Question 435031
.
$2000 total deposit with 2 savings accounts. One pays interest rate of 6%, 
the other at rate of 8% if a total earned interest is $144 how much is each deposit
~~~~~~~~~~~~~~~~~~~~~~~~~



        The solution and the answer in the post by @mananth both are incorrect.

        His solution has arithmetic errors and does not withstand the standard check.

        So, I came to bring a correct solution.

        I will solve the problem using one single unknown, since it provides a shorter way.



<pre>
Let x be the amount invested at 8%, in dollars.

Then the amount invested at 6% is  (2000-x) dollars.


Write the total annual interest equation

    0.08*(x + 0.06(2000-x) = 144  dollars.


Simplify and find x

    0.08x + 120 - 0.06x = 144,

    0.08x - 0.06x = 144 - 120,

         0.02x    =     24

             x    =     24/0.02 = 2400/2 = 1200.


<U>ANSWER</U>.  $1200 invested at 8%;  $the rest,  $2000 - $1200 = $800 invested at 6%.


<U>CHECK</U>.  0.08*1200 + 0.06*800 = 144 dollars.  PRECISELY as it is given in the problem.
</pre>

Solved correctly.


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


This problem can be solved algebraically using one equation in one unknown or two equations in two unknowns.
It also can be solved mentally.


Since this site is to teach algebra, I place here algebraic solution.
Since the solution with one equation is simpler and shorter, I prefer this form with one unknown, which I present here.


What is really important, is to check the final solution for validity.


If you do not check, nothing will prevent you from mistakes.