SOLUTION: Could you please help me with this problem ? Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Could you please help me with this problem ? Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is      Log On


   

Question 7801: Could you please help me with this problem ?
Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per mile. For what mileage is the cost the same? Hint: Using "m" for miles and "c" for cost, write one equation for each rental company.
Answer by prince_abubu(198) About Me  (Show Source):
You can put this solution on YOUR website!
If you're going to drive the Sunset SUV for m miles, it'll cost $21.95 + 0.23m. If you'll rent the Sunrise SUV, you'll pay $24.95 + 0.19m.

It's true that Sunrise makes you pay a higher price up-front but some way down the road (pun intended), it will be a better deal. You want to know how many miles it would take until both deals are break even, so set the equations equal to each other and solve for m.

+21.95+%2B+0.23m+=+24.95+%2B+0.19m+ <---- Start here
+21.95+%2B+0.04m+=+24.95+ <----- subtract 0.19m from both sides
+0.04m+=+3.00+ <---- subtract 21.95 from both sides
+m+=+75+ <----- If you plan to drive exactly 75 miles, you could either choose Sunrise or Sunset and you'll still end up paying the same amount of money. HOWEVER, Sunrise will be a better deal if you plan to drive for more than 75 miles, since you'll only be paying 0.19 per gallon instead of 0.23 per gallon.