GK 2018 Q19
19. Amy, Becky and Chloe went shopping. Becky spent only 15 % of what Chloe spent. However, Amy spent 60 % more than Chloe. Together they spent £55. How much did Amy spend?
- A £3
- B £20
- C £25
- D £26
- E £32
Grey Kangaroo 2018, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E £32
Let the amount Chloe spent be £\(x\). Therefore Amy spent £\(1.6x\) and Becky spent £\(0.15x\). The total amount spent is £55 and hence \(x + 1.6x + 0.15x = 55\). Therefore \(2.75x = 55\), which has solution \(x = 20\). Hence Amy spent £(1.6 × 20) = £32.
Solution © UK Mathematics Trust, from the GK 2018 solutions.