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Question 1139013: You have P50,000 to invest, and two funds that you'd like to invest in. The You-Risk-It Fund (Fund Y) yields 16% interest. The Extra-Dull Fund (Fund X) yields 8% interest. Because of college financial-aid implications, you don't think you can afford to earn more than P5000 in interest income this year. How much should you put in each fund?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800)   (Show Source):
You can put this solution on YOUR website! .
Let x = amount at 16%.
Then the amount at 8% is the rest (50000-x).
The interest from the 16% amount is 0.16*x.
The interest from the 8% amount is 0.08*(50000-x).
Your equation is
interest + interest = total interest, or
0.16*x + 0.08*(50000-x) = 5000.
From the equation, express x and calculate the answer
x =  = 12500.
Answer. The amount at 16% is $12500; the rest $50000-$12500 = $37500 is the amount at 8%.
Check. 0.16*12500 + 0.08*37500 = 5000. ! 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.
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a method for solving "mixture" problems like this that is very different from the usual algebraic method. If you understand it, it will get you to the answer to problems like this much faster and with far less effort.
(1) The P50,000 all invested at 8% would yield P4000 interest; all invested at 16% would yield P8000 interest.
(2) The desired P5000 interest is 1/4 of the way from P4000 to P8000. (P4000 to P8000 is P4000; P4000 to P5000 is P1000; P1000 is 1/4 of P4000).
(3) That means 1/4 of the total should be invested at the higher percentage.
ANSWER: 1/4 of P50,000, or P12,500, at 16%; the rest, P37,500, at 8%.
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