A rental car company offers two rental plans, Plan A and Plan B, for the same economy size car. For both plans, the total rental cost is a function of the number of miles that the car is driven. In addition to a flat fee of $75, Plan A offers a rate of $0.20 per mile for an unlimited number of miles. Plan B offers a higher mileage rate of $0.35 per mile but does not charge a flat fee for the rental. Create a system of linear functions modeling the cost of the car rental plans, A and B, as a function of the miles driven.
For how many miles will the rental fee be the same under both plans A and B?

a. C(x) = 75 + 0.2x and C'(x) = $0.35x b. 500 miles

Step-by-step explanation:

a. Create a system of linear functions modeling the cost of the car rental plans, A and B, as a function of the miles driven.

Let x be the number of miles driven by the car for each plan.

For plan A, since there is a $75 initial flat fee and a charge of $0.20 per mile, after moving x miles, the extra cost is $0.20x. So, the total cost C for plan A is

C(x) = 75 + 0.2x

For plan B since there is no initial flat fee but only a charge of $0.35 per mile, for x miles, the cost for plan B is C'(x) = $0.35x

b. For how many miles will the rental fee be the same under both plans A and B?

When the rental fees are the same, we equate both expressions.

So, 75 + 0.2x = 0.35x

collecting like terms, we have

75 = 0.35x - 0.2x

75 = 0.15x

dividing both sides by 0.15, we have

x = 75/0.15

= 500 miles

So, the rental fee will be the same after 500 miles