To determine how many days \( x \) Bilquis can afford to rent a car while staying within her budget, we need to formulate an inequality based on the costs.
The rental car company charges:
- $48 per day for renting the car
- $0.08 per mile driven
Bilquis plans to drive 175 miles, so the cost for miles can be calculated as follows: \[ \text{Cost for miles} = 0.08 \times 175 \]
Calculating that: \[ 0.08 \times 175 = 14 \]
Now, let's define the total cost for renting the car. The total cost \( C \) is given by: \[ C = 48x + 14 \] where \( x \) is the number of days she rents the car.
Since Bilquis has at most $110 to spend, we set up the inequality: \[ 48x + 14 \leq 110 \]
Next, we will solve this inequality for \( x \):
- Subtract 14 from both sides: \[ 48x \leq 110 - 14 \] \[ 48x \leq 96 \]
- Divide both sides by 48: \[ x \leq \frac{96}{48} \] \[ x \leq 2 \]
Thus, the solution to the inequality indicates that Bilquis can afford to rent the car for a maximum of 2 days while staying within her budget of $110.
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