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 $7\%,$ and on $B$ bonds $12\%.$ 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 $$13,000,$ and the investor wants an annual return of $$940$ on the three investments?

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