Question

Jenny will rent a car for the weekend. She can choose one of two plans. The first plan has an initial fee of $57.98 and costs an additional $0.14 per mile driven. The second plan has an initial fee of 53.98 and costs an additional $0.16 per mile driven. How many miles would Jenny need to drive for the two plans to cost the same?

Answer 1

Answer:

$\boxed{\textbf{200 mi}}$

Step-by-step explanation:

Let x = number of miles driven

Plan 1:  Cost = $57.98 + $0.14x

Plan 2: Cost = $53.98 + $0.16x

Set the costs of the two plans equal.

$\begin{array}{rc ll}\ 57.98 + \ 0.14x & = & \ 53.98 + \ 0.16x & \\57.98 + 0.14x & = & 53.98 + 0.16x &\text{Cancelled the dollar units}\\57.98 & = & 53.98 + 0.02x & \text{Subtracted 0.14x from each side}\\4.00 & = & 0.02x & \text{Subtracted 53.98 from each side}\\x & = & \mathbf{200} & \text{Divided each side by 0.02}\\\end{array}\\\text{Jenny would have to drive \boxed{\textbf{200 mi}} for the two plans to cost the same}$

Check:

$\begin{array}{rcl}\ 57.98 + \ 0.14(200) & = & \ 53.98 + \ 0.16(200)\\\ 57.98 + \ 28.00 & = & \ 53.98 + \ 32.00\\\ 85.98 & = &\ 85.98\\\end{array}$

OK.

Answer 2

Answer:

I think 16 miles

Step-by-step explanation:

if you multiply 57.98 by 52.98 you get  then divide that by 30 (16+14=30)