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# >- Algebra 1 -< Alice and Bob each have a certain amount of money

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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 3 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?

By The Way.....

CPhill got this question wrong (rerember CPhill? it was only yesterday)

Sooo if you get this question correct you've finally solved a problem CPhill GOT WRONG!!!

Guest Oct 10, 2017

#1
+4695
+1

Hey, CPhill is just a human too! remember that!!

Here is the original question. )

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

hectictar  Oct 10, 2017
Sort:

#1
+4695
+1

Hey, CPhill is just a human too! remember that!!

Here is the original question. )

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

hectictar  Oct 10, 2017
#2
+76837
+1

Thahks, for the correction, hectictar.....!!!

Sheesh, guest....OK.....I made a mistake.....it happens....!!!!

CPhill  Oct 10, 2017

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