Gary and Ginger decide to place 10,000 of their savings...

Gary and Ginger decide to place $\$ 10,000$ of their savings into investments. They put some in a money market account earning $3 \%$ interest, some in a mutual fund that has been averaging $7 \%$ a year, and some in a stock that rose $10 \%$ last year. If they put $\$ 3000$ more in the money market than in the mutual fund and the mutual fund and stocks have the same growth in the next year as they did in the previous year, they will earn $\$ 540$ in a year. How much money did they put in each of the three investments?

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Key Concepts

System of Linear Equations

This concept involves setting up multiple equations that represent various conditions described in a problem. In investment problems, these equations are usually based on total amounts, relationships between different investment portions, and aggregate returns. The system is then solved simultaneously to find the values of the unknowns.

Interest and Percentage Calculations

Understanding how to calculate interest based on given percentages is crucial in financial mathematics. Interest calculations involve determining the amount earned by applying a percentage rate to an investment's principal. This concept is key when comparing different investments with varying rates to determine overall returns.

Variable Representation and the Substitution Method

This concept entails assigning variables to unknown quantities and expressing relationships between those variables algebraically. The substitution method, specifically, is a technique where one variable is expressed in terms of another and substituted into a different equation, thereby reducing the complexity of the system and making it easier to solve.

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