$5800 is invested in two different accounts. One account pays 15% simple interest per year and the other account pays 12% simple interest per year. If the total interest earn in one year is $765.00, how much is invested at each rate?

Let $LaTeX: \displaystyle x$ be the amount invested at 15%. Then $LaTeX: \displaystyle 5800-x$ is amount invested at 12%. This gives the equation $LaTeX: \displaystyle 0.15 x+0.12(5800 - x)=765$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 2300$ . So the amount in the other account is $3500.