To Each His Due

A man has four creditors. To the first he owes 624 ducats; to the second, 546; to the third, 492; and to the fourth 368. It happened that the man defaulted and escaped and the creditors found that his goods amounted to 830 ducats in all. In what ratio should they divide this, and what will be the share of each?

General Trattato di Numeri et Misure (General Treatise on Number and Measure), Tartaglia, 1556

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The answer is: the ratio is 312:273:246:184 shares; the first creditor gets \(\dfrac{51792}{203}\approx 255.13\) ducats, the second gets \(\dfrac{6474}{29}\approx 223.24\) ducats, the third gets \(\dfrac{40836}{203}\approx 201.16\) ducats, and the fourth gets \(\dfrac{30544}{203}\approx 150.46\) ducats

"To Each His Due," Convergence (July 2006)

Convergence