Answer: 28.
Step-by-step explanation:
Let's define D = # of marbles in Damon's bag at the beginning.
First, he gave D/2 + 2 marbles to Artemio, so now he has:
(D - D/2 - 2) = (D/2 - 2) marbles left.
Now, he gives 1/4 plus of what he has left plus 5 to Banou, so he gives:
(D/2 - 2)/4 + 5 marbles to Banou.
Then Damon has now:
(D/2 - 2) - (D/2 - 2)/4 - 5 = 3*(D/2 - 2)/4 - 5.
Now Damon gives half of this to Alex, then the amount that he has left is:
(3*(D/2 - 2)/4 - 5)/2
And we know that this is equal to 2, then we can solve this equation as:
(3*(D/2 - 2)/4 - 5)/2 = 2
Let's solve this for D.
(3*(D/2 - 2)/4 - 5) = 2*2 = 4.
3*(D/2 - 2)/4 = 4 + 5 = 9
3*(D/2 - 2) = 9*4 = 36
(D/2 - 2) = 36/3 = 12
D/2 = 12 + 2 = 14
D = 2*14 = 28
Damon initially had 28 marbles.
