1. Now that you are successful in your new position, you have decided to reward yourself with a new (or new to you) vehicle. Sources say you should strive to have your vehicle payment be no more than 10% of your gross monthly salary, which is $58,000.
Write an inequality, using x to represent your gross monthly salary and y to represent your monthly car payment, which could be used to calculate the range of payments that will work in your budget. (Do NOT input your salary on this step):
2. Using the inequality you came up with in the previous question, input your gross monthly salary in the inequality you wrote to determine your range of possible car payments. Show both your replacement of x with your gross monthly salary and the final solution with an appropriate label. Use the equation editor.
3. Using the solution and what we know to be an appropriate domain based on the question, write the possible car payment options in interval notation.
4. Car payments are determined using simple interest. If you don't remember this formula, go back and look it up! To finance your vehicle purchase you have two choices. Write two equations, one for each bank, that models the banks' loan options using x for the price of the vehicle and y to represent the total cost (price, interest and origination fees) paid on each loan. Be sure to label which equation goes with which bank.
Bank A: Finance the full price of the vehicle at 5% with an origination fee of $200 paid over 5 years.
Bank B: Finance the full price of the vehicle at 6% paid over 5 years (no additional fees).
5. You decide you like jeep Cherokee priced at $29,995
Use the equations you came up with for bank financing options to calculate the following:
total cost of your vehicle using bank A
monthly payment of your vehicle using bank A
total cost of your vehicle using bank B
monthly payment of your vehicle using bank B
6. Taking into account your allowed car payment range and the payments you determined for Bank A and Bank B, can you afford to purchase your vehicle? Express your answer in paragraph form. If you cannot afford the vehicle, explain why based on your budget values you determined. If you will purchase the vehicle, which bank will you finance your vehicle through and why?
7. You want to celebrate all of your recent successes. You decide to reward yourself and a special someone with a vacation to a destination of your choosing. For your trip you will need to stay in a hotel/resort and rent a car.
You decide to rent a car for the duration of your trip. You have two options. Write an equation for each company that depicts the total cost of the rental, y, based on the number of days, x.
Cheepers Rent-A-Car:
$39/day with a one-time charge of $20 for insurance/fees
Busters:
$49/day but all additional fees are included in the price of the rental
Be sure to label each equation with the company it corresponds to.
8. Graph the system of equations that you wrote for car rental options to determine the break-even point for the cost of the car rentals. One easy way to do this is using desmos.com, the online graphing calculator and take a screen shot of your graph. If you are unsure how to capture a screen shot visit http://www.take-a-screenshot.org/. You may also choose to graph this by hand and take a picture of your graph but be sure that your graph is easy to read. Insert either option AS A PICTURE using the button.
9. Write your solution to the system as an ordered pair, then interpret the values in the context of the problem.
10. Explain how you would use your graph to determine the cheaper option after one day, two days, three days etc. What would you look for on the graph?
11. Explain how you would use your break even point to determine the cheaper option after one day, two days, three days etc.
12. You also have two options for lodging. Write an equation FOR EACH OPTION that depicts the total cost of your stay, y, based on the number of days, x.
Bilton Hotel:
$100/night but you must pay an additional one-time fee of $40 for parking and other fees
Triple Tree:
$110/night with no additional parking or resort fees.
Be sure to label each equation with the hotel it corresponds to.
13. You will need to use either substitution or elimination to solve this system. Which method will you choose? What factors helped you make that decision?
14. Show your work for solving the system of equations you wrote for your hotel options using the equation editor. Be sure to use the method you decided on in the previous question.
15. Write your solution to the system as an ordered pair, then interpret the values in the context of the problem.