Question 763406: Alice and Bob each have a certain amount of money. If Alice receives dollars from Bob, then she will have 3 times as much money as Bob. If, on the other hand, she gives 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?
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! Alice and Bob each have a certain amount of money.
If Alice receives dollars from Bob, then she will have 3 times
as much money as Bob.
If, on the other hand, she gives 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?
:
Let A = Alice's original amt of money
Let B = Bob's original amt of money
Let d = the dollars they are referring to
:
Write an equation for each statement, simplify:
:
"If Alice receives dollars from Bob, then she will have 3 times as much money as Bob."
A + d = 3(B-d)
A + d = 3B - 3d
A = 3B - 3d - d
A = 3B - 4d
:
"she gives dollars to Bob, then she will have 2 times as much money
as Bob."
A - d = 2(b+d)
A - d = 2B + 2d
A = 2B + 2d + d
A = 2B + 3d
A = A; therefore
3B - 4d = 2B + 3d
3B - 2B = 3d + 4d
B = 7d
:
Find A in terms of d also,
A = 2B + 3d
Replace B with 7d
A = 2(7d) + 3d
A = 17d
"neither gives the other any money, what is the ratio of the amount
of money Alice has to the amount Bob has?"
Find  , replace A and B
Cancel d
A:B ratio: 17:7
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