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?

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.

Answer 3

To solve this problem, let's work backwards.

We know that after three games, each woman had $24. So, let's assume that after the third game, each woman had $x.

Now, let's think about what happened after the second game. We know that the loser of the second game (Cathy) had to double the money of the other two. Therefore, if after the second game, each woman had $x, then Cathy had $2x, and the winner of the second game (Tina) had $2x as well.

Moving on to the first game, we know that the loser (Sara) had to double the money of the other two. Therefore, if after the first game, each woman had $x, then Sara had $2x, and the winner of the first game (Cathy) had $2x as well.

Now, let's summarize what we have:
- After the first game: Sara had $2x, Cathy had $2x, and Tina had $x.
- After the second game: Sara had $2x, Cathy had $2x, and Tina had $2x.
- After the third game: Sara had $x, Cathy had $x, and Tina had $x.

Since we know that after three rounds, each woman had $24, we can set up the following equation:
$2x + $2x + $x = $24 + $24 + $24

Simplifying the equation:
5x = $72
x = $72/5

Now, we can find the initial amounts for each woman:
- Sara: $2x = $2 * ($72/5)
- Cathy: $2x = $2 * ($72/5)
- Tina: $x = $72/5

Evaluating each expression:
- Sara: $2 * ($72/5) = $144/5
- Cathy: $2 * ($72/5) = $144/5
- Tina: $72/5

Therefore, at the start, Sara, Cathy, and Tina each had $144/5 or $28.80.