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Alice and Bob each have a certain amount of money. If Alice receives n dollars from Bob, then she will have 4 times as much money as Bob. If, on the other hand, she gives n dollars to Bob, then she will have 2 times as much money as Bob. If neither gives the other any money, what is the ratio of the amount of money Alice has to the amount Bob has?

 Mar 22, 2020
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We can write two equations from this...

 

A+n  = 3*(B-n) (Bob gives n dollars to Alice)

A - n  =  2 * (B + n) (Alice gives n dollars to Bob)

 

We will get

A+n  =  3B-3n

=A  =  3B - 4n

=3A  =  9B -12n

 

A-n  =  2B+2n

=A  =  3B + 3n 

=4A  =  12B + 12n        

 

Then, we can add these together to get--

 

7A =  17B

=7A / B  =  17

=A / B  =  17 / 7

 

Hope this helped!

 Mar 22, 2020

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