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Changing Averages

Age 14 to 16 Short Challenge Level:

A list of integers has a mode of $32$, mean $22$ and median $m$. $m$ is one of the numbers on the list.

The smallest number on the list is $10$. 

If $m$ were replaced with $m + 10$, the mean would be $24$.

If $m$ were instead replaced with $m-8$, the median would be $m - 4$.

What is $m$?



This problem is adapted from the World Mathematics Championships
You can find more short problems, arranged by curriculum topic, in our short problems collection.