What value of $x$ makes the mean of the first three numbers in this list equal to the mean of the last four?$$15\qquad 5 \qquad x \qquad 7 \qquad 9 \qquad 17 \qquad$$

This problem is taken from the UKMT Mathematical Challenges.

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