Question

A rental car company charges $61.79 per day to rent a car and $0.13 for every mile driven. Tallulah wants to rent a car, knowing that:
She plans to drive 50 miles.
She has at most $230 to spend.

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

Answer 1

To determine how many days Tallulah can rent the car without exceeding her budget of $230, we first need to calculate the total cost based on the daily rental rate and the mileage charge.

The rental car company charges:
- Daily rate: $61.79
- Mileage charge: $0.13 per mile

Given that Tallulah plans to drive 50 miles, we calculate the mileage cost first:
\[
\text{Mileage cost} = 50 \text{ miles} \times 0.13 \text{ dollars/mile} = 6.50 \text{ dollars}
\]

Next, we calculate the total cost for renting the car for \( d \) days, which includes both the daily rental fee and the mileage cost:
\[
\text{Total cost} = \text{Daily cost} + \text{Mileage cost} = (61.79 \times d) + 6.50
\]

We know that this total cost must be less than or equal to Tallulah's budget of $230:
\[
(61.79 \times d) + 6.50 \leq 230
\]

To isolate \( d \), we start by subtracting the mileage cost from both sides:
\[
61.79 \times d \leq 230 - 6.50
\]
\[
61.79 \times d \leq 223.50
\]

Next, we divide both sides by 61.79 to solve for \( d \):
\[
d \leq \frac{223.50}{61.79}
\]
Calculating the right-hand side:
\[
d \leq 3.61
\]

Since \( d \) must be a whole number (as she can only rent the car for entire days), we round down:
\[
d \leq 3
\]

Thus, the maximum number of days Tallulah can rent the car while staying within her budget of $230 is:
\[
\boxed{3}
\]