The answer is 500 miles.
So how you go about this problem is to first write an equation for how much each company will cost.
For Company A, it costs $120 plus some more.
The some more part can just be written as .4x where x is the number of miles
(2 miles = .4+.4 = .4(2) =.8)
So for if the cost for Company A is "A"
[tex]A=120+.4x[/tex]
Do the same thing for Company B but with the different numbers
[tex]B=70+.5x[/tex]
Find the number of miles in a day at which the rental costs for Company A and Company B are the same
"The same" here means equal so set the two equations equal to each other (that means the cost of Company A=the cost of Company B or A=B)
[tex]A=B[/tex]
[tex]120+.4x=70+.5x[/tex]
Now use algebra to solve for x
[tex]120+.4x=70+.5x[/tex]
[tex]50+.4x=.5x[/tex]
[tex]50=.1x[/tex]
[tex] \frac{50}{.1} = \frac{.1x}{.1} [/tex]
[tex]500=x[/tex]
The answer is 500 miles.
