Question 51
A point $(x, y)$ is selected uniformly at random from the unit square $S=\{(x, y) \mid 0 \leq x \leq 1, 0 \leq y \leq 1\}$. If the probability that $(3x+2y, x+4y)$ is in $S$ is $\frac{a}{b}$, where $a, b$ are relatively prime positive integers, compute $100a+b$.