Question 1196217: Juan invested his savings in two investment funds. The $15,000 that he invested in Fund A returned a 3% profit. The amount that he invested in Fund B returned a 10% profit. How much did he invest in Fund B, if both funds together returned a 5% profit?
Answer by ikleyn(52775)   (Show Source):
You can put this solution on YOUR website! .
Juan invested his savings in two investment funds.
The $15,000 that he invested in Fund A returned a 3% profit.
The amount that he invested in Fund B returned a 10% profit.
How much did he invest in Fund B, if both funds together returned a 5% profit?
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Let x be the amount invested in Fund B.
Write an equation for the total annual interest
0.03*15000 + 0.1x = 0.05(15000+x).
Simplify and find x
450 + 0.1x = 750 + 0.05x
0.1x - 0.05x = 750 - 450
0.05x = 300
x = 300/0.05 = 6000.
ANSWER. $6000 invested in Fund B.
Solved.
The key to solution of similar problems is to write a balance equation
for the total annual interest, and then solve it.
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In this problem, a professional term is " the interest ", or " the annual interest ", instead of " profit ".
The term " profit " has different meaning and stands for another concept.
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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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