SOLUTION: James invests a total of $16,500 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 10% loss in the same time

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Question 1194879: James invests a total of $16,500 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 10% loss in the same time period. At the end of one year, the total amount of money gained was $-1,410.00. How much was invested into each account?
$
was invested in the account that gained 14% and
$
was invested in the account that lost 10%.
Found 2 solutions by ankor@dixie-net.com, MathTherapy:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
James invests a total of $16,500 in two accounts.
The first account earned a rate of return of 14% (after a year).
However, the second account suffered a 10% loss in the same time period.
At the end of one year, the total amount of money gained was $-1,410.00.
How much was invested into each account?
:
Since it is -1410, I assume it was a loss.
a = original amt invested at 14%
b = original amt which suffered a 10% loss
Therefore the total value of each after one year: 1.14a and .9b
:
a + b = 16500
b = (16500-a)
and the equation
1.14a + .90b = a + b - 1410
substitute for b and (a+b)
1.14a + .90(16500-a) = 16500 - 1410
1.14a + 14850 - .90a = 15090
1.14a - .9a = 15090 - 14850
.24a = 240
a = 240/.24
a = 240/.24
a = $1000 invested at 14%
then
16500 - 1000 = $15500 amt invested which had a 10% loss
:
:
See if that works out
1.14(1000) = 1140
.9(15500) = 13950
-----------------
1 yr total; 15090
Original total - 1 yr total
16500 - 15090 = 1410 loss
Answer by MathTherapy(10549)   (Show Source): You can put this solution on YOUR website!

James invests a total of $16,500 in two accounts. The first account earned a rate of return of 14% (after a year). However, the second account suffered a 10% loss in the same time period. At the end of one year, the total amount of money gained was $-1,410.00. How much was invested into each account?
$
was invested in the account that gained 14% and
$
was invested in the account that lost 10%.
Let amount invested in account yielding a 14% RoR be F

Then amount invested in account that yielded a 10% loss = 16,500 - F

We then get: .14F - .1(16,500 - F) = - 1,410

                  .14F - 1,650 + .1F = - 1,410

                          .14F + .1F = - 1,410 + 1,650

                                .24F = 240

Amount invested in account yielding a 14% RoR, or 

And, amount invested in account that yielded a 10% loss = $16,500 - 1,000 = $15,500 

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