Question 1143846
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            After seeing the solutions from two our respectful tutors, you, probably, have a wish to see something more simple.


            I will try to satisfy this desire by presenting as simple solution as possible.



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From the condition, it is clear that the number of marbles Josh had initially, is multiple of 4.

Let x be  1/4  of Josh's marbles, that he had initially.

So, Josh had initially 4x marbles; at the first exchange, he gave 1/4 of it, i.e. x marbles, to May.

Thus after first exchange, Josh left with 3x marbles, while May had 3 times 3x marbles, i.e. 9x marbles.



After the second exchange, Josh has (3x+12) marbles, while May has (9x-12) marbles.



These amounts are the same, so you have this simple equation

    3x + 12 = 9x - 12.



You can EASILY solve it :

    12 + 12 = 9x - 3x,   or   24 = 6x,   which implies  x= 24/6 = 4.


Thus Josh had initially 4x = 16 marbles.



After first exchange, May had  9x = 9*4 = 36 marbles; but  4 of them came from Josh  (! remember,  x= 4 !),   

so May had initially  36 - 4 = 32 marbles.    <U>ANSWER</U>
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Solved.