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?
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:
\[
\boxed{4}
\]
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:
\[
\boxed{4}
\]