John invests twice as much money at 6% as he does at 5%. If his investments earn a total of $680 in one year, how much does he have invested at each rate? Solution I will do this question under the assumption that the given interest rates are annual, and the interest is simple interest. Let x represent the amount invested at 6% Let y represent the amount invested at 5% Since twice as much money is invested at 6%: x=2y Given the investments earn a total of $680 x(0.06) + y(0.05) = 680 Noting that x=2y y(0.12) + y(0.05)= 680 y(0.17)= 680 y=$4000 Since x=2y x=$8000 Therefore $8000 is invested at 6% and $4000 is invested at 5% .