2021 April MIMC 10 Problems/Problem 5

Given $x:y=5:3, z:w=3:2, y:z=2:1$, Find $x:w$.

$\textbf{(A)} ~3:1 \qquad\textbf{(B)} ~10:3 \qquad\textbf{(C)} ~5:1 \qquad\textbf{(D)} ~20:3 \qquad\textbf{(E)} ~10:1$

Solution

Clearly, $w$ is the smallest variable here. We can set $w$ to $2$ (other variables also work, but consists more computations). Using our assumption, we can calculate $z=3$, $y=6$, and $x=10$. Therefore, $x:w=10:2=\fbox{\textbf{(C)} 5:1}$.

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