SOLUTION: 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 receiv

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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): You can put this solution on YOUR website!

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(52786)   (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.

-----------------

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(13200)   (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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