Question 1096630: You invested 25,000 in two accounts paying 3% and 4% annual interest, respectively. If the total interest earned for the year was $990, how much was invested at each rate?
Found 3 solutions by addingup, greenestamps, MathTherapy:
Answer by addingup(3677)   (Show Source):
You can put this solution on YOUR website! at 3% = x
at 4% = 25,000-x
0.03x + 0.04(25,000-x) = 990
0.03x + 1,000 - 0.04x = 990
-0.01x = -80
x = 8,000 this is the amount invested at 3%
The amount invested at 4%:
25,000 - 8,000 = 17,000
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
The answer from the first tutor is not right. If you look at the work he shows, there is an arithmetic error.
It was easy to see that his answer was wrong, because $25,000 all invested at 4% would yield $1000 interest, while $25,000 all invested at 3% would earn only $750 interest. Since the actual amount of interest was $990, nearly all of the money must have been invested at 4%. So his answer of $8000 at 3% and $17000 at 4% doesn't make sense.
Here is the beginning of what he showed in his response:
at 3% = x
at 4% = 25,000-x
0.03x + 0.04(25,000-x) = 990
0.03x + 1,000 - 0.04x = 990
-0.01x = -80
...
You can see that the "-80" there is not right.
To continue his solution without the arithmetic error,
-0.01x = -10
x = 1000
The amount invested at 3% is $1000; the amount invested at 4% is $25,000-$1000 = $24,000.
The quick analysis I showed at the beginning of my response leads to a much faster way to solve problems like this.
Take a look at this method and see if it makes sense to you.
I calculated that all of the $25,000 invested at 4% would yield $1000 interest and all of it invested at 3% would yield $750 interest; then I compared the actual amount of interest, $990, to those two amounts. By doing that, I knew that nearly all of the $25,000 had to be invested at 4%.
But I can go further with that analysis. The difference between $1000 and $990 is $10; the difference between $990 and $750 is $240. The ratio of those differences is 10:240, or 1:24. That ratio is exactly the ratio in which the money needs to be split between the two rates.
With a total investment of $25,000, split in the ratio 24:1, it is clear that $24,000 must be invested at 4% and $1000 at 3%.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
You invested 25,000 in two accounts paying 3% and 4% annual interest, respectively. If the total interest earned for the year was $990, how much was invested at each rate?
Correct answer: 
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