2020 AMC 10B Problem 3

Problem 3 of 25EasierAlgebra

The ratio of

w

x

4:3,

the ratio of

y

z

3:2,

and the ratio of

z

x

1:6.

What is the ratio of

w

y?

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Solution

The ratios give

\begin{aligned} &\frac wx=\frac43,\qquad \frac yz=\frac32, \\ &\quad \frac zx=\frac16. \end{aligned}

Then

\begin{aligned} &\frac wy=\frac wx\cdot\frac xz\cdot\frac zy \\ &\quad =\frac43\cdot 6\cdot\frac23=\frac{16}{3}. \end{aligned}

Therefore

w:y=16:3.

Thus, E is the correct answer.