Question

Convert the map scale to a unit rate. How many inches represent one mile? Show your work. Interpret the meaning of the unit rate.
3/10 in. = 7/8 mi

Answer 1

So, the scale is on the map is 3/10 inch equals to an actual 7/8 miles, then how many inches are there in 1 mile?

$\bf \begin{array}{ccll} inches&miles\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ \frac{3}{10}&\frac{7}{8}\\\\ x&1 \end{array}\implies \cfrac{\quad \frac{3}{10}\quad }{x}=\cfrac{\quad \frac{7}{8}\quad }{1}\implies \cfrac{\quad \frac{3}{10}\quad }{\frac{x}{1}}=\cfrac{\quad \frac{7}{8}\quad }{\frac{1}{1}}$

$\bf \cfrac{3}{10}\cdot \cfrac{1}{x}=\cfrac{7}{8}\cdot \cfrac{1}{1}\implies \cfrac{3}{10x}=\cfrac{7}{8}\implies 24=70x\implies \cfrac{24}{70}=x\implies \stackrel{inches}{\cfrac{12}{35}=x}$