Question

Mr. and Mrs. Garcia have a total of $100,000 to Invest in stocks, bonds, and a money market account. The stocks have a rate of return of 12% per year, while the bonds and the money market account pay 8% per year and 4% per year, respectively. The Garcias have stipulated that the amount invested in the money market account should be equal to the sum of 20% of the amount invested in stocks and 10% of the amount invested in bonds. Further, the Garcias require an annual income of $10,000 from their investments. Set up the appropriate system of linear equations that describes this scenario, and use the Gauss-Jordan elimination method on sald system to learn how this couple should allocate their resources.

Answer 1

To solve this problem, we need to set up a system of linear equations and then use the Gauss-Jordan elimination method to find the solution. The solution will indicate how the Garcias should allocate their resources.

Step-by-step explanation:

To set up the appropriate system of linear equations, we need to identify the unknown variables in this problem. Let's denote the amount invested in stocks as S, the amount invested in bonds as B, and the amount invested in the money market account as M. From the given information, we can form the following equations:

Equation 1: S + B + M = $100,000

Equation 2: M = 0.2S + 0.1B

Equation 3: 0.12S + 0.08B + 0.04M = $10,000 (representing the annual income requirement)

We can solve this system of equations using the Gauss-Jordan elimination method or any other appropriate method to find the values of S, B, and M, which will indicate how the Garcias should allocate their resources.

Learn more about Solving systems of linear equations