Question 1162519: 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 $38,000. How much was invested at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52886)   (Show Source):
You can put this solution on YOUR website! .
Let x be the amount invested at 4.5%.
Then the amount invested at 3.5% is (1000000-x) dollars.
The equation for the total 1 year interest is
0.045x + 0.035*(1000000-x) = 38000 dollars.
From the equation,
x =  = 300000.
ANSWER. $300,000 invested at 4.5% and the rest, $1,000,000 - $300,000 = $700,000 invested at 3.5%.
CHECK. 0.045*300000 + 0.035*700000 = 38000 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.
Answer by greenestamps(13209)  (Show Source):
You can put this solution on YOUR website!
Another "mixture" problem that can be solved quickly and easily without using algebra.
(1) All million dollars at 3.5% would earn $35,000 interest; all at 4.5% would earn $45,000 interest; the actual interest earned was $38,000.
(2) $38,000 is 3/10 of the way from $35,000 to $45,000 (picture the three figures on a number line....)
(3) That means 3/10 of the total was invested at the higher rate.
ANSWER: 3/10 of the million dollars, or $300,000, at 4.5%; the other $700,000 at 3.5%.
CHECK:
.045(300,000)+.035(700,000) = 13500+24500 = 38000
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