2006 AMC 8 Problems/Problem 8

Problem

The table shows some of the results of a survey by radiostation KAMC. What percentage of the males surveyed listen to the station?

$\begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & ? & 26 & ?\\ \hline Females & 58 & ? & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular}$

$\textbf{(A)}\ 39\qquad\textbf{(B)}\ 48\qquad\textbf{(C)}\ 52\qquad\textbf{(D)}\ 55\qquad\textbf{(E)}\ 75$

Solution

Filling out the chart, it becomes

$\begin{tabular}{|c|c|c|c|}\hline & Listen & Don't Listen & Total\\ \hline Males & 78 & 26 & 104\\ \hline Females & 58 & 38 & 96\\ \hline Total & 136 & 64 & 200\\ \hline\end{tabular}$

Thus, the percentage of males surveyed that listen to the station is $100 \cdot \frac{78}{104} \%= \boxed{\textbf{(E)}\ 75 \%}$ .

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2006 AMC 8 Problems/Problem 8

Problem

Solution