A rental car company charges \( \$ 50 \) plus 25 cents per each mile driven. Part1. Which of the following could be used to model the total cost of the rental where \( m \) represents the miles driven. \( \begin{array}{l}C=2.5 m+50 \\ C=0.25 m+50 \\ C=25 m+50 \\ \text { Part 2. The total cost of driving } 400 \text { miles is; }\end{array} \)

Let's break down the problem into its two parts. --- ### **Part 1: Modeling the Total Cost** The rental car company's pricing structure is: - **Base Fee:** \$50 - **Variable Fee:** \$0.25 per mile driven To create a mathematical model where \( m \) represents the number of miles driven, we combine the base fee with the variable fee: \[ \text{Total Cost} (C) = \text{Base Fee} + (\text{Cost per Mile} \times \text{Number of Miles}) \] Substituting the given values: \[ C = 0.25m + 50 \] **Among the given options:** 1. \( C = 2.5m + 50 \) → This implies \$2.50 per mile, which is **incorrect**. 2. \( C = 0.25m + 50 \) → This correctly represents \$0.25 per mile, which is **correct**. 3. \( C = 25m + 50 \) → This implies \$25 per mile, which is **incorrect**. **Correct Model:** \[ C = 0.25m + 50 \] --- ### **Part 2: Calculating the Total Cost for 400 Miles** Using the correct model from Part 1: \[ C = 0.25m + 50 \] Substitute \( m = 400 \) miles: \[ C = 0.25 \times 400 + 50 \] \[ C = 100 + 50 \] \[ C = 150 \] **Total Cost for 400 Miles:** \[ \$150 \] --- **Summary:** 1. **Model:** \( C = 0.25m + 50 \) 2. **Total Cost for 400 Miles:** \$150