document.write( "Question 473567: how many liters of pure alcohol must be mixed with 20 liters of 25% alcohol solution to get 85% mixture? \n" ); document.write( "

Algebra.Com's Answer #324812 by oberobic(2304) $\"\"$ $\"About$

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When solving mixture problems, try to figure out how \"pure\" stuff you need.
\n" ); document.write( "In this case, we're told 20 liters of 25% alcohol, which means there are 5 liters of pure alcohol and 15 liters of water.
\n" ); document.write( "We're also told we need to obtain an unknown amount of pure alcohol to obtain an 85% solution.
\n" ); document.write( "Let x be the unknown.
\n" ); document.write( "So when we add that to the 20 liters, that will be (20+x).
\n" ); document.write( ".
\n" ); document.write( "20*25% + x*100% = 85% * (20+x)
\n" ); document.write( "20*.25 + x*1.00 = .85 (20+x)
\n" ); document.write( "5 + x = 17 + .85x
\n" ); document.write( ".
\n" ); document.write( "subtract .85 x from both sides
\n" ); document.write( "subtract 5 from both sides
\n" ); document.write( ".
\n" ); document.write( ".15x = 12
\n" ); document.write( "x = 80
\n" ); document.write( ",
\n" ); document.write( "Does this make sense?
\n" ); document.write( "The best way to tell is to check your answer.
\n" ); document.write( ".
\n" ); document.write( "Adding 80 liters of pure alcohol to the 20 liters of 25% alcohol yields 100 liters.
\n" ); document.write( "We know from above that 20 liters of 25% alcohol contain 5 liters of pure alcohol.
\n" ); document.write( "80+5 = 85
\n" ); document.write( "So we have 85 liters of pure alcohol in the 100 liters of solution, which is 85% alcohol.
\n" ); document.write( ".
\n" ); document.write( "Answer: Add 80 liters of pure alcohol.
\n" ); document.write( ".
\n" ); document.write( "Done. \n" ); document.write( "

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