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?
+37158 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
+33652 "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.
