Question

(25 points) A car rental company's standard charge includes an initial fee plus an additional fee for each mile driven. The standard charge S (in dollars) is given by the function S = 0.40M + 15.75, where M is the number of miles driven.

The company also offers an option to insure the car against damage. The insurance charge I (in dollars) is given by the function I = 0.25M + 3.90.

Let C be the total charge (in dollars) for a rental that includes insurance. Write an equation relating C to M. Simplify your answer as much as possible.

C =

Answer 1

C = 0.65M+19.65

Explanation:

Given the the standard charge S (in dollars) given by the function

S = 0.40M + 15.75, where M is the number of miles driven.

Also the insurance charge I (in dollars) is given by the function

I = 0.25M + 3.90

If C is the total charge (in dollars) for a rental that includes insurance, then:

C = S + I

Substitute the given function into the expression:

C = 0.40M + 15.75 + 0.25M + 3.90

Collect like terms

C = 0.40M+0.25M+15.75+3.90

C = 0.65M+19.65

Hence an equation relating C to M is expressed as C = 0.65M+19.65