AMC8 2016 8, Problem 10

Suppose that $a * b$ means $3a-b.$ What is the value of $x$ if \[2 * (5 * x)=1\]

Solution: Let us plug in $(5 * x)=1$ into $3a-b$. Thus it would be $3(5)-x$. Now we have $2*(15-x)=1$. Plugging $2*(15-x)$ into $3a-b$, we have $6-15+x=1$. Solving for $x$ we have \[-9+x=1\]\[x=\fbox{10}\]

Answer: 10