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Word problem

The number of Roberto's baseball cards is 34\frac {3}{4} the number of David's cards. If Roberto gives 12\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.

Unparseable latex formula:

r = \frac{3d}{4}[br]\[br]\dfrac {r}{2} = \dfrac {3d}{4} + \dfrac {r}{2}[br]\[br]0 = \dfrac{3d}{4}



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

Any help much appreciated!
Reply 1
Avatar for 2710
2710
18
Original post by supreme
The number of Roberto's baseball cards is 34\frac {3}{4} the number of David's cards. If Roberto gives 12\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.

Unparseable latex formula:

r = \frac{3d}{4}[br]\[br]\dfrac {r}{2} = \dfrac {3d}{4} + \dfrac {r}{2}[br]\[br]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?
Reply 2
Avatar for supreme
supreme
OP
4
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)?
Reply 3
Avatar for 2710
2710
18
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.
Reply 4
Avatar for TenOfThem
TenOfThem
18
Original post by supreme



\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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