#### You may also like

Kyle and his teacher disagree about his test score - who is right?

### Tyneside Average Speed

Weekly Problem 12 - 2006
A van travels from Newcastle to South Shields at 30mph and returns at 40mph. What is its average speed?

### For Richer for Poorer

Charlie has moved between countries and the average income of both has increased. How can this be so?

# 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 of the new list would be $24$.

If $m$ were instead replaced with $m-8$, the median of the new list 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.