Name:_____________________________ Rent-A-Car Deal II Scenario: As Thanksgiving approaches, you decide to accept your aunt’s invitation to visit. Since your car isn’t currently reliable, you decide to rent a car for the trip to your aunt’s house. You have narrowed down your choices to two companies. Company A charges $75 per day and $0.30 per mile. Company B charges $25 per day and $0.60 per mile. You decided to analyze these costs in order to decide which company to use. Solve the Problem (Write all your answers up neatly on a separate sheet(s)): 1. As a first step in your analysis, write two equations that represent the daily cost for a car from Company A and a car from Company B. Let x represent miles and y represent the cost. 2. Next, graph both equations on your graphing calculator. Determine your scale. You may use different scales for the x- and y-axes. After you are satisfied with your graph of the equations copy it neatly onto graph paper. Be sure to include your scales, units on each of your axes, and be sure to label each equation. Use your graph to answer questions 3 and 4. Answer all the following questions in complete sentences. 3. If you rent the car for one day and drive 100 miles, which car is a better deal? Explain how you determined this from the graph. 4. If you rent the car for one day and drive 300 miles, which car is a better deal? Explain how you determined this from the graph. 5. On your graph, your two lines should intersect in a point. Find this point algebraically by using substitution or elimination. What is the cost at this point? What is the number of miles? 6. When is Company A a better deal? When is Company B a better deal? Write you answers as inequalities. 7. You find out it is 250 miles to your aunt’s house. If you drive round trip and have the car from Wednesday at 4 pm until you get back Sunday before 4 pm, which car rental company will provide the better deal? Assume you do not drive while at your aunt’s house and you live around the corner from the rental car place. Show your work and how much it will cost for each company.
8. There is the possibility that you could get a ride home on Sunday with your uncle, who will be going past your college. If you drive only one way and drop the car off at the rental agency a block from your aunt’s house, will you choose a different company? Justify your answer.