Question 56
Squares $ABCD$ and $DEFG$ have side lengths $1$ and $\frac{1}{3}$, respectively, where $E$ is on $\overline{CD}$ and points $A$, $D$, $G$ lie on a line in that order. Line $CF$ meets line $AG$ at $X$. The length $AX$ can be written as $\frac{m}{n}$, where $m, n$ are positive integers and $\operatorname{gcd}(m, n)=1$. Find $100m+n$.