Martina is going to rent a truck for one day. There are two companies she can choose from, and they have the following prices. Company A charges $117 and allows unlimited mileage. Company B has an initial fee of $75 and charges an additional $0.70 for every mile driven. For what mileages will Company A charge less than Company B? Use for the number of miles driven, and solve your inequality for .

Let's first determine our inequalities. For Company A, there is unlimited mileage, so you're only paying the set fee of $117. So the equation for A is:

C(x) = 117

For Company B, you're paying a mileage fee plus a set fee. The mileage fee is .70 per mile and can be represented as .7x. The set fee is paid no matter how many miles you drive, where x is the number of miles you drive. So if x = 0, meaning you drive no miles at all, your cost is C(0) = .7(0) + 75 and C(0) = 75. See how that works?

Now for the inequality. We want to know for how many miles is Company A less than Company B:

117 < .7x + 75

Solving that inequality will give you the number of miles:

42 < .7x so

60 < x or, equally,

x > 60

In words this says, "When you drive more than 60 miles, you're paying less for Company A than Company B". If you drive less than 60 miles, Comapny B is cheaper.