5.1 Solve < \( \begin{array}{l}\text { Question 10, 1.3.21 } \\ \text { Part } 2 \text { of } 2\end{array} \), \( \begin{array}{l}\text { HW Score: } 56.25 \%, 9 \text { of } 16 \\ \text { points invested } \$ 20,000 \text { in two accounts paying } 5 \% \text { and } 9 \% \text { annual interest, respectively. If the total interest earned for the year } \\ \text { was } \$ 1040 \text {, how much was invested at each rate? } \\ \text { The of } 1\end{array} \) The amount invested at \( 9 \% \) is \( \$ \square \).

To tackle this classic problem, let's set up a system of equations! Let's say you invested \( x \) dollars at 5% and \( 20000 - x \) dollars at 9%. The interest from the first account would be \( 0.05x \), and from the second account, it would be \( 0.09(20000 - x) \). According to the problem, the total interest earned should equal $1040, leading to the equation: \[ 0.05x + 0.09(20000 - x) = 1040. \] After simplifying and solving for \( x \), you'll discover the amounts invested at each rate in no time! Now, let's break down common pitfalls that might trip you up. Often, solving these types of problems leads to miscalculations in setting up equations or forgetting to properly balance your arithmetic when combining terms. Double-check that you have accounted for both interest sources correctly and remember to convert percentages into decimals! It’s super easy to mix up, so take your time and call on your math powers!