A rental car agency charges a flat fee of $110.00 plus $46.00 per day to rent a certain car. Another agency charges a fee of $70.00 plus $54.00 per day to rent the same car.
Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.
Let's define the cost function for each agency:
Agency A: Cost_A(d) = 110 + 46d
Agency B: Cost_B(d) = 70 + 54d
Where d is the number of days.
To find the number of days for which the costs are the same, we need to solve the equation:
Cost_A(d) = Cost_B(d)
110 + 46d = 70 + 54d
Subtracting 46d and 70 from both sides:
40 = 8d
Dividing both sides by 8:
d = 5
So the costs are the same for 5 days.