Greek Anthology Book XIV: 13. - Problem

Problem

 * We both of us together weigh twenty, I, Zethus, and my brother;
 * and if you take the third part of me and the fourth part of Amphion here, you will find it makes six,
 * and you will have found the weight of our mother.

Solution
Let $z$ be the weight in of Zethus.

Let $a$ be the weight in of Amphion.

We have:

So:


 * Zethus weighs $12$


 * Amphion weighs $8$

and (presumably):


 * their mother weighs $6$.