SOLUTION: An investment of $4500 is made at an interest rate of 8% for one year. How much money must be invested at a rate 5% so that the total interest earned is 6% of the total investment?

Question 1128896: An investment of $4500 is made at an interest rate of 8% for one year. How much money must be invested at a rate 5% so that the total interest earned is 6% of the total investment?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

By traditional algebra....

8% of $4500, plus 5% of an unknown amount x, equals 6% of the total, $4500+x:

That equation is relatively easy to solve, although the decimals might make it take some time.

Here is a MUCH easier way to solve the problem (assuming a formal algebraic solution is not required).

(1) The overall average of 6% is "twice as close" to 5% as it is to 8%.
(2) Therefore, twice as much must be invested at 5% as at 8%.
(3) Since $4500 is invested at 8%, the amount required to be invested at 5% is 2*$4500 = $9000.

ANSWER: $9000 at 5%

CHECK:
.08(4500)+.05(9000) = 360+450 = 810
.06(13500) = 810
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