One car rental agency charges $20 per day plus $0.25 per mile. A different agency charges $37 per day with unlimited mileage. For what mileages is the second rental a better deal? Set up as an inequality
$20 + .25m > $37
Solve for m.
To determine the mileages at which the second rental agency becomes a better deal, we need to compare the costs between the two agencies. Let's denote the number of miles driven as 'm'.
For the first rental agency, the total cost is the sum of the daily charge plus the mileage charge. Therefore, the cost for the first agency is given by the equation:
Cost = 20 + 0.25m
For the second rental agency, the cost is a constant $37 per day, regardless of the number of miles driven.
To figure out when the second rental agency becomes a better deal, we need to set up an inequality by comparing the costs between the two agencies. We want the cost of the second agency to be less than the cost of the first agency. So the inequality is:
37 < 20 + 0.25m
Simplifying the inequality:
37 - 20 < 0.25m
17 < 0.25m
Now, divide both sides of the inequality by 0.25 to isolate 'm':
(17/0.25) < m
68 < m
Therefore, the inequality representing the mileages at which the second rental agency is a better deal is m > 68. In other words, for any mileage greater than 68 miles, the second rental agency will be a better deal than the first agency.