Suppose a car rental agency gives the following choices:
Option A: $30 per day plus 40 cents per mile
Option B: flat $50 per day (unlimited miles)
At what mileage are both rates the same if you rent the car for 3 days?
50 (3) = 30 + 0.40 m
To find the mileage at which both rates are the same, we can set up an equation comparing the total cost of each option.
Let's first calculate the total cost of Option A, which charges $30 per day plus 40 cents per mile:
Total cost of Option A = (Daily rate * Number of days) + (Per mile rate * Number of miles)
Total cost of Option A = (30 * 3) + (0.40 * Number of miles)
Next, let's calculate the total cost of Option B, which charges a flat rate of $50 per day regardless of the number of miles driven:
Total cost of Option B = Flat rate * Number of days
Total cost of Option B = 50 * 3
Now we can set up an equation to find the mileage at which both options have the same total cost:
(30 * 3) + (0.40 * Number of miles) = 50 * 3
Now, let's solve for the number of miles:
90 + 0.40 * Number of miles = 150
0.40 * Number of miles = 60
Number of miles = 60 / 0.40
Number of miles = 150
Therefore, at a mileage of 150, both Option A and Option B will have the same total cost if you rent the car for 3 days.