IMC 2010 Q14
14. Given that \(4x - y = 5\), \(4y - z = 7\) and \(4z - x = 18\), what is the value of \(x + y + z\)?
- A 8
- B 9
- C 10
- D 11
- E 12
Intermediate Mathematical Challenge 2010, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 10
Adding the three equations gives \(3x + 3y + 3z = 30\), so \(x + y + z = 10\).
(The equations may be solved to obtain \(x = 2\), \(y = 3\), \(z = 5\). However, as the above method shows, this is not necessary in order to find the value of \(x + y + z\).)
Solution © UK Mathematics Trust, from the IMC 2010 solutions.