Equations
The first plan has no initial fee and costs $0.80 per mile driven. Let's make:
x = number of miles driven
Thus the cost of the first plan is:
C1 = 0.80x
The second plan has an initial fee of $55 and costs $0.30 per mile driven. The total cost of this plan is:
C2 = 55 + 0.30x
It's required to find the number of miles needed to drive for both plans to cost the same, thus we equate C1 = C2 and solve for x.
0.80x = 55 + 0.30x
Subtracting 0.30x:
0.50x = 55
Dividing by 0.50:
x = 55 / 0.50
x = 110
Ivan needs to drive 110 miles for both plans to cost the same