Question 1207481: Linda Smaoke invests a total of $10,000 in two savings accounts. One account pays 6% interest, and the other,7%. Find the amount placed in each account if the accounts receive a total of $660 in interest after 1 year.
Found 3 solutions by Msexcel , ikleyn, greenestamps:
Answer by Msexcel (1)   (Show Source):
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x + y = 10000
.06x + .07y = 660
From equation (1)
x = 10,000 - y
Substitute into (2)
.06x + .07y = 660
.06(10,000 - y) + .07y = 660
600 - .06y + .07y = 660
- .06y + .07y = 660 - 600
.01y = 60
y = 60/.01
y = 600
Substitute the value of y into equation (1)
x + y = 10,000
x + 600 = 10,000
x = 10,000 - 600
x = 9400
Therefore, $9,400 was placed in the account which pays 6% interest rate and $600 was placed in the account which pays 7% interest rate
Answer by ikleyn(52879)  (Show Source):
You can put this solution on YOUR website! .
Let the 7% investment be x dollars;
then the 6% investment is (10000-x) dollars.
Partial interests from separate accounts are 0.07x and 0.06*(10000-x) dollars, respectively.
The total annual interest equation is
0.07x + 0.06*(10000-x) = 660 dollars.
Simplify this equation and find x
0.07x + 600 - 0.06x = 660
0.07x - 0.06x = 660 - 600
0.01x = 60
x = 60/0.01 = 6000 dollars.
So, the 7% investment is $6000; the 6% investment is the rest, $10000 - $6000 = $4000.
Thus you get the answer.
CHECK. 0.07*6000 + 0.06*4000 = 420 + 240 = 660 dollars. ! precisely correct !
Solved.
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The other person made an arithmetic error on the way and did not fix it.
This led him/her to wrong answer.
Let this example teaches you on how important is to make a full-size check at the end.
Without such full-size check the solution is not complete !
And can not be considered/recognized/accepted as an error-free !
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Here is a quick and easy non-algebraic method for solving any 2-part "mixture" problem like this.
$10,000 all invested at 6% would yield $600 interest; all at 7% would yield $700 interest.
Use any arithmetic method you want (perhaps a number line) to observe/calculate that $660 is 60/100 = 3/5 of the way from $600 to $700.
That means 3/5 of the total was invested at the higher rate.
3/5 of $10,000 is $6000.
ANSWER: $6000 was invested at 7%, the other $4000 at 6%
CHECK: .07($6000)+.06($4000) = $420+$240 = $660
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