Let the miles driven be x;
Let the cost of the plan be c;
The first plan costs (in dollars);
[tex]c=53.96+0.13x[/tex]
Then, the second plan costs (in dollars);
[tex]c=57.96+0.11x[/tex]
When the costs are same, we have;
[tex]53.96+0.13x=57.96+0.11x[/tex]
Simplifying further by collecting like terms, we have;
[tex]\begin{gathered} 0.13x-0.11x=57.96-53.96 \\ 0.02x=4 \\ x=\frac{4}{0.02} \\ x=200 \end{gathered}[/tex]
The miles Ali need to drive so the two plans cost the same is 200 miles.
