# The manipulated balance

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The money from the East, coined in varying sizes and weights to allow travelers to be deceived, is too complex for our mathematicians, so that when describing trade between Orientals we will simplify things by speaking in dollars and cents.

Camel hair, which is used in the manufacture of shawls and expensive carpets, is gathered by what is called ordinary people and sold through a commission agent, in large or small quantities, to merchants. To ensure impartiality, the commission agent never buys for himself but, upon receiving a purchase order, searches for someone who wishes to sell, and charges two percent of the transaction. However, manipulating the balance, he always manages to increase his profits through deception, especially if the client is inexperienced enough to place confidence in his word or in his pious exclamations.

I take this opportunity to direct attention to a beautiful puzzle related to the transaction that illustrates the simplicity of the methods. Upon receiving a shipment of camel hair, the commissioner placed it on the short arm of his scale, as if to earn one more ounce per pound, but when he sold it he changed the saucers to deliver an ounce less for each pound, and thus earned \$ 25 Thanks to your fraud.

(Remember that one pound is 16 ounces). It seems to be, and really is, a very simple problem, with sufficient clear data. However, it will require the intelligence of an expert accountant to calculate the correct answer to the question: How much did the commission agent pay for the merchandise?

#### Solution

If the intermediary weighed the goods at the rate of one more ounce per pound, he got 17 per pound. When he sold them at the rate of one ounce less per pound, he gave 15 ounces per pound, and earned 2 ounces more. If these 2 ounces were sold at the same price, to earn \$ 25 through deception, it is clear that 2 ounces represent 2/15 of what you paid for everything and charged for the 15 ounces. If 1/15 is worth \$ 12.50, 15/15 or the total, it would be \$ 187.50 which, if the commission did not exist, would be the figure paid for the merchandise.

However, we discovered that he received 2% of the seller, \$ 3.75, and \$ 4.25 from the buyer, for the intermediation, which gave him \$ 8 in addition to the \$ 25 he had earned with his fraud.

Now, if I had been honest, I would have paid for 17 ounces which, to be exact, would have given a total of \$ 199,21875. His percentage for buying and selling would then have been \$ 7,96875, so with his deception he achieved an additional 3 cents and 1/8. As history says that he made exactly \$ 25 with the fraud, we must reduce the price of \$ 187.50 so that his two frauds produce exactly \$ 25.

Now, since 3 cents and 1/8 is exactly 1/801 of \$ 25.03125, we must subtract to \$ 187.50 its 1/801 part, which will give \$ 187.27, so that the intermediary will do, with his fraud, the sum of \$ 25 and 0.0006 cents. For those who wish to be very exact, I would say that the seller is paid \$ 187,2659176029973125 less the 2% commission of \$ 3,745.