## Solution to: Buying Books

For each father-son couple holds: the father bought *x* books of *x* shillings,
the son bought *y* books of *y* shillings.
The difference between their expenses is 21 shillings, thus *x*^{2} - *y*^{2} = 21.

Since *x* and *y* are whole numbers (each book costs a whole amount of shillings),
there are two possible solutions: (*x*=5, *y*=2) or (*x*=11, *y*=10).
Because the difference between Alex and Peter is 5 books, this means that father Alex bought 5 books and son Peter 10.
This means that the other son, Tim, bought 2 books, and that his father is Alex.

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