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Tickets for a movie cost $5 for children and $9 for adults. If 83 seats were filled, and the box office revenues were $527. 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 \(\displaystyle C+A=83 \qquad 5C+9A=527\). Writing the system as a matrix gives \(\displaystyle \left[\begin{matrix}1 & 1 & 83\\5 & 9 & 527\end{matrix}\right]\). Using RREF gives \(\displaystyle \left[\begin{matrix}1 & 0 & 55\\0 & 1 & 28\end{matrix}\right]\). The number of children's tickets is 55 and the number of adult tickets is 28.
\begin{question}Tickets for a movie cost \$5 for children and \$9 for adults. If 83 seats were filled, and the box office revenues were \$527. 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
$C+A=83 \qquad 5C+9A=527$. Writing the system as a matrix gives $\left[\begin{matrix}1 & 1 & 83\\5 & 9 & 527\end{matrix}\right]$. Using RREF gives $\left[\begin{matrix}1 & 0 & 55\\0 & 1 & 28\end{matrix}\right]$. The number of children's tickets is 55 and the number of adult tickets is 28.}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Tickets for a movie cost $5 for children and $9 for adults. If 83 seats were filled, and the box office revenues were $527. 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=83 \qquad 5C+9A=527 " src="/equation_images/%20%5Cdisplaystyle%20C%2BA%3D83%20%5Cqquad%205C%2B9A%3D527%20" alt="LaTeX: \displaystyle C+A=83 \qquad 5C+9A=527 " data-equation-content=" \displaystyle C+A=83 \qquad 5C+9A=527 " /> . Writing the system as a matrix gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 1 & 83\\5 & 9 & 527\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%2083%5C%5C5%20%26%209%20%26%20527%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 1 & 83\\5 & 9 & 527\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 1 & 83\\5 & 9 & 527\end{matrix}\right] " /> . Using RREF gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 0 & 55\\0 & 1 & 28\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2055%5C%5C0%20%26%201%20%26%2028%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 55\\0 & 1 & 28\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 0 & 55\\0 & 1 & 28\end{matrix}\right] " /> . The number of children's tickets is 55 and the number of adult tickets is 28.</p> </p>