SOLUTION: James invests a total of $23,000 into accounts. The first account earned a rate of return of 10% after a year. However, the second account suffered a 3% loss and the same time peri

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Question 1201048: James invests a total of $23,000 into accounts. The first account earned a rate of return of 10% after a year. However, the second account suffered a 3% loss and the same time period. at the end of one year the total amount of money gained was -$235 how much was invested into each account.
Answer by math_tutor2020(3816) About Me  (Show Source):
You can put this solution on YOUR website!

x = amount invested in the 1st account
y = amount invested in the 2nd account

x+y = 23000 total invested
That can be solved to y = 23000-x
I'll use it in a substitution step later on.

10% of x = 0.10x = gains from the 1st account
-3% of y = -0.03y = loss from the 2nd account
0.10x-0.03y = -235 net loss

0.10x-0.03y = -235
0.10x-0.03( y ) = -235
0.10x-0.03( 23000-x ) = -235 .... substitution step
0.10x-0.03( 23000 ) - 0.03(-x) = -235
0.10x-690 +0.03x = -235
0.13x-690 = -235
0.13x = -235+690
0.13x = 455
x = 455/0.13
x = 3500

Use this to find y
y = 23000-x
y = 23000-3500
y = 19500

He invested $3500 in the first account and gained 0.10*3500 = 350 dollars.
He also invested $19,500 in the second account and lost 0.03*19500 = 585 dollars.
The net loss is 350-585 = -235 which matches what the instructions mentioned.
The answers are confirmed.


Answers:
$3500 invested in the first account.
$19,500 invested in the second account.