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?
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!
