Question

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=0.60M+ 16.95, where M is the number of miles
driven.
The company also offers an option to insure the car against damage. The insurance charge / (in dollars) is
given by the function /= 0.25M+5.80.
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.

Answer 1

The total charge C for a rental that includes insurance can be found by adding the standard charge S and the insurance charge I:

C = S + I

Substituting the given expressions for S and I, we get:

C = (0.60M + 16.95) + (0.25M + 5.80)

Simplifying and combining like terms, we get:

C = 0.85M + 22.75

Therefore, the equation relating C to M is:

C = 0.85M + 22.75

This equation shows that the total charge C for a rental that includes insurance is a linear function of the number of miles driven M, with a slope of 0.85 and a y-intercept of 22.75.