Greek Anthology Book XIV: 2. - Problem

Problem

On a Statue of Pallas

I, Pallas, am of beaten gold, but the gold is the gift of lusty poets.

Charisius gave half the gold,

Thespis one-eighth,

Solon one-tenth,

and Themison one-twentieth,

but the remaining nine talents and the workmanship are the gift of Aristodicius.

Solution

Let $n$ talents be the weight or worth of the statue of Pallas (it is not clear which is meant, but this detail is immaterial).

Then:

$\dfrac n 2$ was given by Charisius

$\dfrac n 8$ was given by Thespis

$\dfrac n {10}$ was given by Solon

$\dfrac n {20}$ was given by Themison

$9$ talents were given by Aristodicius.

Thus:

\(\ds n\)

\(=\)

\(\ds \dfrac n 2 + \dfrac n 8 + \dfrac n {10} + \dfrac n {20} + 9\)

\(\ds \leadsto \ \ \)

\(\ds 40 n\)

\(=\)

\(\ds 20 n + 5 n + 4 n + 2 n + 360\)

multiplying through by $40$

\(\ds \leadsto \ \ \)

\(\ds 9 n\)

\(=\)

\(\ds 360\)

gathering terms

\(\ds \leadsto \ \ \)

\(\ds n\)

\(=\)

\(\ds 40\)

dividing both sides by $9$

Thus

$20$ talents were provided by Charisius

$5$ talents were provided by Thespis

$4$ talents were provided by Solon

$2$ talents were provided by Themison

and the remaining $9$ talents were provided by Aristodicius.

and it is seen that:

$20 + 5 + 4 + 2 + 9 = 40$

$\blacksquare$

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): $2$. -- Problem