Question

A rental car company charges $71.02 per day to rent a car and $0.12 for every mile driven. Lily wants to rent a car, knowing that:
She plans to drive 475 miles.
She has at most $390 to spend.

What is the maximum number of days that Lily can rent the car while staying within her budget?

Answers

GPT-4o mini
To determine the maximum number of days Lily can rent the car while staying within her $390 budget, we will first calculate the total cost associated with her rental, which includes both the daily rental fee and the cost per mile driven.

1. **Calculate the cost for miles driven:**
- Lily plans to drive 475 miles.
- Cost per mile is $0.12.
\[
\text{Total cost for miles} = 475 \text{ miles} \times 0.12 \text{ dollars/mile} = 57 \text{ dollars}
\]

2. **Calculate the total budget after accounting for mileage:**
- Total budget = $390.
- Total cost for miles = $57.
\[
\text{Remaining budget for rental days} = 390 - 57 = 333 \text{ dollars}
\]

3. **Calculate the daily rental cost:**
- Daily rental cost = $71.02 per day.

4. **Determine the maximum number of rental days:**
\[
\text{Number of days} = \frac{\text{Remaining budget for rental days}}{\text{Daily rental cost}} = \frac{333}{71.02}
\]
Calculating this gives:
\[
\text{Number of days} \approx 4.69
\]
Since Lily cannot rent a fraction of a day, we take the integer part, which is 4 days.

5. **Check if the budget allows for 4 days of rental:**
- Total cost for 4 days = \(4 \times 71.02 = 284.08\) dollars.
- Total cost including mileage = \(284.08 + 57 = 341.08\) dollars.

Since $341.08 is within the budget of $390, we verify if she can afford one more day:

6. **Check if the budget allows for 5 days of rental:**
- Total cost for 5 days = \(5 \times 71.02 = 355.10\) dollars.
- Total cost including mileage = \(355.10 + 57 = 412.10\) dollars.

Since $412.10 exceeds the budget of $390, Lily cannot afford 5 days.

Thus, the maximum number of days that Lily can rent the car while staying within her budget is:
\[
\boxed{4}
\]

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