$8600 is invested in two different accounts. One account pays 24% simple interest per year and the other account pays 9% simple interest per year. If the total interest earn in one year is $849.00, how much is invested at each rate?

Let $LaTeX: \displaystyle x$ be the amount invested at 24%. Then $LaTeX: \displaystyle 8600-x$ is amount invested at 9%. This gives the equation $LaTeX: \displaystyle 0.24 x+0.09(8600 - x)=849$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 500$ . So the amount in the other account is $8100.