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Tickets for a movie cost $7 for children and $11 for adults. If 114 seats were filled, and the box office revenues were $914. How many children's and now many adult tickets were sold?
Let \(\displaystyle C\) be the number of children's tickets and \(\displaystyle A\) be the number of adult tickets. This gives the system of equations \(\displaystyle C+A=114 \qquad 7C+11A=914\). Writing the system as a matrix gives \(\displaystyle \left[\begin{matrix}1 & 1 & 114\\7 & 11 & 914\end{matrix}\right]\). Using RREF gives \(\displaystyle \left[\begin{matrix}1 & 0 & 85\\0 & 1 & 29\end{matrix}\right]\). The number of children's tickets is 85 and the number of adult tickets is 29.
\begin{question}Tickets for a movie cost \$7 for children and \$11 for adults. If 114 seats were filled, and the box office revenues were \$914. How many children's and now many adult tickets were sold?
\soln{9cm}{Let $C$ be the number of children's tickets and $A$ be the number of adult tickets. This gives the system of equations
$C+A=114 \qquad 7C+11A=914$. Writing the system as a matrix gives $\left[\begin{matrix}1 & 1 & 114\\7 & 11 & 914\end{matrix}\right]$. Using RREF gives $\left[\begin{matrix}1 & 0 & 85\\0 & 1 & 29\end{matrix}\right]$. The number of children's tickets is 85 and the number of adult tickets is 29.}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Tickets for a movie cost $7 for children and $11 for adults. If 114 seats were filled, and the box office revenues were $914. How many children's and now many adult tickets were sold?</p> </p>
<p> <p>Let <img class="equation_image" title=" \displaystyle C " src="/equation_images/%20%5Cdisplaystyle%20C%20" alt="LaTeX: \displaystyle C " data-equation-content=" \displaystyle C " /> be the number of children's tickets and <img class="equation_image" title=" \displaystyle A " src="/equation_images/%20%5Cdisplaystyle%20A%20" alt="LaTeX: \displaystyle A " data-equation-content=" \displaystyle A " /> be the number of adult tickets. This gives the system of equations
<img class="equation_image" title=" \displaystyle C+A=114 \qquad 7C+11A=914 " src="/equation_images/%20%5Cdisplaystyle%20C%2BA%3D114%20%5Cqquad%207C%2B11A%3D914%20" alt="LaTeX: \displaystyle C+A=114 \qquad 7C+11A=914 " data-equation-content=" \displaystyle C+A=114 \qquad 7C+11A=914 " /> . Writing the system as a matrix gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 1 & 114\\7 & 11 & 914\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20114%5C%5C7%20%26%2011%20%26%20914%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 1 & 114\\7 & 11 & 914\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 1 & 114\\7 & 11 & 914\end{matrix}\right] " /> . Using RREF gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 0 & 85\\0 & 1 & 29\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2085%5C%5C0%20%26%201%20%26%2029%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 85\\0 & 1 & 29\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 0 & 85\\0 & 1 & 29\end{matrix}\right] " /> . The number of children's tickets is 85 and the number of adult tickets is 29.</p> </p>