Part I: A system of equations can result in 3 possibilities: consistent, inconsistent, and dependent. Discuss each of these types of solution that can be generated, and describe the graph of each possibility.
Part II: Break-Even Analysis and Cost Analysis: As a first-time homeowner, there are going to many decisions that you need to make, such as whom to hire for the upkeep of your lawn. You have just received advertisements from 2 companies in your area: Greener Lawns and Lawns for Less. Greener Lawns charges an initial fee of $200, plus $50 per hour for labor costs. Lawns for Less charges an initial fee of $300, plus $25 per hour for labor costs.
1. If h represents the number of labor hours and C represents the cost, write the total cost equation for Greener Lawns.
2. If h represents the number of labor hours and C represents the cost, write the total cost equation for Lawns for Less.
3. Solve the system of equations for the total cost of lawn care using the desired technique: substitution, elimination, or graphing.
4. Document how you came to these conclusions for accuracy.
Part III: Mathematics of Finance
You have just graduated from college and landed your first big job. You have always dreamed of being a homeowner, and after carefully shopping for your dream home, you find one that you would like to purchase at a cost of $250,000. After researching banks to find the best interest rate, you find that Banks for Homeowners offers the best rate of 6% interest that compounds monthly for 30 years.
What is the monthly payment for this loan?
What is the unpaid balance of the loan at the end of 5 years?
•What is the unpaid balance at the end of the 10th year?