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: $$ \begin{gathered} 15 c-15=g \textbackslash\textbackslash{} 12 c+6=g \end{gathered} $$  Therefore, $15 c-15=12 c+6$. This implies that $c=7$. We therefore have $g=90$. So, our answer is (E) $90$ 
Starting with some gold coins and some empty treasure chests, I tried to put $15$ gold coins in each treasure chest, but that left $$1$$ treasure chests empty. So instead I put $12$ gold coins in each treasure chest, but then I had $6$ gold coins left over. How many gold coins did I have? ( adapted from 2017 AMC8, Questions \#17) 
A. $$36$$ 
B. $$49$$ 
C. $$75$$ 
D. $$84$$ 
E. $$90$$ 