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Weekly Problem 21 - 2007

Stage: 3 and 4 Challenge Level: Challenge Level:1

54kg

Let the weights in kilograms of the head and body of the fish be $h$ and $b$ respectively. Then $h = 9 + \frac{1}{3} b$ and $b = h+9$. So $b = 9 + \frac{1}{3} b + 9$, that is, $\frac{2}{3} b = 18$, which gives $b = 27$. Hence $h = 18$, so the whole fish weighed 54kg.

This problem is taken from the UKMT Mathematical Challenges.

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