Difference between revisions of "2017 AMC 10B Problems/Problem 11"
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<math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math> | <math>\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%</math> | ||
| − | ==Video Solution== | + | ==Video Solution & Solution == |
https://youtu.be/93lThricxLE | https://youtu.be/93lThricxLE | ||
~savannahsolver | ~savannahsolver | ||
| + | |||
| + | The number of people who say they dislike dancing but actually like dancing is, <math>60%*20% = 12%</math> and then the number of people who say they dislike dancing and actually do dislike dancing is, <math>40%*90% = 36%</math>. After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have <math>\frac{12%}{12% + 36%}</math> which would then be <math>\frac{12%}{48%}</math> which is <math>\frac{1}{4}</math> or | ||
| + | <math>\boxed{\textbf{(D)}\ 25%}</math> | ||
==See Also== | ==See Also== | ||
{{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}} | {{AMC10 box|year=2017|ab=B|num-b=10|num-a=12}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 23:08, 6 January 2021
Problem
At Typico High School, 
of the students like dancing, and the rest dislike it. Of those who like dancing, 
say that they like it, and the rest say that they dislike it. Of those who dislike dancing, 
say that they dislike it, and the rest say that they like it. What fraction of students who say they dislike dancing actually like it?
Video Solution & Solution
~savannahsolver
The number of people who say they dislike dancing but actually like dancing is, $60%*20% = 12%$ (Error compiling LaTeX. Unknown error_msg) and then the number of people who say they dislike dancing and actually do dislike dancing is, $40%*90% = 36%$ (Error compiling LaTeX. Unknown error_msg). After this, we would want to find out what percent of the whole school says they dislike dancing but like it, so we would have $\frac{12%}{12% + 36%}$ (Error compiling LaTeX. Unknown error_msg) which would then be $\frac{12%}{48%}$ (Error compiling LaTeX. Unknown error_msg) which is 
or
$\boxed{\textbf{(D)}\ 25%}$ (Error compiling LaTeX. Unknown error_msg)
See Also
| 2017 AMC 10B (Problems • Answer Key • Resources) | ||
| Preceded by Problem 10 |
Followed by Problem 12 | |
| 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 AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
