A glass is half full of pure alcohol and another glass twice the volume is one third full. Both glasses are then filled to the top with water and mixed together. What is the fraction of alcohol in the resulting mixture?

Guest May 19, 2020

#1**+1 **

1/3 full in twice the volume is the same as 2/3 full in SAME volume

1/2 + 2/3 = 7/6 100% alcohol

then 1/2 + 4/3 water is added = 11/6 water

7/6 alcohol and 11/6 water

7/6 /( 7/6 + 11/6) = 7/6 /(3) = 7/18 = 38.8% alcohol

Example : container A is 12 oz 6 oz of alcohol + 6 oz of water

container B is 24 oz 8 oz of alcohol + 16 oz of water

Total : 36 oz 14 oz of alcohol

14/36 = 7/18 is alcohol = 38.89% alcohol

ElectricPavlov May 19, 2020

#2**+1 **

"*A glass is half full of pure alcohol and another glass twice the volume is one third full. Both glasses are then filled to the top with water and mixed together. What is the fraction of alcohol in the resulting mixture?*"

Edited to correct mistake. Thnaks to EP for pointing this out.

Alan May 19, 2020