SOLUTION: 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 m

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: 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 m      Log On


   

Question 1209584: 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
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
Allen a marbles
Byron b marbles

First two sentences: system%284a=5b%2Ca%2Bb=540%29
.
.
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system%28a=300%2Cb=240%29,

x, how much Allen give so he and Byron have same amount?

300-x=240%2Bx

highlight%28x=30%29

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
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. 


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,  %28300-240%29%2F2 = 30 marbles to Brian 
to equate the numbers of their marbles.

Solved.