Questions: Solve using proportions: A map is drawn to a scale such that 0.5 inch represents 15 miles. A pilot of an airplane measures the distance on the map from Dallas to San Antonio in Texas to be about 7.5 inches. About how many miles is it from Dallas to San Antonio? miles

Solution Steps

To solve this problem, we can set up a proportion based on the given scale. The scale tells us that 0.5 inches on the map represents 15 miles in reality. We need to find out how many miles 7.5 inches on the map represents. We can set up the proportion as follows:

\[ \frac{0.5 \text{ inches}}{15 \text{ miles}} = \frac{7.5 \text{ inches}}{x \text{ miles}} \]

We can then solve for \( x \) by cross-multiplying and dividing.

We are given that 0.5 inches on the map represents 15 miles in reality. We need to find out how many miles 7.5 inches on the map represents. We set up the proportion as follows:

\[ \frac{0.5 \text{ inches}}{15 \text{ miles}} = \frac{7.5 \text{ inches}}{x \text{ miles}} \]

To solve for \( x \), we cross-multiply and divide:

\[ x = \frac{7.5 \text{ inches} \times 15 \text{ miles}}{0.5 \text{ inches}} \]

Performing the calculation:

\[ x = \frac{7.5 \times 15}{0.5} = 225.0 \text{ miles} \]

Final Answer