2020 AMC 10 B

Complete problem set with solutions and individual problem pages

Problem 3 Easy

The ratio of w to x is 4: 3, the ratio of y to z is 3: 2, and the ratio of z to x is 1: 6. What is the ratio of Wto y ? (2020 AMC 10B, Question #3)

  • A.

    4: 3

  • B.

    3: 2

  • C.

    8: 3

  • D.

    4: 1

  • E.

    16: 3

Answer:E

Solution 1:

WLOG, let w=4 and x=3. Since the ratio of z to x is 1: 6, we can substitute in the value of x to get \frac{z}{3}=\frac{1}{6} \Longrightarrow z=\frac{1}{2} The ratio of y_{\text {to }} z is 3: 2, so \frac{y}{\frac{1}{2}}=\frac{3}{2} \Longrightarrow y=\frac{3}{4} The ratio of w to yis then\frac{4}{\frac{3}{4}}=\frac{16}{3} so our answer is (E)

Solution 2:

We need to somehow link all three of the ratios together. We can start by connecting the last two ratios together by multiplying the last ratio by two. z: x=1: 6=2: 12, and since y: z=3: 2, we can link them together to get y: z: x=3: 2: 12. Finally, since x: w=3: 4=12: 16, we can link this again to get: y: z: x: w=3: 2: 12: 16, so w: y=(\mathbf{E}) 16: 3

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