SOLUTION: Hi 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.

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Question 1106190: Hi
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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Answer by ikleyn(52781) About Me  (Show Source):
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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+%2B%281%2F3%29x = 160-%282%2F3%29X dollars.


3.  Then Carol gave 1/5 of the amount she had back to Andrew. After that Carol had  %284%2F5%29%2A%28160-2%2F3%29x dollars.

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

    %284%2F5%29%2A%28160-2%2F3%29x = 80.


    It is your equation to find "x".  First, multiply both sides by 5%2F4. You will get

    160 - (2/3)x}}} = 80%2A%285%2F4%29 = 100.  ====>

    %282%2F3%29x = 160 - 100 = 60  ====>  x = 60%2A%283%2F2%29 = 90.


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


Check.   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 !

Solved.