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 :

znk

Answer:

[tex]\boxed{\textbf{200 mi}}[/tex]

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.

[tex]\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}[/tex]

Check:

[tex]\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}[/tex]

OK.

As per linear equation, Jenny needs to drive 200 miles for the two plans to cost the same.

What is a linear equation?

"A linear equation is an equation in which the highest power of the variable is always 1."

Let, Jenny needs to drive 'x' miles for the two plans to cost the same.

For the first plan, the cost for 'x' miles is

= $[tex](57.98+0.14x)[/tex]

For the second plan, the cost for 'x' miles is

= $[tex](53.98+0.16x)[/tex]

We know, $[tex](57.98+0.14x)[/tex] = $[tex](53.98+0.16x)[/tex]

⇒ [tex](0.16x - 0.14x) = 57.98-53.98[/tex]

⇒ [tex]0.02x = 4[/tex]

⇒ [tex]x = \frac{4}{0.02}[/tex]

⇒ [tex]x = 200[/tex]

Learn more about a linear equation here: https://brainly.com/question/2263981

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