2014 AMC 12A Problems/Problem 2

Problem

At the theater children get in for half price. The price for $5$ adult tickets and $4$ child tickets is $24.50$ . How much would $8$ adult tickets and $6$ child tickets cost?

$\textbf{(A) }35\qquad \textbf{(B) }38.50\qquad \textbf{(C) }40\qquad \textbf{(D) }42\qquad \textbf{(E) }42.50$

Solution

Suppose $x$ is the price of an adult ticket. The price of a child ticket would be $\frac{x}{2}$ .

\begin{eqnarray*}
5x + 4(x/2) = 7x &=& 24.50\\

x &=& 3.50\\
\end{eqnarray*} (Error compiling LaTeX. Unknown error_msg)

Plug in for 8 adult tickets and 6 child tickets.

\begin{eqnarray*}

8x + 6(x/2) &=& 8(3.50) + 3(3.50)\\ 
&=&\boxed{\textbf{(B)}\ \ 38.50}\\

\end{eqnarray*} (Error compiling LaTeX. Unknown error_msg)

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2014 AMC 12A Problems/Problem 2

Problem

Solution