Greek Anthology Book XIV: 50. - Problem

Problem
Throw me in, silversmith, besides the bowl itself, the third of its weight, and the fourth, and the twelfth; and casting them into the furnace stir them, and mixing them all up take out, please, the mass, and let it weigh one.

Solution
Let $w$ be the weight in of the bowl.

We have:

Thus the bowl weighs $\dfrac 3 5$ of a.

Assuming $100$ to the, that is, $60$.