One car rental firm charges $125 for a weekend rental and gives unlimited mileage. A second firm charges $95 plus $0.20 a mile. For what range of miles driven is the second firm cheapers. Hint: This is an inequality problem.

Question

One car rental firm charges $125 for a weekend rental and gives unlimited mileage.  A second firm charges $95 plus $0.20 a mile.  For what range of miles driven is the second firm cheapers.  Hint: This is an inequality problem.

anonymous · Answer

As a start, you could write a math equation for both rental firm. Then, you could  compare these.

anonymous · Answer

That was my approach but I'm stuck on how to write the equation.  I was thinking:
0 = 125x and 0 = 95 + 0.20x, is that the right approach?

anonymous · Answer

you don't need to set both equations equal to zero.

But your expressions on the right sides are pretty good.  The first one is for the first company, and the 2nd matches what the 2nd company charges.

The question asks you for the range of miles, x, in which the 2nd firm is cheaper.

So you can take your two expressions and set up the inequality:

1st Firm Cost > 2nd Firm Cost
125x > 0.95 + 0.20x

Then simplify that inequality to isolate "x".... that resulting inequality will tell you the range of miles where Firm 2 is cheaper.

anonymous · Answer

That was a great help, thanks so much.