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Three inches on a map represent 100 miles. The distance on the map between two cities is
7(1)/(2) inches. What is the actual distance between the cities?

Three inches on a map represent $100$ miles. The distance on the map between two cities is $7 \frac{1}{2}$ inches. What is the actual distance between the cities?

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Pythagorean theorem: word problems

Full solution

Q. Three inches on a map represent

100

miles. The distance on the map between two cities is

7 \frac{1}{2}

inches. What is the actual distance between the cities?

Set up proportion: Set up the proportion based on the map scale. $3$ inches = $100$ miles, so $1$ inch = $\frac{100}{3}$ miles.
Multiply by scale factor: Multiply the distance on the map by the scale factor to find the actual distance. The map distance is $7.5$ inches, so the actual distance is $7.5 \times (100/3)$ miles.
Calculate actual distance: Calculate the actual distance. $7.5 \times \left(\frac{100}{3}\right) = 7.5 \times 33.333\ldots = 250$ miles.

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