SOLUTION: Please help me solve Monico invests a total of $13,000 in two accounts. The first account earned a rate of return of 15% (after a year). However, the second account suffered a 1

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Question 686855: Please help me solve
Monico invests a total of $13,000 in two accounts. The first account earned a rate of return of 15% (after a year). However, the second account suffered a 13% loss in the same time period. At the end of one year, the total amount of money gained was $550.00. How much was invested into each account?
$________ was invested at 15% and
$________ was invested at -13%.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
$8000 was invested at 15% and
$5000 was invested at -13%.
The way to solve it depends on what you are studying

IF YOU ARE STUDYING SYSTEMS OF LINEAR EQUATIONS:
x = amount (in $) invested at 15%
y = amount (in $) invested at -13%
highlight%28x%2By=13000%29
The first account earned $0.15x (15% of $x)
The second account "earned" a negative amount (lost 13%),
so the "earnings" from the second account (in $) were -0.13y.
The total earnings (in $) were
highlight%280.15x-0.13y=550%29
Putting both equations together, you get the system of equations
system%28x%2By=13000%2C0.15x-0.13y=550%29
There are many ways to solve such a system,
but the most intuitive way would be by substitution.
You could solve the first equation for y:
x%2By=13000 --> y=13000-x,
and then substitute the expression 13000-x for y in the second equation.
0.15x-0.13%2813000-x%29=550 --> 0.15x-0.13%2A13000%2B0.13x=550 --> 0.15x-1690%2B0.13x=550 --> 0.28x-1690=550 --> 0.28x=550%2B1690 --> 0.28x=2240 --> x=2240%2F0.28 --> highlight%28x=8000%29
Then substitute 8000 for x in y=13000-x to get
y=13000-8000 --> highlight%28y=5000%29

IF YOU HAVE NOT STUDIED SYSTEMS OF EQUATIONS:
x = amount (in $) invested at 15%
amount (in $) invested at -13% = 13000-x
The first account earned $0.15x (15% of $x)
The second account "earned" a negative amount (lost 13%),
so the "earnings" from the second account (in $) were -0.13%2813000-x%29.
The total earnings (in $) were
highlight%280.15x-0.13%2813000-x%29=550%29
Now you simplify and solve for x
0.15x-0.13%2813000-x%29=550 --> 0.15x-0.13%2A13000%2B0.13x=550 --> 0.15x-1690%2B0.13x=550 --> 0.28x-1690=550 --> 0.28x=550%2B1690 --> 0.28x=2240 --> x=2240%2F0.28 --> highlight%28x=8000%29
Then,
amount (in $) invested at -13% = 13000-x=13000-800=highlight%285000%29