A scale

A map scale states that every ¼ of an inch represents 20 miles. If two cities are 3½ inches apart, how many miles are actually between the two cities?

Correct answer:

x =  280 mi

Step-by-step explanation:

$$\begin{gathered} a=1/4=\frac{1}{4}=0.25\text{in} \\ b=3\frac{1}{2}=3+\frac{1}{2}=\frac{3\cdot 2+1}{2}=\frac{6+1}{2}=\frac{7}{2}=3.5\text{in} \\ x=20\cdot \frac{b}{a}=20\cdot \frac{\frac{7}{2}}{\frac{1}{4}}=280\text{mi} \end{gathered}$$

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