\( \left\lvert\, \leftarrow \begin{array}{l}\text { Paul and Donna Petrie invested } \$ 25,000 \text {, part at } 4 \% \text { simple interest and the rest at } 7 \% \text { simple interest for a period of } 1 \text { year. How much did they invest at each rate if their } \\ \text { total annual interest from both investments was } \$ 1030 \text { ? } \\ \text { The amount invested at } 4 \% \text { is } \$ \square \text {. } \\ \text { The amount invested at } 7 \% \text { is } \$ \square \text {. }\end{array} . \begin{array}{l}\text {. }\end{array}\right. \).

Let's label the amount invested at 4% as \( x \). Therefore, the amount invested at 7% will be \( 25,000 - x \). The interest from the 4% investment for one year is \( 0.04x \), and the interest from the 7% investment is \( 0.07(25,000 - x) \). According to the information given, the total interest from both investments is $1030, leading to the equation: \[ 0.04x + 0.07(25,000 - x) = 1030 \] Solving that, we have: \[ 0.04x + 1750 - 0.07x = 1030 \] \[ -0.03x + 1750 = 1030 \] \[ -0.03x = 1030 - 1750 \] \[ -0.03x = -720 \] \[ x = \frac{-720}{-0.03} = 24000 \] Thus, the amount invested at 4% is \( 24000 \), and the amount at 7% is: \[ 25000 - 24000 = 1000 \] So, Paul and Donna invested \( \$24000 \) at 4% and \( \$1000 \) at 7%. Investing your money wisely has a deep-rooted history, especially in the context of simple interest. Simple interest was a popular concept in ancient Mesopotamia, where merchants and lenders documented transactions and contracts on clay tablets, ensuring fair returns on investments for both parties. Fast forward to today, and understanding simple interest is still fundamental for anyone wanting to dip their toes into the world of finance! When tackling interest problems, an essential tip is to clearly define variables at the start. Many make the mistake of mixing up amounts or percentages. Always set your variables, write out your equations neatly, and check your work meticulously as you solve. This will help prevent small mistakes from leading to incorrect conclusions!