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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 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?

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 Jun 4, 2020
 #1
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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.

 Jun 4, 2020
 #2
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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 

 Jun 4, 2020

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