SOLUTION: a) A total of $40,000 was invested, part of it at 12% interest and the remainder at 15%. If the total yearly interest from both investments was $5,800. How much was investe

Algebra ->  Customizable Word Problem Solvers  -> Finance -> SOLUTION: a) A total of $40,000 was invested, part of it at 12% interest and the remainder at 15%. If the total yearly interest from both investments was $5,800. How much was investe      Log On

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Question 1188420: a) A total of $40,000 was invested, part of it at 12% interest and the remainder at 15%.
If the total yearly interest from both investments was $5,800. How much was invested at each rate

Found 2 solutions by greenestamps, josgarithmetic:
Answer by greenestamps(13326) About Me  (Show Source):
You can put this solution on YOUR website!


Bad data, requiring answers that are not whole numbers of dollars, and not even whole numbers of cents....

x = amount invested at 12%
40000-x = amount invested at 15%

The total interest was 5800:

.12%28x%29%2B.15%2840000-x%29=5800

You can do the algebra to try to find the answer.

Here is a quick informal way to find the answer.

All $40,000 invested at 12% would yield $4800 interest; all at 15% would yield $6000.
Look at the three numbers 4800, 5800, and 6000 on a number line and observe/calculate that 5800 is 1000/1200 = 5/6 of the way from 4800 to 6000.
That means 5/6 of the total was invested at the higher rate.

5/6 of $40,000 is not a whole number....


Answer by josgarithmetic(39790) About Me  (Show Source):
You can put this solution on YOUR website!
RATE            AMT.INV.         INTEREST
 12              40000-y         0.12(40000-y)
 15               y              0.15y
                40000             5800

12%2840000-y%29%2B15y=580000

12%2A40000-12y%2B15y=580000
%2815-12%29y=580000-12%2A40000
highlight%28y=%28580000-12%2A40000%29%2F%2815-12%29%29
Just simplify and compute this, and then evaluate the other invested quantity.


The amount at 15% looks like to be 33333.33 dollars.