Question

Damon was on his way to a marble tournament when he met Artemio. Damon's bag of marbles was heavy, so he gave Artemio ½ of his marbles plus 2. Then he met Banou and gave her ¼ of his remaining marbles plus 5. Just before arriving at the tournament, he met Alex and gave him ½ of the marbles he had left. When he got to the tournament, he had 2 marbles left. How many marbles did he start with?

Answer 1

Answer: 28.

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.