Suppose we are given 4 numbers 10, 11, 12, 13 and told to calculate the average which is 11.5. This also means that we can replace all numbers with the average and not affect the total viz. 11.5, 11.5, 11.5, 11.5 shall become the new series that shall be same as old one.

This can be used to solve sums. Suppose you have to find a fifth number that increases their average by 0.5.

So new series is 11.5+0.5, 11.5+0.5, 11.5+0.5, 11.5+0.5, 11.5+0.5. So X has to be such that it is 11.5 + 5 * 0.5 = 14