# 2016 AMC 8 Problems/Problem 3

## Problem

Four students take an exam. Three of their scores are $70, 80,$ and $90$. If the average of their four scores is $70$, then what is the remaining score?

$\textbf{(A) }40\qquad\textbf{(B) }50\qquad\textbf{(C) }55\qquad\textbf{(D) }60\qquad \textbf{(E) }70$

## Solutions

### Solution 1

Let $r$ be the remaining student's score. We know that the average, 70, is equal to $\frac{70 + 80 + 90 + r}{4}$. We can use basic algebra to solve for $r$: $$\frac{70 + 80 + 90 + r}{4} = 70$$ $$\frac{240 + r}{4} = 70$$ $$240 + r = 280$$ $$r = 40$$ giving us the answer of $\boxed{\textbf{(A)}\ 40}$.

### Solution 2

Since $90$ is $20$ more than $70$, and $80$ is $10$ more than $70$, for $70$ to be the average, the other number must be $30$ less than $70$, or $\boxed{\textbf{(A)}\ 40}$.

== Video Solution https://youtu.be/R2jD3a5SXAY?si=brG-V2T2JYRkh_qC A solution so simple a 12-year-old made it! ~Elijahman~

## Video Solution

A solution so simple a 12-year-old made it!

~Elijahman~

## Video Solution (THINKING CREATIVELY!!!)

~Education, the Study of Everything

~savannahsolver

~ pi_is_3.14