The two plans cost the same for 550 miles of driving and $113.5 is the total cost.
Step-by-step explanation:
This problem is about linear equations. We assume Maya drive X miles, and the total cost is $Y, then we can get like, the first plan has an initial fee of $53 and costs an additional $0.11 per mile driven
For plan 1: Y = 53 + 0.11 X
The second plan has an initial fee of $42 and costs an additional $0.13 per mile driven,
For Plan 2: Y= 42 + 0.13 X
When both plans cost the same, then
Plan 1 = Plan 2
53 + 0.11 X = 42 + 0.13 X
0.13 X - 0.11 X = 53 - 42
0.02 X = 11
[tex]X = \frac{11}{0.02} = 550 \text { miles }[/tex]
Put the value of X in equation of Plan 1, we get,
Y = 53 + 0.11(550) = 53 + 60.5= $113.5
