2020 AMC 12B 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

Let

x = 6.

From

z : x = 1 : 6,

we get

z = 1.

From

w : x = 4 : 3,

we get

w = \tfrac43 \cdot 6 = 8.

From

y : z = 3 : 2,

we get

y = \tfrac32 \cdot 1 = \tfrac32.

Therefore

w : y = 8 : \tfrac32 = 16 : 3.

Thus, the correct answer is E.

Concepts: ratio and proportion

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.