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Question 1162179: A state employees' pension fund invested a total of one million dollars in two accounts that earned 3.5% and 4.5% annual simple interest. At the end of the year, the total interest earned from the two investments was $43,000. How much was invested at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52915)   (Show Source):
You can put this solution on YOUR website! .
x dollars invested at 4.5%
(1000000-x) dollars invested at 3.5%
The total interest equation is
0.045x + 0.035*(1000000-x) = 43000 dollars.
From the equation,
x =  = 800000.
ANSWER. $800000 invested at 4.5%, and the rest 200000 dollars invested at 3.5%.
CHECK. 0.045*800000 + 0.035*200000 = 43000 dollars. ! Precisely correct !
Solved.
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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(13216)  (Show Source):
You can put this solution on YOUR website!
A quick and easy non-algebraic way to solve a "mixture" problem like this:
(1) $43,000 interest on an investment of a million dollars is 4.3%.
(2) 4.3% is 4/5 of the way from 3.5% to 4.5%. (picture the three percentages on a number line....)
(3) Therefore, 4/5 of the million dollars was invested at the higher rate.
ANSWER: 4/5 of a million, or $800,000, at 4.5%; the other $200,000 at 3.5%.
CHECK: .045(800,000)+.035(200,000) = 36,000+7000 = 43,000
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