A trust fund worth 25,000 is invested in two different...

A trust fund worth $\$ 25,000$ is invested in two different portfolios. This year, one portfolio is expected to earn $5.25 \%$ interest and the other is expected to earn $4 \%$. Plans are for the total interest on the fund to be $\$ 1150$ in one year. How much money should be invested at each rate?

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Key Concepts

System of Equations

This concept involves setting up and solving equations that relate multiple unknown variables based on given constraints. In many problems, such as those involving allocation of resources or investments, the sum of parts is equal to a total value, and additional conditions provide a second (or more) equation, allowing one to solve for each variable.

Simple Interest Calculation

Simple interest is a method used to calculate the interest earned or paid on an investment or loan. It is determined by multiplying the principal amount, the rate of interest (expressed as a decimal), and the time period of the investment. This calculation is straightforward and does not account for interest compounding.

Percentage Conversion

Converting percentages to decimals is a fundamental step in many algebraic and financial calculations. This process involves dividing the percentage value by 100 so that it can be directly used in mathematical operations, such as determining the amount of simple interest earned or paid.

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