2015 AMC 8 Problem 15

Below is the video solution and professionally curated solution for Problem 15 of the 2015 AMC 8, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2015 AMC 8 solutions, or check the answer key.

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Concepts:inclusion-exclusion

Difficulty rating: 1100

15.

At Euler Middle School, 198198 students voted on two issues in a school referendum with the following results: 149149 voted in favor of the first issue and 119119 voted in favor of the second issue. If there were exactly 2929 students who voted against both issues, how many students voted in favor of both issues?

49 49

70 70

79 79

99 99

149 149

Video solution:
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Written solution:

Since 2929 students voted against both, we know that 19829=169198-29 = 169 people voted for at least one.

As we know that 149149 students voted for the first issue, and 119119 students voted for the second issue, and 169169 students that voted for at least one issue, we conclude that the number of students that voted for both is 149+119169=99.149+119-169 = 99.

Thus, the correct answer is D .

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