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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?

 May 19, 2020
 #1
avatar+26007 
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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

 May 19, 2020
edited by ElectricPavlov  May 19, 2020
 #2
avatar+30655 
+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.

 May 19, 2020
edited by Alan  May 20, 2020

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