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Problem-Solving and Data Analysis / Ratios, rates, proportional relationships, and units Difficulty: Medium

The ratio $x$ to $y$ is equivalent to the ratio $9$ to $5$ . If the value of $x$ is $162$ , what is the value of $y$ ?

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Explanation

The correct answer is $90$ . It’s given that the ratio of $x$ to $y$ is equivalent to the ratio $9$ to $5$ . It follows that $\frac{x}{y} = \frac{9}{5}$ . Multiplying each side of this equation by $5 y$ yields $\frac{(5 y) x}{y} = \frac{9 (5 y)}{5}$ , or $5 x equals 9 y$ . Dividing each side of this equation by $9$ yields $\frac{5 x}{9} = y$ . Substituting $162$ for $x$ in this equation yields $\frac{5 (162)}{9} = y$ , which is equivalent to $\frac{810}{9} = y$ , or $90 equals y$ . Therefore, if the value of $x$ is $162$ , the value of $y$ is $90$ .