Question

Three of four numbers have a sum of 22. If the average of the four numbers is 8, what is the fourth number?

Answer 1

Let $x_1,\ldots,x_4$ be the four numbers. Their average is 8, so

$\dfrac{x_1+x_2+x_3+x_4}4=8$

You know that three of the numbers have a sum of 22, so

$\dfrac{22+x_4}4=8$

Solve for $x_4$:

$\dfrac{22+x_4}4=8\implies22+x_4=32\implies x_4=10$