How Much to Buy a Horse?

Three men wish to buy a horse but none have a sufficient amount of money for the purchase; to do so, they must borrow from each other. The first asks for \(\frac{1}{2}\) of the second's bezants and \(\frac{1}{3}\) of the third's; the second asks for \(\frac{1}{4}\) of the third's bezants and \(\frac{1}{5}\) of the first's; and the third asks for \(\frac{1}{6}\) of the first's bezants and \(\frac{1}{7}\) of the second's. How much money does each man have and what is the price of the horse? [Find the smallest integer solution.]

Liber Abaci, Leonardo of Pisa, 1202

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