Question

Milan will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $48 and costs an additional $0.20 per mile driven. The

second plan has an initial fee of $57 and costs an additional $0.15 per mile driven.
For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?
If you do not have both of the answers do not bother to reply.

Answer 1

For 180 miles of driving the two plans will cost the same, at a price of $84.

Explanation:

1 - Set up the system of equations

Let x represent the miles driven

Let y represent the cost

First Plan:

y = $48 + $0.20x

Second plan:

y = $57 + $0.15x

Note that both are set equal to y, that means we can substitute y in one equation with the other equation because y = y

2 - Substitute

$57 + $0.15x = y = $48 + $0.20x

$57 + $0.15x = $48 + $0.20x

3 - Get the variables on one side and the constants on the other and then get x alone

$57 + $0.15x = $48 + $0.20x

- $48 - $48

$9 + $0.15x = $0.20x

- $0.15x - $0.15x

$9 = $0.05x

$9/0.05 = $0.05x/0.05

x = 180 Miles

"For what amount of driving do the two plans cost the same?

For 180 miles of driving the two plans will cost the same.

4 - Plug 180 in for x in either equation and solve to find the cost at which they equal

y = $48 + $0.20x

y = $48 + $0.20(180)

y = $48 + $36

y = $84

"What is the cost when the two plans cost the same?"

$84 is the cost when the two plans cost the same

Hope this helps