# Enigma in the bookstore

Two friends, Alberto and Benito, went to the bookstore together with their children Carlos and Daniel. Everyone bought a book and each book cost an entire amount of euros. Upon leaving, they realized that the two parents had together spent € 21 more than their children and that each of them paid as many euros as books bought. In addition, the difference between the books that Alberto bought and those that Carlos bought was five books.

Who is Daniel's father?

#### Solution

For each couple of father and son it is fulfilled that the father bought X books by X euros and his son bought Y books by Y Euros In addition, the difference between the cost of one and another couple was € 21, so we have to X2 - Y2 = 21.

Given the X and Y They are whole numbers, we have two possible pairs of solutions:
(x = 5, y = 2) y (x = 11, y = 10). Since the difference between the books that Alberto bought and those that Carlos bought was 5 books, Alberto necessarily bought 5 books and Carlos 10 which means that Daniel bought 2 books and that his father is therefore Alberto.