An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is ​%5, on A bonds ​%6, and on B bonds ​%9. The client wants to invest twice as much in AAA bonds as in B bonds. How much should be invested in each type of bond if the total investment is ​$9,000​, and the investor wants an annual return of ​$560 on the three investments.