"Cars for you" will rent a car for $11 per day plus $.27 per mile driven. "Rent-a-room" will rent the same car for $26 per day plus $.07 per mile driven.

Question

a) Write an equation that represents the situation when the total rental cost for one day is the same at both rental agencies.

b) For how many miles is the total rental cost for one day the same for each car?

c) If you plan to rent a car for one day, and drive 100 miles, which rental agency should you choose? 

 

Please show work.

Answer 1

Amber,

 

Let m represent miles driven. The total cost will be the cost per day times number of days, plus the total cost for mileage.

 

a) 11 + .27m = 26 + .07m

 

b)

 

11 + .27m = 26 + .07m

11 -11 + .27m = 26 - 11 + .07m

.27m - .07m = 15 + .07m - .07m

.2m = 15

.2m / .2 = 15 / .2

m = 75 miles

 

c) Solve both rates where m = 100

 

11 + .27(100) = $38 for Cars for you

26 + .07(100) = $33 for Rent-a-room (choose this as it is cheapest)

 

 

 

Answer 2

a) 11+0.27x=26+0.07x  where x=number of miles

 

b) solve the above equation

    0.27x-0.07x=26-11

              0.20x=15

              0.2x=15

                 2x=150

                   x=75 miles

 

c) 11+0.27*100=11+27=$38

    26+0.07*100=26+7=$33

    What do you think ?