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January 1st, 2011, 04:13 PM  #1 
Senior Member Joined: Oct 2010 Posts: 126 Thanks: 0  Ratios/fractions I understand the first sentence perfectly well. It is the second sentence I'm not understanding. Water : Alcohol = 3 : 1 in the 8gram solution. Water : Alcohol = 2 : x in the 12gram solution. Water : Alcohol = 5 : x in the 20gram solution ( 12 + 8 ) 
January 1st, 2011, 04:26 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Ratios/fractions
....................fraction of alcohol 8 gram solution: 1/(3+1) = 1/4 12 gram solution: 1/(2+1) = 1/3 20 gram total: 
January 1st, 2011, 04:37 PM  #3  
Senior Member Joined: Oct 2010 Posts: 126 Thanks: 0  Re: Ratios/fractions Quote:
Darn, what a way to shine the light on my mathematical vacuity! Anyway, thanks  
January 1st, 2011, 04:55 PM  #4  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 408  Re: Ratios/fractions Hello, MathematicallyObtuse! Quote:
We can babystep our way through this one . . . [color=beige]. [/color] We start with 8 grams which has: 6 grams of water and 2 grams of alcohol. [color=beige]. . . . [/color]We add 12 grams which has: 8 grams of water and 4 grams of alcohol. And we have 20 grams which has: 14 grams of water and 6 grams of alcohol. Therefore . . .  
January 1st, 2011, 05:04 PM  #5 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: Ratios/fractions
That seemed to be the easiest way to answer the question. If you want to add ratios, you need to make sure the two numbers x:y add up to the total grams in the solution. 3:1 (3 + 1 = 4, 8/4 = 2, thus we use 6:2) 2:1 (2 + 1 = 3, 12/3 = 4, thus we use 8:4) 6:2 8:4  14:6 6/(14+6) = 3/10 

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