Greek Anthology Book XIV: Metrodorus: 123

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Arithmetical Epigram of Metrodorus

Take, my son, the fifth part of my inheritance,
and thou, wife, receive the twelfth;
and ye four sons of my departed son and my two brothers, and thou my grieving mother, take each an eleventh part of the property.
But ye, my cousins, receive twelve talents,
and let my friend Eubulus have five talents.
To my most faithful servants I give their freedom and these recompenses in payment of their service.
Let them receive as follows.
Let Onesimus have twenty-five minae
and Davus twenty minae,
Syrus fifty,
Synete ten
and Tibius eight,
and I give seven minae to the son of Syrus, Synetus.
Spend thirty talents on adorning my tomb and sacrifice to Infernal Zeus.
From two talents let the expense be met of my funeral pyre, the funeral cakes, and grave-clothes,
and from two let my corpse receive a gift.


Solution

Let $n$ be the value in talents of the narrator's inheritance.

To friends and relatives:
$\dfrac n 5$ goes to the son
$\dfrac n {12}$ goes to the wife
$\dfrac {7 n} {11}$ goes to $4$ grandsons, $2$ brothers and mother
$12$ talents go to the cousins
$5$ talents go to Eubulus
To the various servants:
$25$ minae go to Onesimus
$20$ minae go to Davus
$50$ minae go to Syrus
$10$ minae go to Synete
$8$ minae go to Tibius
$7$ minae go to Synetus
In addition
$30$ talents are spent on adorning the tomb and the sacrifice to Zeus
$2$ talents are spent on the funeral pyre, party food and gladrags
$2$ talents are spent on the gift for the corpse ("probably precious ointment", suggests W.R. Paton).


First let us add up the specific amounts.

The servants get:

\(\ds \) \(\) \(\ds 25 + 20 + 50 + 10 + 8 + 7\) minae
\(\ds \) \(=\) \(\ds 120\) minae
\(\ds \) \(=\) \(\ds 2\) talents \(\quad\) as there are $60$ minae to the talent


Thus the total of the specific allocations:

\(\ds \) \(\) \(\ds 12 + 5 + 2 + 30 + 2 + 2\) talents
\(\ds \) \(=\) \(\ds 53\) talents


Finally:

\(\ds n\) \(=\) \(\ds \dfrac n 5 + \dfrac n {12} + \dfrac {7 n} {11} + 53\)
\(\ds \leadsto \ \ \) \(\ds 660 n\) \(=\) \(\ds 132 n + 55 n + 420 n + 660 \times 53\) multiplying through by $660 = \lcm \set {5, 12, 11}$ and simplifying
\(\ds \leadsto \ \ \) \(\ds \paren {660 - 132 - 55 - 420} n\) \(=\) \(\ds 660 \times 53\)
\(\ds \leadsto \ \ \) \(\ds 53 n\) \(=\) \(\ds 660 \times 53\)
\(\ds \leadsto \ \ \) \(\ds n\) \(=\) \(\ds 660\)


So the narrator's inheritance is valued at $660$ talents, of which:

$132$ talents go to the son
$55$ talents go to the wife
$420$ talents go to the $4$ grandsons, $2$ brothers and mother

and the remaining $53$ talents are specifically allocated.

$\blacksquare$


Source of Name

This entry was named for Metrodorus.


Sources

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