solve a decimal word problem using a linear equation with a variable on both sides

Question

Kaitlin will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of
$53.96
and costs an additional
$0.13
per mile driven. The second plan has an initial fee of
$57.96
and costs an additional
$0.08
per mile driven. How many miles would Kaitlin need to drive for the two plans to cost the same?

Answer 1

Let m = the number of miles driven

First plan: y = 53.96 + .13m

Second plan: y = 57.96 + .08m

53.96 + .13m = 57.96 + .08m

.05m = 4

m = 80 miles