Lost cents

We present this riddle known as the Covent Garden problem, and that appeared in London half a century ago accompanied by the surprising statement that he had managed to baffle the best English mathematicians. The problem constantly reappears in one way or another, generally accompanied by the statement that it has baffled European mathematicians, which must be taken with due distrust.

Our Yankees scholars would find so little difficulty in revealing the mystery, that I only feel justified to present it as a problem for our younger readers. As some of my other riddles have proven too difficult for many beginners who have interested in these issues, I have decided to act according to a very repeated suggestion of our younger friends to present some simple problems of a mathematical nature and that everyone should be able to solve.

Well, let's go back to Covent Garden, who had almost forgotten. It is said that two ladies, street vendors, were selling apples in the market, when Mrs. Smith, for some reason that it must be the true mystery that baffled the mathematicians, had to leave and asked Mrs. Jones, the other lady of apples, which will take care of the sale instead.

It seems that both had the same number of apples, but those of Mrs. Jones were lar. After accepting the responsibility of taking care of her partner's apples, Mrs. Jones, wishing to be impartial, mixed all the apples and sold them to five by two cents.

The next day, when Mrs. Smith returned, all apples had been sold, but when it was time to distribute the profits, they discovered that they had gained seven cents less than they were responsible for them and this difference in the financial market of apples is the one that has disturbed the mathematical balance for so long.

Assuming that they divided money into equal parts, the problem is to determine How much money Mrs. Jones lost because of her unfortunate association.

To address the problem from a different point of view, it can be easily demonstrated that apples, if sold 1/3 of penny the small and 1/2 penny the large ones, the average would be 5/6 of penny every two apples , or 25/60 of Centa by apple. But as sold at an average of 5 apples per 2 cents, which is the same as 2/5 or 24/60 of Centa by apple, 1/60 of penny was lost for each block.

Since it is mentioned that 7 cents were lost, we will multiply 60 by 7 to obtain 420 which is the original number of apples that there should be, and from which each lady possessed half. Mrs. Jones should have won 105 cents for her 210 apples, but as she received half of the sale of 5 apples to 2 cents (that is, 84 cents), she lost 21 cents . Mrs. Smith instead, who should have received 70 cents for her apples, actually got 85.

The mysterious discrepancy occurs at the end of the seventy -sized sale. The cheap fruit of the Mrs. Smith is exhausted in the seventieth sale, which consumes 210 apples sold three in three and 140 sold two by two, and at that stage of the game Mrs. Smith had the right to half of the income, and should have been withdrawn with her seventy cents. As only seventy of large apples were left, from that moment, each sale was three apples for a penny, which should really be sold to two by a penny, and therefore, Mrs. Jones's finances were affected.