The scale on a map is drawn so that 3.5 inches corresponds to an actual distance of 325 miles. If two cities are 7.75 inches apart on the map, how many miles apart are they? (Round to the nearest tenth) The two cities are miles apart.

To find the distance between the two cities in miles, we can use the scale provided on the map. The scale indicates that 3.5 inches on the map corresponds to 325 miles in real life. Given that the two cities are 7.75 inches apart on the map, we can set up a proportion to find the distance between them in miles: \[ \frac{3.5 \text{ inches}}{325 \text{ miles}} = \frac{7.75 \text{ inches}}{x \text{ miles}} \] Where \( x \) represents the distance between the two cities in miles. Now, we can solve for \( x \) by cross-multiplying and then dividing to find the distance between the two cities in miles. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3.5}{325}=\frac{7.75}{x}\) - step1: Find the domain: \(\frac{3.5}{325}=\frac{7.75}{x},x\neq 0\) - step2: Divide the terms: \(\frac{7}{650}=\frac{31}{4x}\) - step3: Swap the sides: \(\frac{31}{4x}=\frac{7}{650}\) - step4: Rewrite the expression: \(4x=\frac{31\times 650}{7}\) - step5: Divide the terms: \(4x=\frac{20150}{7}\) - step6: Multiply by the reciprocal: \(4x\times \frac{1}{4}=\frac{20150}{7}\times \frac{1}{4}\) - step7: Multiply: \(x=\frac{10075}{14}\) - step8: Check if the solution is in the defined range: \(x=\frac{10075}{14},x\neq 0\) - step9: Find the intersection: \(x=\frac{10075}{14}\) The distance between the two cities is approximately 719.6 miles. Therefore, the two cities are approximately 719.6 miles apart.