Question

A car rental company offers two plans for renting a car: Plan A: 30 dollars per day and 12 cents per mile Plan B: 50 dollars per day with free unlimited mileage

Answer 1

Given:

• Plan A: 30 dollars per day and 12 cents per mile

,

• Plan B: 50 dollars per day with free unlimited mileage.

Let's find the range of miles where plan B will save you money.

Let's create equations representing both equations in slope-intercept form:

Plan A: y = 30 + 0.12x

Plan B: y = 50

Here, x represents the number of miles.

For plan B to save you money, the total cost of plan B will have to be lesser than the total cost of plan A.

Now to find where plan B will save you money set the expression in part B less than that of plan A.

We have:

`50<30+0.12x`

Let's solve for x.

We have:

`\begin{gathered} 50-30<0.12x \\ \\ 20<0.12x \\ \\ (20)/(0.12)<(0.12x)/(0.12x) \\ \\ 166.67166.67 \end{gathered}`

Therefore, to save money the mileage must be greater than 166.67 miles per day.

ANSWER:

166.67 miles