https://file.aiquickdraw.com/mathbot/file/1726161543962222hta5y.jpg

Let's analyze the problem in the image:

The scale of the map is given as \( \frac{1}{4} \) inch = 1 mile. Sarah measures 12.5 inches on the map between Beaver Falls and Chipmonk Cove.

### To find the real distance between the cities:

1. For every \( \frac{1}{4} \) inch on the map, the real-world distance is 1 mile.
2. We first convert the measured distance (12.5 inches) into how many \( \frac{1}{4} \)-inch units are in 12.5 inches:
   \[
   \text{Number of units} = \frac{12.5 \text{ inches}}{\frac{1}{4} \text{ inch/unit}} = 12.5 \times 4 = 50 \text{ miles}.
   \]

Thus, the cities are **50 miles apart**.

The correct answer is **(c) 50 miles**.

Would you like more details or have any further questions on this?

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Here are 5 related questions to expand on this concept:
1. How would the real distance change if the scale was \( \frac{1}{2} \) inch = 1 mile instead?
2. How do you convert distances on maps with a metric scale (e.g., cm to km)?
3. What is the real distance if Sarah measured 15 inches on the same map?
4. How do you calculate the scale factor when given different units like kilometers and miles?
5. Can you explain how map projections affect distances on maps?

**Tip:** When working with scales, always ensure that units are consistent between the measured map distance and the real-world scale.

Sarah notices her map has a scale of 1/4 inch = 1 mile. She measures 12.5 inches between Beaver Falls and Chipmonk Cove. How far apart are the cities?

Solve a map scale problem where Sarah measures 12.5 inches between Beaver Falls and Chipmonk Cove. This problem demonstrates the use of ratios and proportions to convert map distances to real-world miles, suitable for students in Grades 6-8.

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