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six is the price; the expression how much implies the unknown number of the quantity; and four is the number of the sum. The number of the measure, which is ten, is inversely proportionate to the number of the sum, namely, four. Multiply, therefore, ten by four, that is to say, the two known proportionate numbers by each other; the product is forty. Divide this by the other known number, which is that of the price, namely, six. The quotient is six and two-thirds; it is the unknown number, implied in the words of the question “how much?” it is the quantity, and inversely proportionate to the six, which is the price.
For the second case: Suppose that some one ask this question: “ten for eight, what must be the sum for four?” This is also sometimes expressed thus: “What must be the price of four of them?” Ten is the number of the measure, and is inversely proportionate to the unknown number of the sum, which is involved in the expression how much of the statement. Eight is the number of the price, and this is inversely proportionate to the known number of the quantity, namely, four. Multiply now the two known proportionate numbers one by the other, that is to say, four by eight. The product is thirty-two. Divide this by the other known number, which is that of the measure, namely, ten. The quotient is three and one-fifth; this is the number of the sum, and inversely proportionate to the ten which was the divisor. In this manner all computations in matters of business may be solved.
