5. The diameter of the moon is 2160 miles. A model has a scale of 1 inch \( =150 \) miles. What is the diameter of the model( inches)?

To determine the diameter of the model Moon based on the given scale, follow these steps: **Given:** - **Actual diameter of the Moon:** 2,160 miles - **Scale of the model:** 1 inch \( = \) 150 miles **Step 1: Understand the Scale** The scale tells us that **1 inch** on the model represents **150 miles** in reality. **Step 2: Set Up the Proportion** To find out how many inches the model's diameter will be, use the following proportion: \[ \frac{1 \text{ inch}}{150 \text{ miles}} = \frac{x \text{ inches}}{2,160 \text{ miles}} \] **Step 3: Solve for \( x \) (the model's diameter in inches)** \[ x = \frac{2,160 \text{ miles} \times 1 \text{ inch}}{150 \text{ miles}} = \frac{2,160}{150} = 14.4 \text{ inches} \] **Answer:** The diameter of the model Moon is **14.4 inches**.