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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 $7$ 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 23, 2024
 #1
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I think the two equations should be like this....

 

If Alice receives n dollars from Bob, then she will have 3 times as much money as Bob.

A + n  =  3 * (B - n)

 

If she gives n dollars to Bob, then she will have 2 times as much money as Bob.

A - n  =  2 * (B + n)

 

So we have..

A + n  =  3B - 3n    →     A  =  3B  - 4n     →     3A  =  9B   - 12n

A - n  =  2B + 2n    →     A  =  3B + 3n     →     4A  =  12B + 12n        Add these two to get..

 

7A  =  17B     →     7A / B  =  17     →     A / B  =  17 / 7
 

this one was hard

 Mar 23, 2024

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