Solve each problem using the Gauss-Jordan method to solve a system of equations.

Three kinds of tea worth $4.60, $5.75, and $6.50 per lb are to be mixed to get 20 lb of tea worth $5.25 per lb. The amount of $4.60 tea used is to be equal to the total amount of the other two kinds together. How many pounds of each tea should be used?