Amanda will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $44 and costs an additional $0.11 per mile driven. The second plan has an initial fee of $53 and costs an additional $0.07 per mile driven.

Question

For what amount of driving do the two plans cost the same?
What is the cost when the two plans cost the same?

Answer 1

Let's denote the number of miles driven as x.

For the first plan:
Cost = $44 + $0.11x

For the second plan:
Cost = $53 + $0.07x

To find when the two plans cost the same, we need to set the two equations equal to each other and solve for x:

$44 + $0.11x = $53 + $0.07x
$0.11x - $0.07x = $53 - $44
$0.04x = $9
x = $9 / $0.04
x = 225 miles

Therefore, the two plans cost the same when 225 miles are driven.
The cost at this point would be:
$44 + $0.11(225) = $44 + $24.75 = $68.75
$53 + $0.07(225) = $53 + $15.75 = $68.75

So, the cost when the two plans cost the same is $68.75.