In the card game “Match,” the loser has to double the money of the other players. Juan, Jamal and Joey are playing. First Juan loses and doubles the money of Jamal and Joey. Joey loses the next hand and doubles the money of Jamal and Juan. Jamal loses the next hand and doubles the money of Juan and Joey. At this point they quit and each has $10. How much did each start with and how much did each win or lose relative to the money they started with?

Answer 1

If the start with amounts x,y,z

after the 3 rounds, the holdings are

x-y-z, 2y, 2z

2(x-(y+z)),4y,2z-(x-(y+z))-2y
= 2x-2y-2z, 4y, 3z-x-y

2(2x-2y-2z), 4y-(2x-2y-2z)-(3z-x-y), 2(3z-x-y)
= 4x-4y-4z, 7y-x-z, 6z-2x-2y

So, now we have three equations:

4x-4y-4z = 10
-x+7y-z = 10
-2x-2y+6z = 10

x = 16.25
y = 5.00
z = 8.75
Note: total=30 as desired.

check the holdings after each round.
round 1: 2.50, 10.00, 17.50
round 2: 5.00, 20.00, 5.00
round 3: 10.00, 10.00, 10.00

Answer 2

In retrospect, it would probably have been easier to work this one backwards, with no algebra:

After round 3: 10,10,10
After round 2: 5,20,5
and so on...