Questions: A rental car company charges 63.25 per day to rent a car and 0.07 for every mile driven. Ella wants to rent a car, knowing that: - She plans to drive 50 miles. - She has at most 130 to spend. Write and solve an inequality which can be used to determine x, the number of days Ella can afford to rent while staying within her budget.

Solution Steps

To determine the number of days Ella can afford to rent the car while staying within her budget, we need to set up an inequality that accounts for both the daily rental cost and the cost per mile driven. We then solve this inequality for the number of days, \( x \).

1. Calculate the total cost for driving 50 miles.
2. Set up the inequality for the total cost (daily rental cost plus the cost for miles driven) being less than or equal to $130.
3. Solve the inequality for \( x \).

The cost for driving 50 miles is calculated as follows: \[ \text{Total Mile Cost} = 0.07 \times 50 = 3.50 \]

The total cost for renting the car for \( x \) days, including the cost for miles driven, must be less than or equal to the budget of $130. This can be expressed as: \[ 63.25x + 3.50 \leq 130 \]

To isolate \( x \), we first subtract the total mile cost from both sides: \[ 63.25x \leq 130 - 3.50 \] \[ 63.25x \leq 126.50 \] Next, we divide both sides by 63.25: \[ x \leq \frac{126.50}{63.25} \approx 2.00 \]

Final Answer