Question

a truck can be rented from company A for $120 a day plus $0.40 per mile. Company B charges $70 a day plus $0.50 per mile to rent the same truck. Find the number of miles in a day at which the rental costs for Company A and Company B are the same

Answer 1

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"
$A=120+.4x$

Do the same thing for Company B but with the different numbers
$B=70+.5x$

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)

$A=B$
$120+.4x=70+.5x$

Now use algebra to solve for x
$120+.4x=70+.5x$
$50+.4x=.5x$
$50=.1x$
$\frac{50}{.1} = \frac{.1x}{.1}$
$500=x$

The answer is 500 miles.