SOLUTION: Susan invested a total of $10000 in two accounts. One account pays 4 interest and the other account pays 6% Interest. The total retum from both accounts was $560. Answer the fo

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Question 1183978: Susan invested a total of $10000 in two accounts. One account pays 4 interest and the other account pays 6% Interest. The total retum from both accounts was $560.
Answer the following questions.
How much was invested at 4%?
How much was invested at 6%?


Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52921) About Me  (Show Source):
You can put this solution on YOUR website!
.
Let x be the amount invested at 6%.

Then the amount invested at 4% is (10000-x) dollars.


The 6% investment generates 0.06x dollars as the annual interest.

The 4% investment generates 0.04*(10000-x) dollars as the annual interest.


The total annual interest is the sum  0.06 + 0.04*(10000-x)  dollars.

It is equal to $560  (given).


So we have this equation for the total annual interest


    0.06x + 0.04*(10000-x) = 560  dollars.


From the equation


    x =  %28560+-+0.04%2A10000%29%2F%280.06-0.04%29 = 8000.


ANSWER.  $8000 invested at 6% and the rest,  10000-8000 = 2000  dollars invested at 4%.


CHECK.  0.06*8000 + 0.04*2000 = 560 dollars, total annual interest.    ! Correct !

Solved.




Answer by greenestamps(13216) About Me  (Show Source):
You can put this solution on YOUR website!


The other tutor showed a good formal algebraic solution using the standard method.

If a formal algebraic solution is not required, and if the speed of getting an answer is important (as in a timed math competition), then here is a very fast and easy way to solve this problem (and many similar problems) mentally.

(1) $10000 all invested at 4% would yield $400 interest; all at 6% would yield $600 interest.
(2) The actual interest $560 is 4/5 of the way from $400 to $600. (Picturing the three numbers 400, 560, and 600 on a number line might help: 400 to 600 is a difference of 200; 400 to 560 is a difference of 160; 160/200 = 4/5.)
(3) That means 4/5 of the $10000 was invested at the higher rate.

ANSWER: 4/5 of $10000, or $8000, was invested at 6%; the other $2000 at 4%.

CHECK: .06(8000)+.04(2000) = 480+80 = 560