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?
:
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 {{{A/B}}}, replace A and B
{{{(17d)/(7d)}}}
Cancel d
A:B ratio: 17:7