IMC 2005 Q10
10. Granny has taken up deep-sea fishing! Last week, she 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 9 kg and 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?
- A 18 kg
- B 27 kg
- C 54 kg
- D 77 kg
- E 84 kg
Intermediate Mathematical Challenge 2005, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 54 kg
Let the weights in kg of the head and body of the fish be \(h\) and \(b\) respectively. Then \(h = 9 + \tfrac{1}{3}b\) and \(b = h + 9\). So \(b = 9 + \tfrac{1}{3}b + 9\), that is \(\tfrac{2}{3}b = 18\), which gives \(b = 27\). Hence \(h = 18\), so the whole fish weighed 54 kg.
Solution © UK Mathematics Trust, from the IMC 2005 solutions.