Greek Anthology Book XIV: Metrodorus: 117

Arithmetical Epigram of Metrodorus

 * $A$. Where are thy apples gone, my child?


 * $B$. Ino has two-sixths and Semele one-eighth, and Autonoe went off with one-forth, while Agave snatched from my bosom and carried away a fifth. For thee ten apples are left but I, yes I swear it by dear Cypris, have only this one.

Solution
Let $n$ be the total number of apples.


 * $\dfrac {2 n} 6$ were taken by Ino.


 * $\dfrac n 8$ were taken by Semele.


 * $\dfrac n 4$ were taken by Autonoe.


 * $\dfrac n 5$ were taken by Agave.


 * $10$ remained for the child's parent.


 * $1$ remained for the child.

Hence:

So the narrator started with $120$ apples, of which:


 * $40$ were taken by Ino


 * $15$ were taken by Semele


 * $30$ were taken by Autonoe


 * $24$ were taken by Agave

and as we know:


 * $10$ remained for the child's parent

and $1$ remained for the child.

It is understood that $\dfrac {2 n} 6$ is not expressed in canonical form,that is: $\dfrac n 3$, but such is the nature of the epigram.