Hi, I need help on this word problem:

You have already invested 550$ in a stock with an annual return of 11%. How much of an additional 1100 should be invested at 12% and how much at 6% so that the total return on the entire 1650$ is 9%

I tried to set up my equations as (550 times .11) + (.12x times 1100) + (.06y times 1100) = (1650 times .09)

and x + y = 1100

I am wondering if i am going in the right direction. The answer in the book says 366.67 at 12% and 733.33 at 6% but i tried to work my math and i got nowhere close to that answer.

can anyone help please?