IMC 2012 Q14
14. What value of \(x\) makes the mean of the first three numbers in this list equal to the mean of the last four?
15 5 \(x\) 7 9 17
- A 19
- B 21
- C 24
- D 25
- E 27
Intermediate Mathematical Challenge 2012, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 19
The mean of the first three numbers is \(\tfrac{1}{3}(20 + x)\); the mean of the last four numbers is \(\tfrac{1}{4}(33 + x)\). Therefore \(4(20 + x) = 3(33 + x)\), that is \(80 + 4x = 99 + 3x\), so \(x = 99 - 80 = 19\).
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).