Question

Sara, Cathy, and Tina have just finished playing three games. There was only one loser in each game. Sara lost the first game, Cathy lost the second game, and tina 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. How much did each have at the start?

Answer 1

start ... S , C , T

1st ... S-C-T , 2C , 2T

2nd ... 2(S-C-T) , [(2C - 2T - (S-C-T)] , 4T

3rd ... 4(S-C-T) , 4(C-T) - 2(S-C-T) ,
... 4T - 2(S-C-T) - 2(C-T) + (S-C-T)

4(S-C-T) = 24 ... S-C-T = 6

4(C-T) - 2(S-C-T) = 24 ... 2(C-T) - (6) = 12
... C-T = 9

4T - 2(6) - 2(9) + 6 = 24 ... 4T = 48
... T = 12
... C = 21
... S = 39

Answer 2

I truly don't understand this at all. Is there another way you can explain it to me.