Let Amy's, Ben's, and Chris's ages be $a$, $b$, and $c$, respectively. We have the equations \begin{align*} \tag{1}
\frac{a+b+c}{3}=6 \Rightarrow a+b+c&=18 \\ \tag{2}
c-4&=a\\ \tag{3}
b+4&=\frac{3}{5}(a+4)
\end{align*} From Equation (3), we have $b=\frac{3}{5}(a+4)-4$. We substitute Equation (2) into Equation (3) to eliminate $a$, to get $b=\frac{3}{5}(c)-4$. Substituting this last equation and Equation (2) into Equation (1) to eliminate $a$ and $b$, we have  \[[c-4]+[\frac{3}{5}(c)-4]+c=18\] Solving for $c$, we find that $c=10$. Thus, Chris's age is $\boxed{10}$.
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<|im_start|>user
The average of Amy's, Ben's, and Chris's ages is 6. Four years ago,  Chris was the same age as Amy is now. In four years, Ben's age will be $\frac{3}{5}$ of Amy's age at that time. How many years old is Chris now?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
10
The average of Amy's, Ben's, and Chris's ages is 6. Four years ago,  Chris was the same age as Amy is now. In four years, Ben's age will be $\frac{3}{5}$ of Amy's age at that time. How many years old is Chris now?
test