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 $$13,000,$ and the investor wants an annual return of $$680$ on the three investments?

The client should invest $ $$ in AAA bonds, $ $$ in A bonds, and $ $$ in $B$ bonds.