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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 8 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?

 Jun 23, 2023
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A + n = 4(B - n)

A - n = 8(B + n)

 

The following equations result from the above information. The rest is just clever manipulation of algebra.

A + n = 4(B - n)

A + n = 4B - 4n

A = 4B - 5n

 

A - n = 8(B + n)

A - n = 8B + 8n

A = 8B + 9n

 

4B - 5n = 8B + 9n

-4B = 14n

B = -7/2 * n

 

A = 4 * -7/2 * n - 5n

A = -14n - 5n

A = -19n

 

Since we seek the ratio, A/B = -19n/(-7/2) * n = 38/7

 

Just make sure I did not make any mistakes!

 Jun 23, 2023

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