We overheard two boys playing marbles near Quizmaster Towers, and this is what they said.
A: I've got more marbles than you have!
B: I bet you haven't - see for yourself
A: Okay, you have got more than me, but I'm the better player so I'll soon have more than you
B: You think so?
A: I do, and if I win three marbles from you I'll have twice as many as you'll have
B: You're on
[pause while they played]
A: Oh you're so lucky, I've never seen such a fluke
B: Told you I'd win
A: Yes, but you only won two
B: I might've won only two from you, but now I've three times as many marbles as you have
A: Right, you won't beat me again
[pause while they played again]
A: Oh I give up
B: Well you're going to have to give up, as I've got all your marbles
So how many marbles does player B now have?
From A's statement about winning three marbles we have A + 3 = 2(B - 3) or
A + 3 = 2B - 6 [1]
And from B's statement about winning two marbles we have 3(A - 2) = B + 2 or
3A - 6 = B + 2
Doubling both sides of this gives
6A - 12 = 2B + 4 [2]
If we subtract [1] from [2] we get
5A - 15 = 10
Adding 15 to both sides gives
5A = 25
And so A started with five marbles
Putting A = 5 back into [1] we get
5 + 3 = 2B - 6
So
2B = 5 + 3 + 6 = 14
B = 7
So B started with seven marbles and has won all of A's five marbles, and he now has 12