With How Much Money Did Each Start the Game?

Date: 04/24/2002 at 22:06:50
From: John Sorci
Subject: Math word problems

Ferne, Donna, and Susan have just finished playing three games. There 
was only one loser in each game. Ferne lost the first game, Donna lost 
the second game, and Susan lost the third game. After each game, the 
loser was required to double the money of the other two. After three 
rounds, each woman had $24.00. How much did each have at the start of 
the game?

Date: 04/25/2002 at 10:43:25
From: Doctor Ian
Subject: Re: Math word problems

Hi John,

Have you tried working through it backward? 

Susan lost the third game, and she had to double what Ferne and Donna 
had. They ended up with $24, which means that they had $12 before 
that, and Susan ended up with $24, which means she had $48 before 
that, since she had to give $12 each to Ferne and Donna:

          Game 3
          ----------
  Ferne:  $12 -> $24
  Donna:  $12 -> $24
  Susan:  $48 -> $24
  
Donna lost the second game, so Susan must have started with $24 to end 
up with $48; and Ferne must have started with $6 to end up with $12:

          Game 2        Game 3
          ----------    ----------
  Ferne:   $6 -> $12    $12 -> $24   
  Donna:    ? -> $12    $12 -> $24
  Susan:  $24 -> $48    $48 -> $24
  
We know that Donna ended up with $12, so how much did she have to have 
at the beginning of this game?

You can follow the same strategy to figure out what happened during 
the first game.

Does this help? 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/