# 2016 AMC 8 Problems/Problem 3

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

## Solution

We can call the remaining score $r$. We also 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 ten more than 70, for 70 to be the average, the other number must be thirty less than 70, or $\boxed{\textbf{(A)}\ 40}$.

## Video Solution

https://www.youtube.com/watch?v=LqnQQcUVJmA (has questions 1-5)

 2016 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 2 Followed byProblem 4 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions

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