document.write( "Question 1194698: How many quarts of pure alcohol should be added to 10 quarts of 10% alcohol solution to obtain a mixture of 25% alcohol? \r
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Algebra.Com's Answer #826951 by greenestamps(13200) $\"\"$ $\"About$

You can put this solution on YOUR website!

\n" ); document.write( "Here is another way you can solve any 2-part \"mixture\" problem like this mentally, if your mental arithmetic skills are good.

\n" ); document.write( "You are starting with a 10% alcohol solution and adding 100% alcohol, stopping when you get to 25%.

\n" ); document.write( "Picture that as \"walking\" on the number line from 10 towards 100, stopping when you get to 25. The total distance of that walk was 100-10=90; you stopped when the distance you had traveled was 25-10=15.

\n" ); document.write( "Here is the key to this method:

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document.write( "* The fraction of the total distance you traveled was 15/90 = 1/6; *\r\n" );
document.write( "*   that means 1/6 of the final mixture is what you ADDED.         *\r\n" );
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\n" ); document.write( "Since 1/6 of the final mixture is the 100% alcohol you added, the 10 quarts of 10% alcohol you started with is 5/6 of the mixture; that means you added 2 quarts of 100% alcohol.

\n" ); document.write( "The words of explanation make this sound like a long and difficult process; but without the words the calculations are quick and easy:

\n" ); document.write( "100-10=90; 25-10=15; 15/90 = 1/6
\n" ); document.write( "1-1/6 = 5/6
\n" ); document.write( "5/6 = 10 quarts --> 1/6 = 2 quarts

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