SOLUTION: you invested $5000 between two accounts paying 7% and 9% annual interest, respectively. If the total interest earned for the year was $390 how much was invest at each rate?

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Question 1152966: you invested $5000 between two accounts paying 7% and 9% annual interest, respectively. If the total interest earned for the year was $390 how much was invest at each rate?
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52847)   (Show Source): You can put this solution on YOUR website!
.

Let x = amount invested at 9%.

Then amount invested at 7% is (5000-x).


The total interest equation is


    0.07*(5000-x) + 0.09x = 390   dollars.


From the equation


    x =  = 2000.


ANSWER.  Investments are $2000 at 9% and the rest,  5000-2000 = 3000 dollars at 7%.


CHECK.   0.09*2000 + 0.07*3000 = 390  dollars.   ! Precisely correct !

Solved.

----------------

Every day we solve 3 - 5 similar problems at this forum.

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(13203)   (Show Source): You can put this solution on YOUR website!


Here is a very different non-algebraic way for solving many kinds of problems similar to this one.

All $5000 invested at 7% would yield $350 interest; all at 9% would yield $450 interest.

Use any method you want to determine that the actual interest of $390 is "40/100 = 2/5 of the way from $350 to $450".

That means 2/5 of the money was invested at the higher rate.

ANSWER: 2/5 of the $5000, or $2000, at 9%; $3000 at 7%

CHECK: .09(2000)+.07(3000) = 180+210 = 390
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