$10100 is invested in two different accounts. One account pays 13% simple interest per year and the other account pays 11% simple interest per year. If the total interest earn in one year is $1259.00, how much is invested at each rate?

Let $LaTeX: \displaystyle x$ be the amount invested at 13%. Then $LaTeX: \displaystyle 10100-x$ is amount invested at 11%. This gives the equation $LaTeX: \displaystyle 0.13 x+0.11(10100 - x)=1259$ . Solving for $LaTeX: \displaystyle x$ gives $LaTeX: \displaystyle x = 7400$ . So the amount in the other account is $2700.