Greek Anthology Book XIV: Metrodorus: 122

Arithmetical Epigram of Metrodorus

After staining the holy chaplet of fair-eyed Justice that I might see thee, all-subduing gold, grow so much, I have nothing;

for I gave forty talents under evil auspices to my friends in vain,

while, O ye varied mischances of men, I see my enemy in possession of the half, the third, and the eighth of my fortune.

Solution

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

We have:

\(\ds n\)

\(=\)

\(\ds 40 + \dfrac n 2 + \dfrac n 3 + \dfrac n 8\)

\(\ds \leadsto \ \ \)

\(\ds 24 n\)

\(=\)

\(\ds 12 n + 8 n + 3 n + 24 \times 40\)

multiplying through by $24 = \lcm \set {2, 3, 8}$ and simplifying

\(\ds \leadsto \ \ \)

\(\ds \paren {24 - 12 - 8 - 3} n\)

\(=\)

\(\ds 24 \times 40\)

\(\ds \leadsto \ \ \)

\(\ds n\)

\(=\)

\(\ds 24 \times 40\)

\(\ds \)

\(=\)

\(\ds 960\)

\(\ds \)

\(=\)

\(\ds 40 + 480 + 320 + 120\)

So the narrator started with $960$ talents.

$\blacksquare$

Source of Name

This entry was named for Metrodorus.

Sources

• 1918: W.R. Paton: The Greek Anthology Book XIV ... (previous) ... (next): Metrodorus' Arithmetical Epigrams: $122$