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You have already invested $400 in a stock with an annual return of 11%. How much of an additional $1,000 should be invested at 12% and how much at 6% so that the total return on the entire $1,400 is 9%?
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0.11*400 + 0.12x + 0.06(1000-x) = 0.09*1400 Solve for x I get $366.67
That is $366.67 at 12% and $633.33 at 6%
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