# Difference between revisions of "2015 AMC 8 Problems/Problem 15"

At Euler Middle School, $198$ students voted on two issues in a school referendum with the following results: $149$ voted in favor of the first issue and $119$ voted in favor of the second issue. If there were exactly $29$ students who voted against both issues, how many students voted in favor of both issues?

$\textbf{(A) }49\qquad\textbf{(B) }70\qquad\textbf{(C) }79\qquad\textbf{(D) }99\qquad \textbf{(E) }149$

## Solution

We can see that this is a Venn Diagram Problem. First, we analyze the information given. There are $198$ students. Let's use A as the first issue and B as the second issue. $149$ students were for the A, and $119$ students were for B. There were also $29$ students against both A and B. Solving this without a Venn Diagram, we subtract $29$ away from the total, $198$. Out of the remaining $169$ , we have $149$ people for A and $119$ people for B. We add this up to get $268$ . Since that is more than what we need, we subtract $169$ from $268$ to get $D$

 2015 AMC 8 (Problems • Answer Key • Resources) Preceded byProblem 14 Followed byProblem 16 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