Starting with some gold coins and some empty treasure chests, I tried to put $9$ gold coins in each treasure chest, but that left $2$ treasure chests empty.  So instead I put $6$ gold coins in each treasure chest, but then I had $3$ gold coins left over.  How many gold coins did I have?
$\textbf{(A) }9\qquad\textbf{(B) }27\qquad\textbf{(C) }45\qquad\textbf{(D) }63\qquad\textbf{(E) }81$
We can represent the amount of gold with $g$ and the amount of chests with $c$. We can use the problem to make the following equations:
\[9c-18 = g\]
\[6c+3 = g\]
We do this because for 9 chests there are 2 empty and if 9 were in each 9 multiplied by 2 is 18 left.
Therefore, $6c+3 = 9c-18.$ This implies that $c = 7.$ We therefore have $g = 45.$ So, our answer is $\boxed{\textbf{(C)}\ 45}$.
~CHECKMATE2021