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

10

Explanation:

Let's call the four numbers x1, x2, x3, and x4. Their average is (x1 + x2 + x3 + x4)/4 = 8, so x1 + x2 + x3 + x4 = 4 × 8 = 32. And we know that three of the numbers have a sum of 22, so x1 + x2 + x3 = 22.

Subtracting this last equation from the first equation, we have:

`\sf:\implies{x4 = 32 - (x1 + x2 + x3) = }`

`\sf:\implies{32 - 22 = 10}`

So the fourth number is 10.

Answer 2

`a+b+c=22\\ \\ (a+b+c+x)/(4)=8\\ \\ a+b+c+x=32\\ \\ 22+x=32\\ \\ \boxed{x=10}`