Question 1106190
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Andrew and Carol had 160 dollars altogether. Andrew gave 1/3 of his money to Carol. Then carol gave 1/5 of the amount 
she had back to Andrew. Finally both had 80 dollars each. How much did Andrew have at first. 
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1.  Let x = "How much did andrew have at first".

    Then Carol had (160-x) dollars.


2.  When Andrew gave 1/3 of his money to Carol, Carol had  {{{160-x +(1/3)x}}} = {{{160-(2/3)X}}} dollars.


3.  Then Carol gave 1/5 of the amount she had back to Andrew. After that Carol had  {{{(4/5)*(160-2/3)x}}} dollars.

    And the condition says that this amount is exactly 80 dollars:

    {{{(4/5)*(160-2/3)x}}} = 80.


    It is your equation to find "x".  First, multiply both sides by {{{5/4}}}. You will get

    160 - (2/3)x}}} = {{{80*(5/4)}}} = 100.  ====>

    {{{(2/3)x}}} = 160 - 100 = 60  ====>  x = {{{60*(3/2)}}} = 90.


<U>Answer</U>.  Andrew had 90 dollars at first.   // which means that Carol had 160-90 = 70 dollars at first.


<U>Check</U>.   After n.2 exchange  Andrew had 90-30 = 60;  Carol had  70+30 = 100 dollars.

         After n.3 exchange Andrew had 60+20 = 80;  Carol had  100-20 = 80.

         80 = 80.    ! Correct !
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Solved.