Challenge Level

Body weighs $b$ kg, head $h$ kg, tail $9$ kg

$h=9+\frac13b$ and $b=h+9$, so $$\begin{align}b&=h+9\\

&=\left(9+\tfrac13b\right)+9\\

&=\tfrac13b+18\\

\Rightarrow\tfrac23b&=18\\

\Rightarrow\ \ b&=27\end{align}$$

So $h=9+\frac13\times27=18$ and the fish weighs $27+18+9=54$ kg

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.