document.write( "Question 1088063: A bartender needs to make 5 gallons of a mixed drink containing 12% alcohol. she is going to combine a 10% with a 15% alcohol. how much of each should she use? \n" ); document.write( "

Algebra.Com's Answer #702343 by Tatiana_Stebko(1539) $\"\"$ $\"About$

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Let $\"x\"$ be the number of gallons with a 10% alcohol
\n" ); document.write( "Let $\"y\"$ be the number of gallons with a 15% alcohol
\n" ); document.write( "A bartender needs to make 5 gallons of a mixed drink => $\"x%2By=5\"$
\n" ); document.write( "a mixed drink contains 12% alcohol => $\"0.10x%2B0.15y=0.12%2A5\"$
\n" ); document.write( "The system of equations
\n" ); document.write( " $\"system%28x%2By=5%2C+0.10x%2B0.15y=0.6%29\"$
\n" ); document.write( "Multiply the second equation by 10
\n" ); document.write( " $\"system%28x%2By=5%2C+x%2B1.5y=6%29\"$
\n" ); document.write( " $\"system%28x=5-y%2C+x%2B1.5y=6%29\"$
\n" ); document.write( "substitute $\"x=5-y\"$ into the second equation
\n" ); document.write( " $\"system%28x=5-y%2C+5-y%2B1.5y=6%29\"$
\n" ); document.write( " $\"system%28x=5-y%2C+0.5y=1%29\"$
\n" ); document.write( " $\"system%28x=5-y%2C+y=2%29\"$
\n" ); document.write( " $\"system%28x=5-2%2C+y=2%29\"$
\n" ); document.write( " $\"system%28x=3%2C+y=2%29\"$
\n" ); document.write( "A bartender needs to combine 3 gallons with a 10% alcohol and 2 gallons with a 15% alcohol \n" ); document.write( "

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