Question 1151787: An executive invests $27,000, some at 5% and the rest at 4% annual interest. If he receives an annual return of $1,180, how much is invested at each rate?
Answer by greenestamps(13209)   (Show Source):
You can put this solution on YOUR website!
The setup for a traditional algebraic solution, which I will let you finish....
Let x be the amount invested at 5%
Then (27000-x) is the amount invested at 4%
The total amount of interest is $1180:
Solve using basic algebra....
A different solution method, without algebra....
This method, if you understand it, will get you to the answer to this kind of "mixture" problem much faster than the algebraic method.
(1) All $27,000 invested at 5% would yield $1350 interest; all invested at 4% would yield $1080 interest.
(2) Look at the three interest amounts -- $1080, $1180, and $1350 -- on a number line. The actual interest, $1180, is 10/27 of the way from $1080 to $1350. ($1080 to $1350 is a difference of $270; $1080 to $1180 is a difference of $100; $100/$270 = 100/270 = 10/27).
That means 10/27 of the total was invested at the higher rate.
ANSWER: 10/27 of $27,000, or $10,000, at 5%; the other $17,000 at 4%
CHECK:
.04(17000)+.05(10000) = 680+500 = 1180
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