document.write( "Question 1142452: A chemist has two alcohol solutions of different strengths, 30% alcohol and 45% alcohol solutions respectively. how many cubic cm of each must be used so as to make a mixture of 30cc that will contain 39% alcohol? \n" ); document.write( "

Algebra.Com's Answer #763187 by greenestamps(13200) $\"\"$ $\"About$

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\n" ); document.write( "The standard algebraic approach for mixture problems like this would be something like this:

\n" ); document.write( "x cc of 30% alcohol, plus (30-x) cc of 45% alcohol, yields 30 cc of 39% alcohol:

\n" ); document.write( " $\".30%28x%29%2B.45%2830-x%29+=+.39%2830%29\"$

\n" ); document.write( "You can solve that using basic algebra.

\n" ); document.write( "That method gives good practice with algebra; you should understand why and how it works.

\n" ); document.write( "But mixture problems like this can be solved much faster informally, with only logical reasoning and basic arithmetic.

\n" ); document.write( "Here is the solution using this alternate method.

\n" ); document.write( "(1) 39% is 3/5 of the way from 30% to 45%. (Easy to determine if you are good with mental math; otherwise, picturing the three percentages on a number line might help.)

\n" ); document.write( "(2) That means 3/5 of the mixture must be the 45% alcohol.

\n" ); document.write( "So...

\n" ); document.write( "ANSWER: 3/5 of 30 cc = 18cc of 45% alcohol; the rest, 12cc, of 30% alcohol. \n" ); document.write( "

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