How many pints did I drink in total?

Question

I have a pint of orange juice. I drink half of it and then give it to you. You drink half of what's remaining, and then pass it back to me. I drink half of what's remaining and then give it to you. This process continues forever. How many pints did I drink in total?

Answer 1

Here's a good way to look at it...

 

The first drink you have is 1/2 pint, and the first drink I have is 1/2 of that.

 

The second drink you have is 1/2 of what I had, and the second drink I have is 1/2 of your second drink.

 

So every time you have a drink, I have a drink that's half that amount.

 

So continue that forever, and you end up having twice as much as I do.

 

In order for that to be true, and for the total to add up to 1 pint, you have to have 2/3 pint, and I have to have 1/3 pint.

 

So the answer is, you have 2/3 pint.