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Question 1166530: A retired couple has $192,000 to invest. A safe investment yields 9.5% per year, but a riskier investment yields 12.5% per year. How much should they invest at each rate to earn $21,000 per year?
Answer by ikleyn(52769)   (Show Source):
You can put this solution on YOUR website! .
Let x be the 12.5% investment.
Then the other investment is (192000-x) dollars,
and you have this equation for the total interest
0.125x + 0.095*(192000-x) = 21000 dollars.
From the equation,
x =  = 92000 dollars.
ANSWER. $92000 invested at 12.5% and the rest, 192000-92000 = 100000 dollars invested at 9.5%.
CHECK. 0.125*92000 + 0.095*100000 = 21000 total interest. ! Correct !
Solved.
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It is a standard and typical problem on investments.
If you need more details, or if you want to see other similar problems solved by different methods, 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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