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Question 1147504: Joy invests a total of $16,000 in two accounts. The first account earned a rate of return of 14% after a year. However, the second account suffered a 12% loss in the same time period. At the of one year, the total amount of money gained was $1,980. How much was invested into each account?
Answer by ikleyn(52748)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount invested at 14%, in dollars.
Then the second amount, which suffered the 12% loss, is the rest (16000-x) dollars.
The interest from the 14% interest account is 0.14*x dollars.
The 12% loss from the second account is 0.12*(16000-x) dollars.
Your equation is
interest - loss = final interest, or
0.14*x - 0.12*(16000-x) = 1980 dollars.
From the equation, express x and calculate the answer
x =  = 15000.
Answer. The amount at 14% is $15000; the rest $16000-$15000 = $1000 is the account suffered 12% loss.
Check. 0.14*15000 - 0.12*1000 = 1980 dollars. ! Precisely correct !
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It is a typical and standard problem on investment.
To see many other similar solved problems on investment, look into the lesson
- Using systems of equations to solve problems on investment
in this site.
You will find there different approaches (using one equation or a system of two equations in two unknowns), as well as
different methods of solution to the equations (Substitution, Elimination).
Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.
The referred lesson is the part of this online textbook under the topic "Systems of two linear equations in two unknowns".
Save the link to this online textbook together with its description
Free of charge online textbook in ALGEBRA-I
https://www.algebra.com/algebra/homework/quadratic/lessons/ALGEBRA-I-YOUR-ONLINE-TEXTBOOK.lesson
to your archive and use it when it is needed.
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