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


`\frac{x_1+x_2+x_3+x_4}4=8`

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


`\frac{22+x_4}4=8`

Solve for
`x_4`:


`\frac{22+x_4}4=8\implies22+x_4=32\implies x_4=10`