Question

Lia can rent a van for either $40 with unlimited mileage or $30 with 100 free miles and an extra charge of 15 cents for each mile over 100. For what numbers of miles traveled would the unlimited mileage plan save Lia money?

Answer 1

Let's write a linear equation to represent both situations:

Situation A: Unlimited mileage

Pa = 40

Pa = Price of renting a car in A.

Situation B: Not unlimited mileage

Pb = 30 + 0.15x

Pb = Price of renting a car in B.

x = mile over 100.

If plan A saves Lia money:

`30+0.15x>40`

To find x, let's subtract 30 from both sides and then divide the sides by 0.15:

`\begin{gathered} 30+0.15x-30>40-30 \\ 0.15x>10 \\ (0.15)/(0.15)x>(10)/(0.15) \\ x>66.7 \end{gathered}`

Considering that x is the miles over 100, in order to save money, Lia has to travel 100 + 66.7 miles = 166.7 miles.

Answer: 166.7 miles.