Greek Anthology Book XIV: 2. - Problem

Problem

 * On a Statue of Pallas

I, Pallas, am of beaten gold, but the gold is the gift of lusty poets. Charisius gave half the gold, Thespis one-eighth, Solon one-tenth, and Themison one-twentieth, but the remaining nine talents and the workmanship are the gift of Aristodicius.

Solution
Let $n$ talents be the weight or worth of the statue of Pallas (it is not clear which is meant, but this detail is immaterial).

Then:
 * $\dfrac n 2$ was given by Charisius


 * $\dfrac n 8$ was given by Thespis


 * $\dfrac n {10}$ was given by Solon


 * $\dfrac n {20}$ was given by Themison


 * $9$ talents were given by Aristodicius.

Thus:

Thus


 * $20$ talents were provided by Charisius


 * $5$ talents were provided by Thespis


 * $4$ talents were provided by Solon


 * $2$ talents were provided by Themison

and the remaining $9$ talents were provided by Aristodicius.

and it is seen that:
 * $20 + 5 + 4 + 2 + 9 = 40$