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

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