# 1992 AHSME Problems/Problem 7

## Problem

The ratio of $w$ to $x$ is $4:3$, of $y$ to $z$ is $3:2$ and of $z$ to $x$ is $1:6$. What is the ratio of $w$ to $y$? $\text{(A) } 1:3\quad \text{(B) } 16:3\quad \text{(C) } 20:3\quad \text{(D) } 27:4\quad \text{(E) } 12:1$

## Solution $\fbox{B}$

Converting from ratios to fractions $\frac{w}{x}=\frac{4}{3}$, $\frac{y}{z}=\frac{3}{2}$, $\frac{z}{x}=\frac{1}{6}$ $\frac{y}{z} \cdot \frac{z}{x} = \frac{3}{2} \cdot \frac{1}{6}$ $\frac{y}{x} = \frac{1}{4}$ $\frac{(\frac{w}{x})}{(\frac{y}{x})}=\frac{\frac{4}{3}}{\frac{1}{4}}$ $\frac{w}{y} = \frac{16}{3}$ $w$ to $y$ is $16:3$

## See also

 1992 AHSME (Problems • Answer Key • Resources) Preceded byProblem 6 Followed byProblem 8 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions

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