IMC 2010 Q22
22. Curly and Larry like to have their orange squash made to the same strength. Unfortunately, Moe has put 25 ml of squash with 175 ml of water in Curly's glass and 15 ml of squash with 185 ml of water in Larry's glass. How many millilitres of the mixture in Curly's glass must be put into Larry's glass so that they end up with drinks of the same strength?
- A 5
- B 7
- C 10
- D 12
- E it is not possible
Intermediate Mathematical Challenge 2010, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E it is not possible
Curly's drink has squash and water in the ratio 1: 7, whilst the corresponding ratio for Larry's drink is 3 : 37. This ratio is less than 1 : 7. When some of Curly's mixture is poured into Larry's, the strength will be between 1 : 7 and 3 : 37, but not equal to either.
Solution © UK Mathematics Trust, from the IMC 2010 solutions.