Question 1174081: An executive invests $28,000, some at 6% and the rest at 4% annual interest. If he receives an annual return of $1,440, how much is invested at each rate?
at 6% interest $
at 4% interest $
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52754)   (Show Source):
You can put this solution on YOUR website! .
x dollars invested at 6%, and
(28000-x) invested at 4%.
The total annual interest equation is
0.06x + 0.04*(28000-x) = 1440 dollars.
From the equation
x =  = 16000.
ANSWER. $16000 invested at 6%, and the rest 28000-16000 = 12000 dollars invested at 4%.
CHECK. 0.06*16000 + 0.04*12000 = 1440 dollars, the total annual interest. ! 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(13195)  (Show Source):
You can put this solution on YOUR website!
Here is a quick and easy non-algebraic alternative to the standard formal algebraic solution provided by the other tutor.
The algebraic solution is of course fine. But if obtaining a solution quickly is beneficial and a formal algebraic solution is not required (as in a timed math competition), this alternative method is very useful.
All $28,000 invested at 6% would earn $1680 interest.
All invested at 4% would earn $1120 interest.
The actual interest was $1440.
Determine, perhaps with the help of a number line, that the actual interest $1440 is $320/$560 = 32/56 = 16/28 of the way from $1120 to $1680.
That means 16/28 of the total was invested at the higher rate. (Note I left 16/28 in unsimplified form, because the total investment was $28,000.
ANSWER: 16/28 of the $28,000, or $16,000, was invested at the higher 6% interest rate; the other $12,000 was invested at 4%.
CHECK: .06(16000)+.04(12000) = 960+480 = 1440
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