Math (ratio) question

[Scrapster]

2 glasses. 1st glass is filled with x ounces of wine. 2nd glass is filled with x ounces of water. x is greater or equal to 1. One ounce of wine is taken out of the first glass and poured into the 2nd glass. The wine and the water in glass 2 mix uniformly. Now we remove one ounce from glass 2 and pour it into glass one.

Question: what is the ratio of water and wine in that one ounce that was poured into glass 1?

Would it be something like 1/x ounces of wine? Anyone have a guess?

 

[thEnEuRoMancER]

Exactly.

 

[enginjon]

ok so you first put one ounce wine in with water. Concentration of wine = 1/(x+1) Concentration of water x/(x+1)

Now one ounce is taken out:
Concentration of water : (x/(x+1))*1oz
Concentration of Wine : (1/(x+1))*1oz

 

[Handle]

Ratio of water to wine in the 2nd glass:
(x)/(1)

Ratio of water to total weight in 2nd glass:
(x)/(x+1)

Amount of water in that one ounce removed from 2nd glass:
[ (x)/(x+1) ] * 1 ounce = (x)/(x+1) ounces of water

Amount of wine in that one ounce removed from 2nd glass:
[ (1}/(x+1) ] * 1 ounce = (1)/(x+1) ounces

Ratio of water to wine in that one ounce removed from 2nd glass:
[ (x)/(x+1) ] / [ (1)/(x+1)]

= [ x*(x+1) ] / [ (x+1) * 1]

= x

The answer to your question is x.


It makes sense too... if x = 1, then the first glass is filled with one ounce and so is the second. When one ounce of wine is taken from the first glass and is mixed with one ounce of water, obviously the ratio is 1:1. The mathematical ratio of water to wine is 1, which is also the value of x.

 

[Moonbeam]

1/x oz of wine or 1/x oz of wine to water? It seems so, off hand, wine to water that is, but I'm not sure cause I'm drinking something stronger.

 

[thEnEuRoMancER]

He should've specified if he's interested in concentration of water/wine to mixture or water/wine to wine/water.

 

[phantom505]

I can turn water into wine, does that count?

 

[thEnEuRoMancER]

I can turn wine into urine, hehe

 

[enginjon]

i shall complete the circle and turn wine into urine

 

[Moonbeam]

A number of wineries, as it happens, turn wine into vinigar.