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Question 1151783: 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 $42,000. How much was invested at each rate?
Found 2 solutions by greenestamps, ikleyn:
Answer by greenestamps(13215)   (Show Source):
You can put this solution on YOUR website!
You can answer this problem in about 10 seconds if your are reasonably good with mental arithmetic, and if you understand the method I'm going to show you.
I will leave it to other tutors to show a solution using the traditional algebraic method.
(1) $42,000 interest on $1,000,000 is a return rate of 4.2%.
{2) Look at where that overall interest rate compares to the two individual interest rates on a number line: 4.2% is 7/10 of the way from 3.5% to 4.5%.
(3) That means 7/10 of the total was invested at the higher rate.
ANSWER: 7/10 of the million dollars, or $700,000 at 5%; the other $300,000 at 4%.
CHECK:
.045($700,000)+.035($300,000) = $31,500+$10,500 = $42,000
Answer by ikleyn(52914)  (Show Source):
You can put this solution on YOUR website! .
Let x be the amount invested at 4.5 annual interest.
Then the amount invested at 3.5% is (1000000-x) dollars.
The annual interest earned by the 4.5% investment is 0.045x dollars.
The annual interest earned by the 3.5% investment is 0.035*(1000000-x) dollars.
The total interest is the sum of the partial interests
0.045x + 0.035*(1000000-x) = 42000.
From this equation, express x and calculate
x =  = 700000.
ANSWER. $700000 was invested at 4.5%, and the rest $300000 was invested at 3.5%.
CHECK. 0.045*700000 + 0.035*300000 = 42000 dollars. ! Precisely 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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