When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation for each option. Graph each line and use the graph to answer the question.

When renting a car two options listed below are given. You need the car for 3 days. How many miles must you travel in order for option 2 to be the better option? Tell me your variable and what it represents. Then use that variable to set up an equation you can solve to get the answer.

Option 1

Daily fee $50

Cost per mile $0.15

Option 2

Daily fee $65

Unlimited miles

Solution:

The equation of a straight line is given by:

y = mx + b; where m is the slope of the line (that is rate of change) and b is the y intercept (value of y when x is 0).

Let x represent the number of miles travelled in one day and let y represent the total cost incurred for travelling x miles.

Therefore, for option 1, the total cost per day is:

y = 50 + 0.15x (1)

For option 2, the total cost per day is:

y = 65 (2)

Since, we want to determine, how many miles must you travel in order for option 2 to be the better, hence:

65 < 50 + 0.15x

15 < 0.15x

x > 100 miles

Therefore for option 2 to be better, the car must travel more than 100 miles per day.