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Ye Olde Piero-Polo-Zuanne Problem

Three merchants have invested their money in a partnership, whom to make the problem clearer I will mention by name. The first was called Piero, the second Polo, and the third Zuanne. Piero put in 112 ducats, Polo 200 ducats, and Zuanne 142 ducats. At the end of a certain period they found that they had gained 563 ducats. Required is to know how much falls to each man so that no one shall be cheated.

Solution:

Suggested Solution (Jonathan Stiles & Carley Tallman, WWU students)

Piero = 112 implies 112/454 = a and 563a = 138.89 (about 139) and 112 + 139 = 251

Polo = 200 implies 200/454 = b and 563b = 248.01 (about 248) and 200 + 248 = 448

Zuanne = 142 implies 142/454 = c and 563c = 176.09 (about 176) and 142 + 176 = 381

Checking work, 112 + 200 + 142 = 454 (total to start) and 139 + 248 + 176 = 563 (at end).

So, Piero should have 251 ducats, Polo should have 448 ducats, and Zuanne should have 318 ducats.

Source: Treviso Arithmetic, 1478
[Earliest known printed mathematics book in Europe]