\documentclass{article}
\usepackage{mwe} % new package from Martin scharrer
\usepackage{lipsum,caption,mathtools}
\usepackage{comment}
\usepackage{mdframed}
\usepackage[dvipsnames*,svgnames]{xcolor}
\includecomment{Answer}
\mdfdefinestyle{mystyle}{leftmargin=0pt,%
linecolor=Lavender,backgroundcolor=Ivory}
\setlength{\parindent}{0in}
\begin{document}
\section*{Problem 1}
\paragraph*{a) } Prove that donkeys can fly if and only if they have more arms than penguins. \medskip
\begin{mdframed}[style=mystyle]
\lipsum[1]
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\begin{figure}[!htbp]
\centering
\includegraphics[width=3.0in]{example-image-a}
\caption{Caption for image}
\label{fig:some figure to accompany the answers}
\end{figure}
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\lipsum[2]
Q.E.D
\end{mdframed}
\newpage
\section*{Problem 2}
\paragraph*{a) } If $(x+y)^2=99$ and $x^2+y^2 = 11$ what is $x\cdot y$? \medskip
\begin{Answer}
\begin{mdframed}[style=mystyle]
\lipsum[2]
\begin{align*}
(x+y)^2 & = 99 \\
x^2 + y^2 + 2x\cdot y & = 99 \\
x\cdot y & = 44 \\
\end{align*}
\lipsum[3]
Q.E.D
\end{mdframed}
\end{Answer}
\medskip
Now is it posible finding $x-y$ from the information above? \medskip
\begin{Answer}
\lipsum[6]
Therefore it is not possible finding $x-y$ from the information given.
\end{Answer}
\end{document}