On a tourist map, 3 cm represents 180 km of distance. How many kilometers does 7.5 cm represent on the same map?

Step-by-step solution

1. The map scale is $3\text{cm}:180\text{km}$.
2. Set up the proportion $\frac{3}{180}=\frac{7.5}{x}$ where $x$ is the real distance for 7.5 cm.
3. Cross multiply: $3x=180\times 7.5$.
4. Compute $180\times 7.5=1350$.
5. Solve $3x=1350$ to get $x=450$.
6. Thus 7.5 cm on the map represents 450 km.

Concept tested: Using proportions to convert map scale

Published 4 October 2026 · How this solution was prepared and checked