\( \$ 1,500 \) is invested in two different accounts paying \( 4 \% \) and \( 5 \% \) interest. If a total of \( \$ 67 \) interest is earned after one year, then how much money was invested at \( 4 \% \) ? \( \$ 700 \) \( \$ 800 \) \( \$ 900 \)

To solve this, let's call the amount invested at 4% "x" and the amount invested at 5% "y". According to the problem, we have two equations: 1. \( x + y = 1500 \) (the total investment) 2. \( 0.04x + 0.05y = 67 \) (the total interest earned) From the first equation, we can express \( y \) as \( y = 1500 - x \). Now substitute this into the second equation: \( 0.04x + 0.05(1500 - x) = 67 \) Expanding this gives: \( 0.04x + 75 - 0.05x = 67 \) Combining like terms: \( -0.01x + 75 = 67 \) Now, isolate \( x \): \( -0.01x = 67 - 75 \) \( -0.01x = -8 \) Dividing both sides by -0.01: \( x = 800 \) So, \( \$ 800 \) was invested at \( 4 \% \). Now let's get into some fun facts! Every penny counts! Interest earned on investments can add up over time, and understanding how different rates impact your overall earnings can dramatically change your investment decisions. If you ever find yourself stuck, just remember that a little math can go a long way! Moreover, did you know that Albert Einstein called compound interest the "eighth wonder of the world"? Just imagine how much your \( \$ 800 \) could grow over decades if reinvested rather than just sitting idle in a bank account! So always keep an eye on those interest rates and let your money work for you!