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 (ProblemsAnswer KeyResources)
Preceded by
Problem 6
Followed by
Problem 8
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