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, $60$.