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

If $\frac{4 a}{b} = 6.7$ and $\frac{a}{b n} = 26.8$ , what is the value of $n$ ?

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Explanation

The correct answer is $.0625$ . It's given that $\frac{4 a}{b} = 6.7$ and $\frac{a}{b n} = 26.8$ . The equation $\frac{4 a}{b} = 6.7$ can be rewritten as $(4) (\frac{a}{b}) = 6.7$ . Dividing both sides of this equation by $4$ yields $\frac{a}{b} = 1.675$ . The equation $\frac{a}{b n} = 26.8$ can be rewritten as $(\frac{a}{b}) (\frac{1}{n}) = 26.8$ . Substituting $1.675$ for $\frac{a}{b}$ in this equation yields $(1.675) (\frac{1}{n}) = 26.8$ , or $\frac{1.675}{n} = 26.8$ . Multiplying both sides of this equation by $n$ yields $1.675 equals 26.8 n$ . Dividing both sides of this equation by $26.8$ yields $n equals 0.0625$ . Therefore, the value of $n$ is $0.0625$ . Note that .0625, 0.062, 0.063, and 1/16 are examples of ways to enter a correct answer.