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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 x² - y² = 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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