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: \[ \boxed{3} \]
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