2015 AMC 8 Problems/Problem 15

Revision as of 19:00, 25 November 2015 by Budu (talk | contribs) (Solution)

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 $\boxed{(D) 99}$

See Also

2015 AMC 8 (ProblemsAnswer KeyResources)
Preceded by
Problem 14
Followed by
Problem 16
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All AJHSME/AMC 8 Problems and Solutions

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