Assignment
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 charge 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.
Mathematics of Finance
Part III: To purchase your first home, you may be required to borrow funds from a bank. You have just graduated from college, and your dream is to own your first home. Before you begin looking for your dream home, you need to learn more about funding options and the process required to finance a home.
Research online to find more information about home loans and mortgages.
1. Discuss your options for obtaining a home loan and how mortgages work.
2. Discuss the process/procedures for obtaining the loan and the ideal interest rates for home loans.
3. Report your findings in 2 paragraphs.
-3x = 3-y
2y = 6x+6
-2x+6=1y
Part I:
A system of equations can result in three types of solutions: consistent, inconsistent, and dependent.
1. Consistent: A consistent system of equations has at least one solution. This means that the equations have a common point of intersection. On a graph, this would appear as two lines intersecting at a single point. The solution to the system of equations represents the values that satisfy both equations simultaneously.
2. Inconsistent: An inconsistent system of equations has no solution. This means that the equations are parallel and do not intersect. On a graph, this would appear as two parallel lines that never cross. Since there is no common point of intersection, there are no values that satisfy both equations.
3. Dependent: A dependent system of equations has infinitely many solutions. This means that the equations are essentially the same line or are proportional to each other. On a graph, this would appear as two overlapping lines. Any point on the line(s) would satisfy both equations simultaneously.
Part II:
1. The total cost equation for Greener Lawns can be written as C = 200 + 50h. This equation represents the initial fee of $200 plus $50 per hour for labor costs. The variable h represents the number of labor hours, and C represents the total cost.
2. The total cost equation for Lawns for Less can be written as C = 300 + 25h. This equation represents the initial fee of $300 plus $25 per hour for labor costs. Similarly, h represents the number of labor hours, and C represents the total cost.
3. To solve the system of equations for the total cost of lawn care, you can use different techniques such as substitution, elimination, or graphing. For example, if you want to find the point of intersection or the number of hours when the costs are equal for both companies, you can set the two equations equal to each other and solve for h.
4. To document the process, you can write down the equations, explain the chosen technique (substitution, elimination, or graphing), and show the steps taken to find the solution. For example, if using substitution, you would substitute one equation into the other and solve for h. Once the value of h is found, you can substitute it back into either equation to find the corresponding total cost.
Part III:
1. Options for obtaining a home loan include traditional banks, credit unions, mortgage brokers, and online lenders. Home loans, also known as mortgages, are loans provided by financial institutions to individuals for the purpose of purchasing a home. The lender provides a specific amount of money upfront, and the borrower agrees to repay the loan over an agreed-upon term, typically with interest. Mortgages can be fixed-rate or adjustable-rate, depending on the terms agreed upon.
2. The process of obtaining a home loan involves several steps. First, the borrower needs to research and compare different lenders and loan options to find the best rates and terms. Then, they need to gather all necessary documentation, such as proof of income, credit history, and employment verification, to submit a loan application. The lender will evaluate the borrower's creditworthiness and assess the loan-to-value ratio before making a decision. If approved, the borrower will receive a loan commitment letter detailing the loan terms. Interest rates for home loans are influenced by factors such as the borrower's credit score, loan amount, loan term, and prevailing market rates.
3. In summary, obtaining a home loan involves researching lenders, submitting a loan application with the necessary documentation, undergoing the lender's evaluation process, and receiving a loan commitment with specific interest rates and terms. It is essential to compare offers from different lenders to get the most favorable rates and conditions that align with one's financial goals.