Coffee Math

J

johnjones

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Sep 8, 2005
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I do not know how coffee and cream work. I mean, it's a simple question, but I don't even know to get to the answer or what reasoning I can use to justify this:

Question:
In front of you is a cup filled with coffee, and a jug with an equal amount of cream. You pour some of the coffee into the cream jug, stir it up, and then refill the coffee cup to its original level from the cream jug. Which is greater, the amount of coffee in the cream jug, or the amount of cream in the coffee cup.

If I start w/ the same amt, shouldn't I end with that?! I'm a bit confused, thanks. I could let x be the amount of coffee in the jug or something?
 
Your logic is impecable. Whatever coffee is replaced with cream in the cup is now in the cream jug and vice-versa. They are equal. Good job.

BTW it doesn't matter whether that the amounts are the same. You could have twice as much coffee as cream and it would work the same. Still equal.
 
I can't say it any clearer.
Never mind mixing it. Just take some coffee out, replace it with THE SAME AMOUNT of cream to fill the cup. Put in THE SAME AMOUNT of coffee to refill the jug. They have to be equal.

It matters not how much was in either when you started. You are moving a certain amount and replacing it with THE SAME AMOUNT.
 
Gene is absolutely correct!

Urn R has 20 red balls.
Urn G has 30 green balls.

Take 10 green balls from urn G and add them to urn R.
Mix the balls thoroughly and remove any 10 balls and place them in urn G.

Which is larger: the number of green balls in urn R or the number of red balls in urn G?


At the end of the exchange of balls, urn R will probably have some green balls.
. . Let's say, there are g green balls in urn R.

Then urn R contains: g green balls and 20 - g red balls.
. . That is, urn R is missig g red balls . . .which are in urn G.

Urn R contains: g green balls and 20 - g red balls.
Urn G contains: g red balls and 30 - g green balls.

Get it? .The amounts of 'foreign matter' in each urn are always equal
 
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