You invested \( \$ 26,000 \) in two accounts paying \( 3 \% \) and \( 7 \% \) annual interest, respecively. If the total interest eamed for the year was \( \$ 1580 \), how much was invested at each rate? The amount invested at \( 3 \% \) is \( \$ \square \).

To find out how much was invested at each rate, let's set up some equations! Let \( x \) be the amount invested at \( 3\% \), and \( (26000 - x) \) be the amount invested at \( 7\% \). The interest earned from the two investments can be expressed as: \[ 0.03x + 0.07(26000 - x) = 1580. \] Solving this equation will give you the amounts invested at each rate. After simplifying and solving, you will find that you invested \( \$ 8,000 \) at \( 3\% \) and \( \$ 18,000 \) at \( 7\% \). So, the amount invested at \( 3\% \) is \( \$ 8,000 \). Every penny counts! While the numbers tell a story of investment strategy, remember that diversification is key to managing risk. By splitting your funds between different interest rates, you’ve harnessed the potential for varying returns -- smart move! If you're curious about similar problems, diving into algebraic word problems can be an exciting challenge. A variety of resources, from textbooks to online platforms, offer practice scenarios, guiding you to hone your problem-solving skills while keeping your math game strong and sharp!