### Home > INT2 > Chapter 12 > Lesson 12.2.3 > Problem12-111

12-111.

Arik has purchased a used car. To help pay for his expenses, Arik uses his car to run errands for his neighbors, such as picking up groceries and going to the hardware store.

1. Arik charges a flat fee of $\5.00$ for errands that require driving less than three miles, and an additional $\1.50$ per mile for longer errands. Write a piecewise-defined function that represents Arik’s earnings.

$f ( x ) = \left\{ \begin{array} { l l } { 5 } & { 0 < x < 3 } \\ { 5 + 1.5 x } & { 3 \leq x } \end{array} \right.$

2. Arik keeps careful records of his expenses. Gas is about $\3.00$/gal, and his gas mileage averages $28$ mi/gal. His maintenance costs are predicted to be $\0.60$/mile. Write a function that represents Arik’s fuel and maintenance costs per mile driven.

How can you compare the price of gas to the gas mileage of his car?

3. Write a new piecewise function that represents the profit Arik makes. What is Arik’s predicted profit for an errand that requires $2.5$ miles of driving? $10$ miles of driving?

Incorporate your answers from part (b) into the piecewise function from part (a) to create the new piecewise function.