When renting a car two options listed below are given .Use variables to set up an equation for each option

Question

When renting a car two options listed below are given .You need the car for 3days. How many miles must you travel in order for option 2 to be the better option?Use variables to set up an equation for each option. Graph each line and use the line to answer the question.

OPTION 1:

Daily fee $50

Cost per mile$0.15

Option2:

Daily fee $65

Unlimited miles

Answer 1

3(50) + .15M = 3(65)

3(65-50) = .15M

3(15) =.15M

M = 45/.15 = 300 Miles makes the cost of each option the same

Drive more than 300 Miles and Option 2 is less expensive

For Option One: C(m) = 150+.15m

For Option Two C(m) = 195

the graph of the 1st equation is a slightly upward sloping line y=150+.15x

with slope=.15 and y intercept = 150

2nd equation is a flat horizontal line y=195

Cost measured on the y axis, Miles measured on the x axis

they intersect at (300,195) $195 for 300 miles