Question

dan will rent a car for the weekend. he can choose one of two plans. the first plan has an initial fee of $73.98 and costs an additional $0.07 per mile driven. the second plan has an initial fee of $0.12 per mile driven. how many miles for the two plans to cost the same?

Answer 1

1479.6 miles

Step-by-step explanation:

   First plan has an initial fee of $73.98 and an additional $0.07 per mile, while the second plan has a cost of $0.12 per mile.

   The total cost in first plan can be modeled linearly in number of miles as $C_{1}(x)=73.98+0.07x$.

   The total cost in second plan can be modeled linearly in number of miles as $C_{2}(x)=0.12x$

   For both the plans to cost the same, $C_{1}(x)=C_{2}(x)$

$73.98+0.07x=0.12x$

$73.98=0.05x$

$x=1479.6$ miles

∴ On travelling 1479.6 miles, both the plans cost the same.