Greek Anthology Book XIV: Metrodorus: 144

Arithmetical Epigram of Metrodorus

 * $A$. How heavy is the base I have to stand on together with myself!


 * $B$. And my base together together with myself weighs the same number of.


 * $A$. But I alone weigh twice as much as your base.


 * $B$: And I alone weigh three times the weight of yours.

Solution
Presumably $A$ and $B$ are talking statues.

Let $a$ be the weight of $A$.

Let $b$ be the weight of $B$.

Let $c$ be the weight of $A$'s base.

Let $d$ be the weight of $B$'s base.

We have:

We have $3$ simultaneous equations in $4$ unknowns.

Hence we cannot calculate the actual weights, but the proportions only.

So:

So, taking the base of $A$ as a unit, we have:


 * $A$ weighs $4$ times its base


 * $B$ weighs $3$ times the base of $A$


 * the base of $B$ weighs twice the base of $B$.