Thread: Which is more pure?

Hmm. Hard to say. I would say the one that is primarily milk.

You take a full cup of milk out and put it into the chocolate syrup, and mix the two. Then you take a cup out of that (which has less than a cup of chocolate syrup in it) out of that and put it in the jug of milk. I would think there is (percentage-wise) more milk in the first jug than chocolate syrup in the second jug...

...but then...I'm sick and have been drinking, so I probably got it wrong in there somewhere.

In what sense do you use the word 'pure'?

Originally Posted by grasshoppa

In what sense do you use the word 'pure'?

"Pure," as in "which bucket has the highest percentage of its original substance"?

First cup doesn't change the purity of the first jug, and contaminates the second by an amount of one cup of liquid.

Second cup reduces the amount of milk in the second jug, and also the amount of chocolate syrup. Depending on how you measure, this is either an increase of purity(lowering the amount of milk) or a decrease of purity (removing much more syrup than milk). The first jug would similarly increase or decrease, but by a different amount because the liquid moved contained a much larger volume of chocolate syrup than milk.

Are we measuring purity by the ratio of milk to chocolate syrup, or by the quantity of milk in the syrup jug(and vice versa)?

They're equally pure

Code:

milk                             suryp
12 out of 12 cups                12 out of 12 cups
11 out of 11 cups                12 out of 13 cups
Add a cup containing 1/13 milk   Remove a cup containing 12/13 suryp
11 and 1/13 out of 12 cups       11 and 1/13 out of 12 cups

Originally Posted by Abra

You've got two gallon jugs. The first is 3/4 filled with milk, the second is 3/4 filled with chocolate syrup. You take a cup of milk from the first jug, and pour it into the second. You mix the second, and then take a cup from the second and mix it into the first jug.

Which jug is more pure?

1. Convert everything to cups
12 cups of milk
12 cups of chocolate syrup

2. Take a cup of milk from the first jug and pour it into the second
11 cups of milk
13: 12 cups of chocolate syrup/1 cups of milk
Now the second solution has 1/13 milk.

3. Take a cup from the second and pour it into the first
11 cups + 1/13 and 12/13 cups of chocolate syrup
1/13 milk in the second solution.

Urgh...my math is rusty. don't know what else to do there.

Anyway, I think John11 has it right.

You're removing a cup of milk from the original jug, so it has less milk to help dilute the chocolate syrup additive, making this question much harder than it appears.

Therefor, I don't care, I hate chocolate milk anyways.

They're both equally pure.