To determine the number of days \( d \) that Xin can afford to rent the car, we need to account for both the daily rental fee and the cost per mile driven.
The rental car company's charges are:
- Daily rental fee: $24 per day, so for \( d \) days, the total charge is \( 24d \).
- Mileage charge: $0.10 per mile. If Xin drives 200 miles, the total charge for the mileage is \( 0.10 \times 200 = 20 \) dollars.
Now we can express the total cost \( C \) of renting the car for \( d \) days as: \[ C = 24d + 20 \]
Since Xin has a budget of at most $140, we can write the inequality: \[ 24d + 20 \leq 140 \]
Next, we will solve this inequality for \( d \).
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First, subtract 20 from both sides: \[ 24d \leq 140 - 20 \] \[ 24d \leq 120 \]
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Now, divide both sides by 24: \[ d \leq \frac{120}{24} \] \[ d \leq 5 \]
Thus, the solution to the inequality is: \[ d \leq 5 \]
This means that Xin can rent the car for a maximum of 5 days while staying within her budget of $140.