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 .

Step-by-step explanation:

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.

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