\( \$ 5,000 \) is invested in two different accounts yielding \( 3 \% \) and \( 3.5 \% \) interest. The interest earned on the two accounts is \( \$ 155 \). How much money was invested at \( 3 \% \) interest? \( \$ 1,000 \) \( \$ 3,000 \) \( \$ 4,000 \)

Let the amount invested at \( 3\% \) be \( x \). Then, the amount invested at \( 3.5\% \) would be \( 5,000 - x \). The total interest earned on both investments is given by: \[ 0.03x + 0.035(5000 - x) = 155 \] Expanding the equation: \[ 0.03x + 175 - 0.035x = 155 \] Combining like terms: \[ -0.005x + 175 = 155 \] Now, isolate \( x \): \[ -0.005x = 155 - 175 \] \[ -0.005x = -20 \] \[ x = \frac{-20}{-0.005} = 4000 \] Thus, the amount invested at \( 3\% \) interest is \( \$ 4,000 \). Did you know that simple interest problems like this have been a staple in finance education for centuries? It's fascinating that the concept of earning interest can be traced back to ancient Mesopotamia, where scribes recorded transactions and started recognizing the value of lending money. The early rules helped shape modern banking! In real-world applications, understanding how to allocate investments between different interest rates can have significant implications for personal finance. By evaluating where to place your money based on expected return, you can maximize your earnings, whether saving for a home or investing for retirement. Don't forget to consider factors like inflation and tax implications when investing, as they can affect your net gain!