An investment firm recommends that a client invest in bonds rated​ AAA, A, and B. The average yield on AAA bonds is 4%, on A bonds 5%, and on B bonds 8​%. 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 ​$23,000 and the investor wants an annual return of ​$1,200 on the three​ investments?