First, let's define expressions for the different rental plans. Let x be the miles driven for both of the plans.
We would have the following:
Plan A: $59.96 initial fee, $0.15 per mile driven
[tex]A=59.96+0.15x[/tex]Plan B: $53.96 initial fee, $0.20 per mile driven
[tex]B=53.96+0.20x[/tex]Now, since we want to know the required miles driven for the plans to cost the same, we'll have the relation
[tex]A=B[/tex]This way, we would have the equation
[tex]59.96+0.15x=53.96+0.20x[/tex]Solving for x,
[tex]\begin{gathered} 59.96+0.15x=53.96+0.20x \\ \rightarrow59.96-53.96=0.20x-0.15x \\ \rightarrow6=0.05x \\ \rightarrow x=\frac{6}{0.05} \\ \Rightarrow x=120 \end{gathered}[/tex]Therefore, Tom would have to drive 120 miles for the two plans to cost the same.
ANSWER: 120