ALLIGATION Medial

ALLIGATION Medial, from the rates and quantities of the simples given, discovers the rate of the mixture.

Rule. As the total quantity of the simples, To their price or value; So any quantity of the mixture, To the rate.

Examp. A grocer mixeth 30lb. of currants, at 4d. per lb. with 10lb. of other currants, at 6d. per lb.: What is the value of 1lb. of the mixture? Ans. 4$\backslash frac\{1\}\{2\}$d.

If 40 : 180 :: 1 : 4$\backslash frac\{1\}\{2\}$.

Note 1. When the quantity of each simple is the same, the rate of the mixture is readily found by adding the rates of the simples, and dividing their sum by the number of simples. Thus,

Suppose a grocer mixes several sorts of sugar, and of each an equal quantity, viz. at 50s. at 54s. and at 60s. per cwt. the rate of the mixture will be 54s. 8d. per cwt. for

Note 2. If it be required to increase or diminish the quantity of the mixture, say, As the sum of the given quantities of the simples, to the several quantities given; so the quantity of the mixture proposed, to the quantities of the simples sought.

Note 3. If it be required to know how much of each simple is an assigned portion of the mixture, say, As the quantity of the mixture, to the several quantities of the simples given; so the quantity of the assigned portion, to the quantities of the simples sought. Thus,

Suppose a grocer mixes 10lb. of raisins with 30lb. of almonds and 40lb. of currants, and it be demanded how many ounces of each sort are found in every pound, or in every 16 ounces of the mixture, say,

Proof 16

Note 4. If the rates of two simples, with the total value and total quantity of the mixture, be given, the quantity of each simple may be found as follows: viz. Multiply the lesser rate into the total quantity, subtract the product from the total value, and the remainder will be equal to the product of the excess of the higher rate above the lower, multiplied into the quantity of the higher-priced simple; and consequently the

said remainder, divided by the difference of the rates, will quote the said quantity. Thus,

Suppose a grocer has a mixture of 400lb. weight, that cost him 7l. 10s. consisting of raisins at 4d. per lb. and almonds at 6d. how many pounds of almonds were in the mixture?