Sunset rents an SUV at $21.95 plus $0.23 per mile. Sunrise rents the same vehicle for $24.95 plus $0.19 per m?

Question

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 1

Sunset cost = 21.95+0.23m

Sunrise cost = 24.95+0.19m

for m = 0, sunrise cost> sunset cost, but as m increases, the costs become closer until they are equal. Afterwards, it becomes cheaper to rent from sunrise. The even point is when

sunset cost=sunrise cost

or

21.95+0.23m = 24.95+0.19m

0.04m = 3
m = 3/0.04
m = 300/4 = 75 miles.

Therefore if you are going to drive less thn 75 miles, rent from sunset. If you are going to drive more than 75 miles, rent from sunrise.

Answer 2

Step by step:
Set up the equation for each car and set them equal to each other to determine at what mileage they are the same price:
21.95 + 0.23m = 24.95 + 0.19m
get like terms the same side:
0.04m = 3.00
divide through by 0.04 to solve for m:
m = 75
So when both cars have driven 75 miles the cost is the same.
Hope this helps!!

Answer 3

This is easy to set up if we take it one step at a time:

sunset = 21.95 + 0.23m
sunrise = 24.95 + 0.19m

we want a value for m where sunset = sunrise, so:

21.95 + 0.23m = 24.95 + 0.19m
21.95 - 21.95 + 0.23m - 0.19m = 24.95 - 21.95 + 0.19m - 0.19m
0.04m = 3
0.04m/0.04 = 3/0.04
m = 75 miles

Hope this helps!

Answer 4

sunset: c=.23m + 21.95
sunrise: c= .19m + 24.95

.19m + 24.95 = .23m + 21.95 set equal to each other

.19m + 3 = .23m group like terms

3 = .04m group like terms

m = 75 divide

75 miles