SOLUTION: If mark gives john 6 apples, mark will have 2/3 of the apples that john will have. Now if jaime gives 9 apples to mark then john will have 2/3 of the apples that mark will help

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Question 1168371: If mark gives john 6 apples, mark will have 2/3 of the apples that john will have.
Now if jaime gives 9 apples to mark then john will have 2/3 of the apples
that mark will help. How many apples eache have?
Found 3 solutions by CubeyThePenguin, MathTherapy, ikleyn:
Answer by CubeyThePenguin(3113)   (Show Source): You can put this solution on YOUR website!
mark = M
john = J

M - 6 = 2J/3
J - 9 = 2M/3

(M, J) = (117/5, 108/5)
Answer by MathTherapy(10551)   (Show Source): You can put this solution on YOUR website!
If mark gives john 6 apples, mark will have 2/3 of the apples that john will have. Now if jaime gives 9 apples to mark then john will have 2/3 of the apples that mark will help. How many apples eache have?
Doesn't the other person know that apples are in INTEGER-form, and NOT FRACTIONAL-form? Apparently NOT!! 

Needless to say, he/she is WRONG!!

Correct answer:  

Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
 .

If Mark gives John 6 apples, Mark will have 2/3 of the apples that John will have. 

Now if   JOHN gives 9 apples to Mark then John will have 2/3 of the apples 

that Mark will  HAVE. How many apples each  HAS ? 

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These "virtual exchange" problems all have a standard setup.








    M - 6 =     (1)    (If mark gives john 6 apples, mark will have 2/3 of the apples that john will have)

     = J - 9.   (2)    (if John gives 9 apples to Mark then John will have 2/3 of the apples that Mark will have)


Simplify these equations

    3M - 18   = 2*(J+6)            (1')

    2*(M + 9) = 3*(J-9)            (2')


Simplify more

    3M - 2J =  30                  (1'')

    2M - 3J = -45                  (2'')


Prepare for elimination

    6M - 4J =  60                  (1''')

    6M - 9J = -135                 (2''')


Subtract (2''') from (1''')

         5J = 60 - (-135) = 195

          J               = 195/5 = 39.


Finally, from (1'')  find  M = 36.


ANSWER.  M = 36;  J = 39.





Solved.





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On  "virtual exchange"  problems,  see the lesson



    - Virtual exchange between two persons



in this site.







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In parallel with Math,  learn  English from my post and have doubled benefits (!)









 

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