\(\text{www.the}\beta\text{etafunction.com}\)
Home
Login
Questions: Algebra BusinessCalculus
Please login to create an exam or a quiz.
Tickets for a movie cost $6 for children and $9 for adults. If 99 seats were filled, and the box office revenues were $696. 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 \(\displaystyle C+A=99 \qquad 6C+9A=696\). Writing the system as a matrix gives \(\displaystyle \left[\begin{matrix}1 & 1 & 99\\6 & 9 & 696\end{matrix}\right]\). Using RREF gives \(\displaystyle \left[\begin{matrix}1 & 0 & 65\\0 & 1 & 34\end{matrix}\right]\). The number of children's tickets is 65 and the number of adult tickets is 34.
\begin{question}Tickets for a movie cost \$6 for children and \$9 for adults. If 99 seats were filled, and the box office revenues were \$696. 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
$C+A=99 \qquad 6C+9A=696$. Writing the system as a matrix gives $\left[\begin{matrix}1 & 1 & 99\\6 & 9 & 696\end{matrix}\right]$. Using RREF gives $\left[\begin{matrix}1 & 0 & 65\\0 & 1 & 34\end{matrix}\right]$. The number of children's tickets is 65 and the number of adult tickets is 34.}
\end{question}
\documentclass{article}
\usepackage{tikz}
\usepackage{amsmath}
\usepackage[margin=2cm]{geometry}
\usepackage{tcolorbox}
\newcounter{ExamNumber}
\newcounter{questioncount}
\stepcounter{questioncount}
\newenvironment{question}{{\noindent\bfseries Question \arabic{questioncount}.}}{\stepcounter{questioncount}}
\renewcommand{\labelenumi}{{\bfseries (\alph{enumi})}}
\newif\ifShowSolution
\newcommand{\soln}[2]{%
\ifShowSolution%
\noindent\begin{tcolorbox}[colframe=blue,title=Solution]#2\end{tcolorbox}\else%
\vspace{#1}%
\fi%
}%
\newcommand{\hideifShowSolution}[1]{%
\ifShowSolution%
%
\else%
#1%
\fi%
}%
\everymath{\displaystyle}
\ShowSolutiontrue
\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Tickets for a movie cost $6 for children and $9 for adults. If 99 seats were filled, and the box office revenues were $696. 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=99 \qquad 6C+9A=696 " src="/equation_images/%20%5Cdisplaystyle%20C%2BA%3D99%20%5Cqquad%206C%2B9A%3D696%20" alt="LaTeX: \displaystyle C+A=99 \qquad 6C+9A=696 " data-equation-content=" \displaystyle C+A=99 \qquad 6C+9A=696 " /> . Writing the system as a matrix gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 1 & 99\\6 & 9 & 696\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%201%20%26%2099%5C%5C6%20%26%209%20%26%20696%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 1 & 99\\6 & 9 & 696\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 1 & 99\\6 & 9 & 696\end{matrix}\right] " /> . Using RREF gives <img class="equation_image" title=" \displaystyle \left[\begin{matrix}1 & 0 & 65\\0 & 1 & 34\end{matrix}\right] " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%5B%5Cbegin%7Bmatrix%7D1%20%26%200%20%26%2065%5C%5C0%20%26%201%20%26%2034%5Cend%7Bmatrix%7D%5Cright%5D%20" alt="LaTeX: \displaystyle \left[\begin{matrix}1 & 0 & 65\\0 & 1 & 34\end{matrix}\right] " data-equation-content=" \displaystyle \left[\begin{matrix}1 & 0 & 65\\0 & 1 & 34\end{matrix}\right] " /> . The number of children's tickets is 65 and the number of adult tickets is 34.</p> </p>