Difference between revisions of "2015 AMC 8 Problems/Problem 15"
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We can see that this is a Venn Diagram Problem. | We can see that this is a Venn Diagram Problem. | ||
First, we analyze the information given. There are <math>198</math> students. Let's use A as the first issue and B as the second issue. | First, we analyze the information given. There are <math>198</math> students. Let's use A as the first issue and B as the second issue. | ||
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<math>149</math> students were for the A, and <math>119</math> students were for B. There were also <math>29</math> students against both A and B. | <math>149</math> students were for the A, and <math>119</math> students were for B. There were also <math>29</math> students against both A and B. | ||
| − | Solving this without a Venn Diagram, we subtract <math>29</math> away from the total, <math>198</math>. Out of the remaining <math>169</math> , we have <math>149</math> people for A and <math>119</math> people for B. We add this up to get <math>268</math> . Since that is more than what we need, we subtract <math>169</math> from <math>268</math> to get <math>\boxed{\text{(D)}~99}</math> | + | |
| + | Solving this without a Venn Diagram, we subtract <math>29</math> away from the total, <math>198</math>. Out of the remaining <math>169</math> , we have <math>149</math> people for A and | ||
| + | |||
| + | <math>119</math> people for B. We add this up to get <math>268</math> . Since that is more than what we need, we subtract <math>169</math> from <math>268</math> to get | ||
| + | |||
| + | <math>\boxed{\text{(D)}~99}</math> | ||
==See Also== | ==See Also== | ||
Revision as of 18:23, 25 November 2015
At Euler Middle School, 
students voted on two issues in a school referendum with the following results: 
voted in favor of the first issue and 
voted in favor of the second issue. If there were exactly 
students who voted against both issues, how many students voted in favor of both issues?
Solution
We can see that this is a Venn Diagram Problem.
First, we analyze the information given. There are students. Let's use A as the first issue and B as the second issue.
students were for the A, and students were for B. There were also students against both A and B.
Solving this without a Venn Diagram, we subtract away from the total, . Out of the remaining 
, we have people for A and
people for B. We add this up to get 
. Since that is more than what we need, we subtract from to get
See Also
| 2015 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
