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    The number of Roberto's baseball cards is \frac {3}{4} the number of David's cards. If Roberto gives \frac {1}{2} of his cards to David, what will be the ratio of Roberto's cards to David's cards?

    I have tried the get the solution but just don't seem to come up with a solvable equation:

    Let r represent the number of card's that Roberto has.
    Let d represent the number of card's David has.

    r = \frac{3d}{4}

\

\dfrac {r}{2} = \dfrac {3d}{4} + \dfrac {r}{2}

\

0 = \dfrac{3d}{4}

    Obviously this makes no sense. Where am I going wrong?

    Any help much appreciated!
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    (Original post by supreme)
    The number of Roberto's baseball cards is \frac {3}{4} the number of David's cards. If Roberto gives \frac {1}{2} of his cards to David, what will be the ratio of Roberto's cards to David's cards?

    I have tried the get the solution but just don't seem to come up with a solvable equation:

    Let r represent the number of card's that Roberto has.
    Let d represent the number of card's David has.

    r = \frac{3d}{4}

\

\dfrac {r}{2} = \dfrac {3d}{4} + \dfrac {r}{2}

\

0 = \dfrac{3d}{4}

    Obviously this makes no sense. Where am I going wrong?

    Any help much appreciated!
    I'm not sure that equation is entirely correct. But look at it this way:

    So we have r:d ratio

    = (3d)/4 : d

    This is the beginning ratio, with Roberto on the left

    Now, roberto gives half to david, what would the new ratio be?

    x:y?
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    (Original post by 2710)
    I'm not sure that equation is entirely correct. But look at it this way:

    So we have r:d ratio

    = (3d)/4 : d

    This is the beginning ratio, with Roberto on the left

    Now, roberto gives half to david, what would the new ratio be?

    x:y?
    Thanks but I don't get how this helps because what am I meant to do with:

    r/d = (3d/4 - 3d/8)/(d + 3d/8)?
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    (Original post by supreme)
    Thanks but I don't get how this helps because what am I meant to do with:

    r/d = (3d/4 - 3d/8)/(d + 3d/8)?
    Lol, thats you answer! Just simplify it tho.
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    (Original post by supreme)

    [latex]
    \dfrac {r}{2} = \dfrac {3d}{4} + \dfrac {r}{2}
    latex]
    This is the error as you have said they have the same cards after the exchange

    Try with numbers

    Let David have 40 and Roberto have 30
    Roberto gives 15 to David

    R : D = 15 : 55 = 3 : 11


    So now try with letters

    Let David have d and Roberto have 3/4 d
    Roberto gives 3/8 d to David

    R : D = 3/4 d - 3/8 d : d + 3/8 d = 3d/8 : 11d/8 = 3 : 11
 
 
 
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