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Starting with some gold coins and some empty treasure chests, I tried to put $8$ gold coins in each treasure chest, but that makes $1$ gold short to fill all the chests. So instead I put $6$ gold coins in each treasure chest, but then I had $15$ gold coins left over. How many gold coins did I have? ( adapted from 2017 AMC8, Questions \#17) 
Overseas Competition->Knowledge Point->Calculation Modules->Basic Concepts of Equation->Linear Equations with Multiple Variables
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: $$ \begin{gathered} 8 c-1=g \textbackslash\textbackslash{} 6 c+15=g \end{gathered} $$  Therefore, $8 c-1=6 c+15$. This implies that $c=8$. We therefore have $g=63$. So, our answer is (D) $63$ 