Greek Anthology Book XIV: Metrodorus: 118

Arithmetical Epigram of Metrodorus

 * Myrto once picked apples and divided them among her friends;
 * she gave the fifth part to Chrysis,
 * the fourth to Hero,
 * the nineteenth to Psamathe,
 * and the tenth to Cleopatra,
 * but she presented the twentieth part to Parthenope
 * and gave only twelve to Evadne.


 * Of the whole number a hundred and twenty fell to herself.

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


 * $\dfrac n 5$ were given to Chrysis.


 * $\dfrac n 4$ were given to Hero.


 * $\dfrac n {19}$ were given to Psamathe.


 * $\dfrac n {10}$ were given to Cleopatra.


 * $\dfrac n {20}$ were given to Parthenope.


 * $12$ were given to Evadne.


 * $120$ were kept by Myrto.

Hence:

So the narrator started with $380$ apples, of which:


 * $76$ were given to Chrysis


 * $95$ were given to Hero


 * $20$ were given to Psamathe


 * $38$ were given to Cleopatra


 * $19$ were given to Parthenope

and as we know:


 * $12$ were given to Evadne

and $120$ were kept by Myrto.