The sum of the three numbers x, y and z is 3x, so y + z = 2x.

So the mean of y and z is the same as the mean of 2x.

Therefore the mean of y and z is x.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Creating and manipulating expressions and formulae. Simultaneous equations. Generalising. Mathematical reasoning & proof. Expanding and factorising quadratics. Regular polygons and circles. Inequalities. Polynomial functions and their roots. Working systematically. Circle properties and circle theorems.