Question

a car rental companys 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 $s = 18.95 + 0.60m$, 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 $i = 4.90 + 0.15m$. 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. $c = \square$

Explanation:

Step1: Understand total charge formula

Total charge \( C \) is the sum of standard charge \( S \) and insurance charge \( I \). So \( C = S + I \).

Step2: Substitute \( S \) and \( I \) functions

Given \( S = 18.95 + 0.60M \) and \( I = 4.90 + 0.15M \), substitute into \( C = S + I \):
\( C=(18.95 + 0.60M)+(4.90 + 0.15M) \)

Step3: Combine like terms

Combine the constant terms: \( 18.95 + 4.90 = 23.85 \)
Combine the \( M \)-terms: \( 0.60M + 0.15M = 0.75M \)
So \( C = 23.85 + 0.75M \)

Answer:

\( 23.85 + 0.75M \)