SOLUTION: Larry Mitchell invested part of his $ 32,000 advance at 4% annual simple interest and the rest at 7% annual simple interest. If his total yearly interest from both accounts was $1

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Question 1133271: Larry Mitchell invested part of his $ 32,000 advance at 4% annual simple interest and the rest at 7% annual simple interest. If his total yearly interest from both accounts was $1,670​, find the amount invested at each rate.
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.

Each day we solve  2-3-4  similar problems at this forum.

Therefore,  I will give here only shortest version of the solution,  referring for more complete solutions/explanations to the lesson
    - Using systems of equations to solve problems on investment
in this site.


Solution 

Let x = the amount invested at 7% annual simple interest.

Then the amount invested at 4% is (32000-x) dollars.


Your basic equation is


    interest + interest       = total interest,    or

    0.07x    + 0.04*(32000-x) = 1670


Simplify and solve for x:


    x = %281670+-0.04%2A32000%29%2F%280.07+-+0.04%29 = 13000.


ANSWER.  $13000 were invested at 7% and the rest,  $32000- $13000 = $19000 were invested at 4%.


CHECK.    0.07*13000 + 0.04*19000 = 1670 dollars.    ! Correct !

Solved and completed.

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

It is a standard and typical problem on investments.

As I just said,  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.