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

Question

For some reason I'm drawing blanks on how to solve this type of question. You have $3$ of $4$ numbers that have a sum of $22$. The average of the $4$ numbers is $8$, so what's the formula for solving for the $4^{th}$ number?

Answer 1

Let $a,b,c,d$ be the number then without loss of generality we have:

$$a+b+c = 22$$

From the second condition we have:

$$\frac{a+b+c+d}{4} = 8 \implies a+b+c+d = 32$$

If we subtract the first eqaution from the second we have:

$$(a+b+c+d) - (a+b+c) = 32 - 22 \implies d = 10$$

Answer 2

Let the four numbers be $a,b,c$ and $d$. Also by the given relations we have, $$a+b+c=22$$ and $$\frac{a+b+c+d}{4}=8$$ or $$d=32-a-b-c=32-22=10$$

Answer 3

Hint. Turn the info on the average into info on the sum of the numbers. Write everything down. Done.