Fred picked four numbers out of a hat. The average of the four numbers is 9. If three of the numbers are 5, 9 and 12, then what is the fourth number?

If the average of 4 numbers is X, then the sum of the
differences between each of the numbers and X has to be equal to
zero.

Here we have the average as 9. Let the fourth number
to be found be D.

So we have the differences as (5-9) , (9
- 9), (12 - 9) and (D-9)

Now , (5-9) + ( 9 -9) + (12 - 9) +
(D-9) = 0

=> -4 + 0 + 3 + D - 9
=0

=> D - 10 =
0

=> D =
10.

Therefore the fourth number is
10.