Greek Anthology Book XIV: 11. - Problem

Problem
I desire my two sons to receive the thousand of which I am possessed, but let the fifth part of the legitimate one's share exceed by ten the fourth part of what falls to the illegitimate one.

Solution
Let $s$ be the share received by the legitimate heir.

Then:

Thus the legitimate heir inherits $577 \frac 7 9$, while the illegitimate one receives $1000 - 577 \frac 7 9 = 422 \frac 2 9$.