Big fish
Granny has taken up deep-sea fishing! Last week, she caught a fish so big that she had to cut it into three pieces in order to weigh it...
Age
14 to 16
Challenge level
Problem
Granny caught a fish so big that she had to cut it into three pieces (head, body and tail) in order to weigh it.
The tail weighed 9kg.
The head weighed the same as the tail plus one third of the body.
The body weighed as much as the head and tail together.
How much did the whole fish weigh?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
Student Solutions
Answer: $54$ kg
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