# 2017 AMC 10B Problems/Problem 11

## Problem

At Typico High School, $60\%$ of the students like dancing, and the rest dislike it. Of those who like dancing, $80\%$ say that they like it, and the rest say that they dislike it. Of those who dislike dancing, $90\%$ 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?

$\textbf{(A)}\ 10\%\qquad\textbf{(B)}\ 12\%\qquad\textbf{(C)}\ 20\%\qquad\textbf{(D)}\ 25\%\qquad\textbf{(E)}\ 33\frac{1}{3}\%$

## Video Solution & Solution

~savannahsolver

The number of people who say they dislike dancing but actually like dancing is, $60%$ (Error compiling LaTeX. ! Missing $inserted.) times$20%$(Error compiling LaTeX. ! Missing$ inserted.) which is $12%$ (Error compiling LaTeX. ! Missing $inserted.). Then the number of people who say they dislike dancing and actually do dislike dancing is,$40%$(Error compiling LaTeX. ! Missing$ inserted.) times $90%$ (Error compiling LaTeX. ! Missing $inserted.) which is$36%$(Error compiling LaTeX. ! Missing$ inserted.). 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. ! File ended while scanning use of \frac .) which would then be $\frac{12%}{48%} = \frac{1}{4}$ (Error compiling LaTeX. ! File ended while scanning use of \frac .) or $\boxed{\textbf{(D) }\ 25%}$ (Error compiling LaTeX. ! File ended while scanning use of \boxed.)