Question

A car rental company offers two plans for renting a car.

Plan A: $30 per day and 10¢ per mile
Plan B: $50 per day with free unlimited mileage
For what range of miles will Plan B save you money?

Answer 1

To find the range of miles where Plan B saves you money, we need to set up an equation where the total cost for each plan is equal and then solve for the number of miles.

Let's say we rent the car for x days and drive y miles.

For Plan A, the total cost would be:

Cost = 30x + 0.1y

For Plan B, the total cost would be:

Cost = 50x

To find the range of miles where Plan B saves you money, we can set these two equations equal to each other and solve for y:

30x + 0.1y = 50x

0.1y = 20x

y = 200x

This tells us that if we drive less than 200x miles, then Plan A will be cheaper. If we drive more than 200x miles, then Plan B will be cheaper.

To find the exact range of miles, we need to know how many days we will be renting the car for. Let's say we rent the car for 5 days:

For Plan A, the total cost would be:

Cost = 30(5) + 0.1y
Cost = 150 + 0.1y

For Plan B, the total cost would be:

Cost = 50(5)
Cost = 250

Now we can set these two equations equal to each other and solve for y:

150 + 0.1y = 250

0.1y = 100

y = 1000

So if we rent the car for 5 days, Plan B will be cheaper if we drive more than 1000 miles. Therefore, the range of miles where Plan B saves you money is more than 1000 miles.