$11100 is invested in two different accounts. One account pays 29% simple interest per year and the other account pays 6% simple interest per year. If the total interest earn in one year is $1586.00, how much is invested at each rate?

Let $LaTeX: \displaystyle x$ be the amount invested at 29%. Then $LaTeX: \displaystyle 11100-x$ is amount invested at 6%. This gives the equation $LaTeX: \displaystyle 0.29 x+0.06(11100 - x)=1586$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 4000$ . So the amount in the other account is $7100.