You're on the right track, but you put "too much" in your equations.
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% ?
Let = amounted invested at 12%.
Let = amount invested at 6%.
Then: . .
$550 at 11% returns $60.50 in interest.
dollars at 12% returns dollars in interest.
dollars at 6% returns dollars in interest.
The total interest is: .
. . and we want this to be equal to 9% of $1650 = $148.50
There is our equation: .
Multiply by 100: . .
Solve the system of equation.
And we get: .
Substitute into : .