Question 1122512
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Here is a really fast way to solve this kind of problem, without algebra.<br>
(Of course, if a solution using algebra is required, this method won't do....)<br>
(1) $810 return on a $10,000 investment is 8.1%.
(2) 8.1% is 7/10 of the way from 6% to 9%.  (Plot the numbers on a number line if you need help seeing this).
(3) Therefore 7/10 of the $10,000 must be invested at the higher rate.<br>
Answer: $7000 at 9%; so $3000 at 6%.