Systems of Linear Equations: Three Variables: Apply It

  • Solve systems of three equations in three variables.
  • Identify inconsistent systems of equations containing three variables.
  • Express the solution of a system of dependent equations containing three variables.

Maya just graduated from college and landed her first job with a starting bonus of $8,400. She wants to invest this money wisely across three different investment options to diversify her portfolio and maximize her returns while managing risk.

Investing is a process of using your money to buy something (stocks, real estate, bitcoin, etc) that you expect will be worth more in the future.Thanks to compound interest, when your money earns money, and then that new money earns money too, your investments can grow quickly. A $1,000 investment at age 20 could become $20,000+ by retirement, but the same investment at age 40 might only become $7,000.Learn more about investing at dowjanes.com.

Investment Options

After researching different investment vehicles, Maya has identified three options:

  • High Yield Savings Account: 3% annual interest (low risk)
  • Money Market Account: 6% annual return (medium risk)
  • Stock Market Index Funds: 9% annual return (higher risk)

Maya has set some guidelines for her investment strategy:

  • She wants to invest twice as much in the stock market index funds as in the high yield savings account to take advantage of higher returns while she’s young
  • She wants to earn $540 in total returns during the first year

Let:

  • [latex]x[/latex] = amount invested in high yield savings account (3%)
  • [latex]y[/latex] = amount invested in money market account (6%)
  • [latex]z[/latex] = amount invested in stock market index funds (9%)
The interest earned in one year can be calculated using simple interest: [latex]I=Prt[/latex]. Where [latex]P[/latex] is the initial investment, [latex]r[/latex] is the interest rate as a decimal, and [latex]t[/latex] is fixed at [latex]1[/latex] year.
Solve the investment system.

Choose Your Own Investment Plan