6. A map has a scale of 1 inch \( =4 \) miles. a. You measure 3 inches between your house and the movie theater. How many miles is it from your house to the movie theater? b. It is 17 miles to the mall. How many inches is that on the map?

Let's solve each part step by step using the given scale: **1 inch = 4 miles**. ### a. Distance from House to Movie Theater **Given:** - Measured distance on the map = 3 inches **Calculation:** - Since 1 inch represents 4 miles, multiply the number of inches by the scale factor. \[ \text{Actual distance} = 3 \text{ inches} \times 4 \text{ miles/inch} = 12 \text{ miles} \] **Answer:** The distance from your house to the movie theater is **12 miles**. --- ### b. Distance to the Mall on the Map **Given:** - Actual distance to the mall = 17 miles **Calculation:** - To find the map distance, divide the actual distance by the scale factor. \[ \text{Map distance} = \frac{17 \text{ miles}}{4 \text{ miles/inch}} = 4.25 \text{ inches} \] Alternatively, 4.25 inches can be expressed as 4 inches and 1/4 inch. **Answer:** The mall is **4¼ inches** away on the map.