Greek Anthology Book XIV: Metrodorus: 144/Historical Note

Historical Note on Metrodorus' Arithmetical Epigram no. $144$
In 's $1918$ translation of, he gives the answer as:


 * From these data not the actual weights but the proportions alone can be determined. The statue $A$ was a third part heavier than $B$, and $B$ only weighed $\dfrac 3 4$ of the statue $A$. The base of $B$ weighed thrice as much as the base of $A$.

This appears to be incorrect

Proof
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.

Let us assume the solution given by.

Let us assume that $B$'s first statement is true.


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

We have:

That is, $B$ weighed $6$ times as much as the base of $A$, which deviates from the initial statement of the problem:


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