Hello, soccer49!

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: . .[1]

$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: . .[2]

Solve the system of equation.

And we get: .

Substitute into [1]: .