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 January 1st, 2011, 04:13 PM #1 Senior Member   Joined: Oct 2010 Posts: 126 Thanks: 0 Ratios/fractions $\text{In an 8-gram solution of water and alcohol, the ratio by mass of water\\to alcohol is 3 to 1.\\If 12 grams of a solution consisting of 2 grams water for each gram of\\alcohol is added to the 8-gram solution, what fraction by mass of the\\new solution is alcohol?}$ I understand the first sentence perfectly well. It is the second sentence I'm not understanding. Water : Alcohol = 3 : 1 in the 8-gram solution. Water : Alcohol = 2 : x in the 12-gram solution. Water : Alcohol = 5 : x in the 20-gram 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: $\frac{\frac{1}{4}\cdot8+\frac{1}{3}\cdot12}{20}=\f rac{3}{10}$
January 1st, 2011, 04:37 PM   #3
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Re: Ratios/fractions

Quote:
 Originally Posted by MarkFL ....................fraction of alcohol 8 gram solution: 1/(3+1) = 1/4 12 gram solution: 1/(2+1) = 1/3 20 gram total: $\frac{\frac{1}{4}\cdot8+\frac{1}{3}\cdot12}{20}=\f rac{3}{10}$
Hmm...You simply added the amount of alcohol in the 8 and 12 gram solutions; the rest followed.
Darn, what a way to shine the light on my mathematical vacuity!

Anyway, thanks

January 1st, 2011, 04:55 PM   #4
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Re: Ratios/fractions

Hello, MathematicallyObtuse!

Quote:
 In an 8-gram solution of water and alcohol, the ratio by mass of water to alcohol is 3 to 1. If 12 grams of a solution consisting of 2 grams water for each gram of alcohol is added to the 8-gram solution, what fraction by mass of the new solution is alcohol?

We can baby-step 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

### in an 8 gram solution of water and alcohol

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