $. 2 at 12 3 at 12 Note. These seven answers arise from as many different ways of linking the rates of the simples together. 6. How much alioy must I mix with bullion of 10 oz. fine to abase the same to 8 oz. fine? Ans. to every 8 oz. of bullion of 10 oz. fine, put 2 oz. of alloy, and that will abase it to 8 oz. fine. CASE 2. OF ALTERNATION PARTIAL. Q. What do you observe in this second case? A. When the rates of all the things, the quantity of but one of them, and the mean rate of the whole mixture are given to find the several quantities of the rest in proportion to the quantity given; take the difference between each price, and the mean rate, and place them alternately as in case 1. Then say, As the difference of the same name with the quantity given, Is to the rest of the differences severally; So is the quantity given, To the several quantities required. EXAMPLES 1. A man being determined to mix 10 bushels of wheat, at 4s. per bushel, with rye at 3s. with barley at 2s. and with oats at 1s. per bushel; I demand how much rye, barley and oats, must be mixed with the 10 bushels of wheat, that the whole may be sold at 28d per bushel ? B. 50 of Barley 20 of Oats B. 1 Ans. 40 of Rye 5 O of Barley 2 Ans. 2 of Oats 8 of Rye 14 of Oats B. 2 of Rye 5 Ans. 5 17 0 of Barley 6 Ans. 14 of Barley 10 of Oats B. 50 of Rye 7 Ans. 70 of Barley 20 of Oats 2. A man being determined to mix 12 bushels of oats at 18d per bushel with barley at 2s. 6d. with rye at Ss. and with wheat at 4s per bushel-I demand how much barley, rye and wheat must be mixed with the 12 bushels of oats, that it may bear the price of 22d. per bushel Answ. 1 bushel of each sort. 3. A man being determined to mix 12 bushels of oats at 18d per bushel, with barley at 2s 6d. with rye at 3s. and with wheat at 4s. per bushel-I demand how much barley, rye and wheat must be mixed with the 12 bushels of oats, that the whole may bear the price of 2s 9d per bushel. 10 of Wheat 12 of Wheat B. p. 15 141 of Barley 12 12 of Rye 15 14 1 of Wheat 7 Answer, 12 bushels of each sort. 4. A man being determined to mix 12 bushels of oats, at 18d per bushel, with barley at 2s. 6d. with rye at 3s. and with wheat at 4s per bushel-I demand how much barley, rye and wheat must be mixed with the 12 bushels of oats, that the whole quantity may bear the price of 3s 6d per bushel? 5. A man intends to mix 28 bushels of oats, at 18d per bushel, with barley at 2s. 6d. with rye at 3s. and with wheat at 4s. I would know how much barley, rye and wheat ought to be added to the 28 bushels of oats, that the whole quantity may be afforded at 2s. per bushel? Answer, 4 bushels of each sort. 6. A Farmer would mix 27 bushels of peas, at 18d per bushel, with oats at 28d. and with beans at sod. per bushel, that the whole quantity may bear the price of 20d per bushel-I demand how much oats and beans must be mixed with the 27 bushels of peas? Answer, S bushels of each sort. K CASE 3. OF ALTERNATION TOTAL. Q. What do you observe in this third case? A. When the rates of the several things, the quantity to be compounded, and the mean rate of the whole mixture are given, to find how much of each sort will make up the quantity; place the differences between the several prices, and the mean rate, alternately, as in case 1, then say, As the sum of the differences, Is to the whole composition: So is the difference of each rate, EXAMPLES. 1. A grocer had 4 sorts of sugar, viz. at 8d per lb. at 6d. at 4d and at 2d. per lb. and he would have a composition of an Cwt. worth 5d per lb. I demand how much of each sort he must take? 7 Answ. 28 lb. of each sort. 2. A Vintner hath 4 sorts of Wine, viz. Canary at 10s. per gallon, Malaga at 8s. Rhenish at 6s. and Oporto at 4s. |