SOLUTION: I am not sure how to set this word problem up in order to solve. Helen Weller invested $12000 in an account that pays 12% interest. How much additional money must be invested in

Question 776043: I am not sure how to set this word problem up in order to solve.
Helen Weller invested $12000 in an account that pays 12% interest. How much additional money must be invested in an account that pays 11% interest so that the average rate of return on her investment is 11.667%.
Answer by DrBeeee(684) (Show Source): You can put this solution on YOUR website!
Let x = amount invested @ 11%
Let y = amount invested @ 12%
Your balance, B, is
(1) B = 1.11x + 1.12y
You want the balance to look like yoir total investment looks like it pays out at 11.667% or
(2) B = 1.11667*(x + y)
So you now equate (1) and (2) to get
(3) 1.11x + 1.12y = 1.11667*(x + y)
Now we are given that y is 12,000, so we have
(4) 1.11x - 1.11667x = (1.11667-1.12)*12000 or
(5) x = 12000*(1.12-1.11667)/(1.11667-1.11) or
(6) x = 5991
Let's check this be equating (1) and (2).
Is (1.11*5991+1.12*12000 = 1.11667*(5991+12000))?
Is (6650+13440 = 1.11667*(17991))?
Is (20090 = 20090)? Yes
Answer: Helen needs to invest $5,991 @ 11% to get the result she wants.
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