Question

Ruben will rent a car for the weekend. He can choose one of two plans. The first plan has an initial fee of $49 and costs an additional 0.12 per mile driven. The second plan has an initial fee of $36 and costs an additional .14 per mile driven.

Answer 1

650 miles

Explanation:

Plan A 49+.12m where m is the miles

Plan B = 36+.14m

We want where they cost the same, so set them equal

49+.12m = 36+.14m

Subtract .12m from each side

49+.12m-.12m = 36+.14m-.12m

49 = 36+.02m

Subtract 36 from each side

49 - 36 = 36-36+.02m

13 = .02m

Divide each side by .02

13/.02 = .02m/.02

650 = m

Answer 2

The plans would cost the same for 650 miles; It would cost $127.

Explanation:

Let x= number of miles driven

Let y= price of plan

Now, we can set up the equations.

Plan 1:

y=49+0.12x

Plan 2:

y=36+0.14x

Now, we can perform substitution.

Our goal is to make it so that the equation has only 1 variable, so we can find it and then use it to find the other variable.

That said, we can substitute "36+0.14x" in for y in the first equation.

36+0.14x=49+0.12x

We need to move the variables to one side, and the numerical values to the other.

Let's first subtract 36 from both sides.

0.14x=13+0.12x

Subtract 0.12x from both sides.

0.02x=13

Divide both sides by 0.02

x=650

We can use that information to find y now.

Let's use the equation for plan 1.

y=49+0.12x

Plug in x.

y=49+0.12(650)

Simplify.

y=49+78

y=127

Therefore, the plans would cost the same for 650 miles. It would cost $127.