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.

Question

Using a graphing calculator, find the number of days for which the costs are the same. Round your answer to the nearest whole day.

Answer 1

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.