Math Is Fun Forum

hotgal24

Member

Registered: 2008-01-12

Posts: 4

solve this and u are an absolute genius

Two identical glasses, one filled two thirds with water and the other filled completely with a mixed solution of 60% alcohol and 40% water.

One third of the mixed solution in the second glass is then poured into the first glass. After mixing, a third of the content of the first glass is poured into the second glass.

What is the concentration of the alcohol in the second glass now?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: solve this and u are an absolute genius

Draw a big picture, or at least I did.
Then I noticed that when I drew vertical lines
on the 2nd glass to divide it into 3 parts,
I saw that 40% and 60% can be 2 and 3 instead.
4 is to 6 as 2 is to 3.  4/6 = 2/3   4:6 = 2:3
So I put 2  2  2 and 3 3 3 in the 2nd glass locations.
That added up to 15.
Then the 1st glass I noticed was 5 air and 10 water.
Both glasses are 15 in this pretend scenario.

Then I put the 3 and 2 from 2nd to 1st glass.
Then I tried to divide 1st glass up into 3 parts.
The 3 grain alcohols divide by 3 good: just 1 + 1 + 1.
The 2 + 10 waters divide by 3 good: 4 + 4 + 4.
So I took the 4 water and the 1 alcohol and put
them back in the 5 airy space of 2nd glass to finish.
Then I counted up the alcohol and got 1 + 3 + 3.
And I counted up the water and got 4 + 2 + 2.
So that is (1 + 3 + 3) : (4 + 2 + 2).
"seven to eight" is the ratio of alcohol to water.
There are 7 alcohol units to every 8 water units.
That's about half and half, right?
So make sure your answer is about half, but not exactly.

---

igloo myrtilles fourmis

JaneFairfax

Member

Registered: 2007-02-23

Posts: 6,868

Re: solve this and u are an absolute genius

Let the volume of each glass be V. Then there is

alcohol in the second glass. So one third of it will contain

alcohol. Take this and mix it into the first glass. When it’s well mixed, one third of the contents of the first glass will contain

alcohol. Take this and put it back into the second glass. Now the second glass has

alcohol. Hence the ABV is

Last edited by JaneFairfax (2008-05-23 12:26:37)