# Lost cents

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

Our Yankee scholars would find so little difficulty in unveiling the mystery, that I only feel justified to present it as a problem for our younger readers. As some of my other riddles have proved too difficult for many beginners who have been interested in these topics, I have decided to act on a very repeated suggestion from 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 the problem of Covent Garden, which I had almost forgotten. It is said that two ladies, street vendors, were selling apples in the market, when Mrs. Smith, for some reason that must be the true mystery that baffled the mathematicians, had to leave and asked Mrs. Jones, the other lady of apples, which will deal with the sale instead.

It seems that they both had the same number of apples, but Mrs. Jones's were larger and she sold them for two cents, while Mrs. Smith sold three of her own for a penny. 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 for five cents.

The next day, when Mrs. Smith returned, all the apples had been sold, but when it was time to share the profits, they discovered that they had earned seven cents less than their share and this difference in the financial market of apples is which has disturbed the mathematical equilibrium for so long.

Assuming that they divided the money equally, the problem is to determine how much money Mrs. Jones lost because of her unfortunate association.

#### Solution

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

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 should have, and of which each lady owned half. Mrs. Jones should have earned 105 cents for her 210 apples, but since she received half of the profit from the sale of 5 apples to 2 cents (that is, 84 cents), she lost 21 cents. Mrs. Smith, on the other hand, who should have received 70 cents for her apples, actually got 85.

The mysterious discrepancy occurs at the end of the seventy combined sale. Ms. Smith's cheap fruit is sold out in the seventieth sale, which consumes 210 apples sold three by three and 140 sold two by two, and at that stage of the game Mrs. Smith was entitled to half the income, and he should have retired with his seventy cents. Since there were only seventy of the big apples left, from that moment on, each sale was three apples for a penny, which really should be sold for two for a penny, and therefore, Mrs. Jones' finances were affected.