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 3 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).........................(1)
A - n =3(B +n).........................(2)
Solve these two simultaneous equations and should get:
A / B = 31 / 9 - the original ratio before they exchaned money.
+36916 a +n = 4 (b-n) a = 4b - 5n and
a-n = 3 (b+n) a = 3b + 4n multiply THIS equation by 1.25
1.25 a = 3.75 b + 5n add this equation to the top one
2.25 a = 7.75b divide both sides by b
2.25 a/b = 7.75 divide both sides by 2.25
a/b = 7.75/2.25 = 31/9
