Question 1209584
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40% of Alan's marbles is equal to 50% of what Bryan has. 
They both have 540 marbles altogether. 
How many marbles must Alan give to Bryan so that they each have the same number of marbles
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                Below is my mental solution.



<pre>
The statement 

    "40% of Alan's marbles is equal to 50% of what Bryan has"

is equivalent to  

    "80% of Alan's marbles is equal to 100% of what Bryan has."


    +---------------------------------------------------------------+
    |                    Or, in other words,                        |
    |    for each 20 marbles that Bryan has, Alan has 25 marbles.   |
    +---------------------------------------------------------------+


It means that we can group their marbles evenly in sets (25 Alan's marbles, 20 Bryan's marbles).


Each such a set has 25+20 = 45 marbles;  so, the number of all such sets is  540/45 = 12.



So, Alan has  25*12 = 300 marbles;  Bryan has 20*12 = 240 marbles.



Thus, Alan should give half of the difference,  {{{(300-240)/2}}} = 30 marbles to Brian 
to equate the numbers of their marbles.
</pre>

Solved.