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 .

Accepted Solution

Answer: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 + 75Solving that inequality will give you the number of miles:42 < .7x so60 < x or, equally, x > 60In 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.