Systems, Matrices, and Determinants · Challenge problem

Elena invests $\$12{,}000$ in three funds paying $4\%$, $6\%$, and $9\%$ simple annual interest. After one year the total interest is $\$780$, and the amount in the $9\%$ fund is $\$1000$ more than the amount in the $4\%$ fund. Find the amount invested in the $6\%$ fund.