IMC 2010 Q13
13. At Corbett's Ironmongery a fork handle and a candle cost a total of £6.10. The fork handle costs £4.60 more than the candle. What is the cost of two fork handles and four candles?
- A £14.45
- B £13.70
- C £12.95
- D £12.20
- E £8.35
Intermediate Mathematical Challenge 2010, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B £13.70
Let the prices of a fork handle and a candle be £\(x\) and £\(y\) respectively.
Then \(x + y = 6.1\) and \(x - y = 4.6\). Adding these two equations gives \(2x = 10.7\).
So a fork handle costs £5.35 and a candle costs £0.75.
Therefore the required total is £10.70 + £3.00 = £13.70.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.