Question 1143317
he loses 1/3 in the first game.
1/3 * 1 = 1/3
he is left with 1 - 1/3 = 2/3 * his original money.


he loses 3/5 * what he is left with from the first game in the second game.
3/5 * 2/3 = 6/15.
he is left with 2/3 - 6/15 = 10/15 - 6/15 = 4/15 * his original money.


he loses 4/7 of what he is left with from the second game in the third game.
4/7 * 4/15 = 16/105.
he is left with 4/15 - 16/105 = 28/105 - 16/105 = 12/105 of his original money.


that should be your solution.
he is left with 12/105 of his original money.


let's see if this is correct.
assume that he started with 12000 dollars.
he loses 1/3 of 12000 = 4000.
he is left with 8000.


he then loses 3/5 * 8000 = 4800.
he is left with 8000 - 4800 = 3200.


he then loses 4/7 * 3200 = 1828.571428571
he is left with 3200 - 1818.571428571 = 1371.428571429


1372.428571429 / 12000 = 0.114285714


0.114285714 * 105/105 = 12/105.


this confirms the solution is correct.