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Question 1161816: Cabin Financial Service Group recommends that a client purchase for $10,000 a corporate bond that earns 6% annual simple interest. How much additional money must be placed in an investment that earns a simple interest rate of 4.5% so that the total annual interest earned from the two investments is 5% of the total investment?
Found 3 solutions by ikleyn, MathTherapy, greenestamps:
Answer by ikleyn(52787)   (Show Source):
You can put this solution on YOUR website! .
0.06*10000 + 0.045*x = 0.05*(10000+x)
600 + 0.045x = 500 + 0.05x
600 - 500 = 0.05x - 0.045x
100 = 0.005x
x =  = 20000.
ANSWER. Additional money amount / (deposit) is $20000.
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.
Answer by MathTherapy(10552)  (Show Source):
You can put this solution on YOUR website!
Cabin Financial Service Group recommends that a client purchase for $10,000 a corporate bond that earns 6% annual simple interest. How much additional money must be placed in an investment that earns a simple interest rate of 4.5% so that the total annual interest earned from the two investments is 5% of the total investment?
Additional investment: 
Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
Here is a method for solving "mixture" problems like this using logical reasoning instead of formal algebra.
If you understand this method, it will get you to the answer much faster and with far less work than a formal algebraic solution.
(1) The target average interest rate of 5% is "twice as close to 4.5% as it is to 6%".
(If it's hard for you to see that, imagine the three numbers 4.5, 5, and 6 on a number line. 5 is twice as close to 4.5 as it is to 6.)
(2) That means the amount to be invested at 4.5% is twice the amount invested at 6%.
ANSWER: twice $10,000, which is $20,000.
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