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The problem describes a map scale where 4.5 inches represents 450 miles. You are asked to determine how many miles correspond to 8.5 inches on the map.

We can solve this using a proportion:

\[
\frac{4.5 \, \text{inches}}{450 \, \text{miles}} = \frac{8.5 \, \text{inches}}{x \, \text{miles}}
\]

Where \( x \) is the distance in miles we need to find. Let's solve for \( x \):

\[
x = \frac{8.5 \times 450}{4.5}
\]

I'll calculate this.The two cities are 850 miles apart.

Would you like further details or have any questions? Here are five related questions you might explore:

1. How would the distance change if the scale was different (e.g., 3 inches = 450 miles)?
2. How can we convert inches to kilometers instead of miles on this map?
3. What is the formula for scaling distances on a map in general terms?
4. How does this calculation change if the map uses a different unit of measure (e.g., centimeters)?
5. How could we estimate the real-world distance between two cities if the map scale is not provided directly?

**Tip:** When dealing with map scales, it's important to keep the units consistent. Always check if the scale uses the same units for both measurements.

The scale on a map is drawn so that 4.5 inches corresponds to an actual distance of 450 miles. If two cities are 8.5 inches apart on the map, how many miles apart are they? (Round to the nearest tenth)

This problem demonstrates how to solve a proportion using map scales. It involves calculating the actual distance between two cities that are 8.5 inches apart on a map with a scale of 4.5 inches representing 450 miles. Suitable for students in Grades 7-9.

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