IMC 2008 Q22
22. At a cinema, a child's ticket costs £4.20 and an adult's ticket costs £7.70. When a group of adults and children went to see a film, the total cost was £\(C\). Which of the following is a possible value of \(C\)?
- A 91
- B 92
- C 93
- D 94
- E 95
Intermediate Mathematical Challenge 2008, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 91
Both £4.20 and £7.70 are multiples of 70p, so £\(C\) must also be a multiple of 70p. Of the options given, only £91 is a multiple of 70p, but it remains to check that a total cost of £91 is possible. If there are 7 children and 8 adults, then the total cost is 7 × £4.20 + 8 × £7.70 = £29.40 + £61.60 = £91.
Solution © UK Mathematics Trust, from the IMC 2008 solutions.