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Tickets for a movie cost $8 for children and $10 for adults. If 129 seats were filled, and the box office revenues were $1094. 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 \(\displaystyle C+A=129 \qquad 8C+10A=1094\). Writing the system as a matrix gives \(\displaystyle \left[\begin{matrix}1 & 1 & 129\\8 & 10 & 1094\end{matrix}\right]\). Using RREF gives \(\displaystyle \left[\begin{matrix}1 & 0 & 98\\0 & 1 & 31\end{matrix}\right]\). The number of children's tickets is 98 and the number of adult tickets is 31.
\begin{question}Tickets for a movie cost \$8 for children and \$10 for adults. If 129 seats were filled, and the box office revenues were \$1094. 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
$C+A=129 \qquad 8C+10A=1094$. Writing the system as a matrix gives $\left[\begin{matrix}1 & 1 & 129\\8 & 10 & 1094\end{matrix}\right]$. Using RREF gives $\left[\begin{matrix}1 & 0 & 98\\0 & 1 & 31\end{matrix}\right]$. The number of children's tickets is 98 and the number of adult tickets is 31.}
\end{question}
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\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Tickets for a movie cost $8 for children and $10 for adults. If 129 seats were filled, and the box office revenues were $1094. 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=129 \qquad 8C+10A=1094 " src="/equation_images/%20%5Cdisplaystyle%20C%2BA%3D129%20%5Cqquad%208C%2B10A%3D1094%20" alt="LaTeX: \displaystyle C+A=129 \qquad 8C+10A=1094 " data-equation-content=" \displaystyle C+A=129 \qquad 8C+10A=1094 " /> . Writing the system as a matrix gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 1 & 129\\8 & 10 & 1094\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%20129%5C%5C8%20%26%2010%20%26%201094%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 1 & 129\\8 & 10 & 1094\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 1 & 129\\8 & 10 & 1094\end{matrix}\right] " /> . Using RREF gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 0 & 98\\0 & 1 & 31\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2098%5C%5C0%20%26%201%20%26%2031%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 98\\0 & 1 & 31\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 0 & 98\\0 & 1 & 31\end{matrix}\right] " /> . The number of children's tickets is 98 and the number of adult tickets is 31.</p> </p>