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\begin{document}

\noindent
\vfil \noindent
\large
\hfil Math 120 A - Spring 2007 \hfil \pp
\hfil Mid-Term Exam Number One Answers\hfil  \pp
\hfil April 19, 2007 \hfil \pp
\normalsize


Version A: In problem 1, Rose will sell 150 tickets if she sets the price at \$20.

\begin{enumerate}

\item Rose should charge \$18.75 to make the most money.

\item 

\begin{enumerate}
\item Area is 0.2 square feet.

\item Area is 1.61538 square feet.

\item 
\[
A(m) = \left\{ \begin{array}{ll}
				2m & \mbox{if $0 \le m \le \frac{1}{2}$} \\
				2 - \frac{1}{2m} & \mbox{if $m > \frac{1}{2}$ } 
			\end{array}
			\right.
\]

\end{enumerate}


\item She will be 16.4915 km south of the center when she is due south of it.

\item 

\begin{enumerate}
\item The multipart rule if 
\[
g(f(x)) = \left\{ \begin{array}{ll}
2x+3 & \mbox{if $x \ge -\frac{3}{2}$} \\
-2x-3 & \mbox{if $x < -\frac{3}{2}$}
\end{array}
\right.
\]

\item $x=\frac{6}{5}$ is the only solution to the equation
$g(f(x))=-3x+9$.

\end{enumerate}
\end{enumerate}


Version B: In problem 1, Rose will sell 174 tickets if she charges \$22.

\begin{enumerate}

\item Rose should charge \$26.77 per ticket to make the most money.

\item \begin{enumerate}
\item Area is 0.6 square feet.
\item Area is 1.6875 square feet.
\item 
\[
A(m) = \left\{ \begin{array}{ll}
				2m & \mbox{if $0 \le m \le \frac{1}{2}$} \\
				2 - \frac{1}{2m} & \mbox{if $m > \frac{1}{2}$ } 
			\end{array}
			\right.
\]
\end{enumerate}

\item She will be 14.4136 km south of the center when she is due south of it.

\item 
\begin{enumerate}
\item 
\[
g(f(x)) = \left\{ \begin{array}{ll}
4x+1 & \mbox{if $x \ge -\frac{1}{4} $} \\
-4x-1 & \mbox{if $x < -\frac{1}{4} $}
\end{array}
\right.
\]
\item The solutions are $x=-3$ and $x=\frac{2}{3}$.
\end{enumerate}


\end{enumerate}

\end{document}


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