document.write( "Question 677693: A pharmacist needs 70 liters of a 50% alcohol solution. She has availble a 30% alcohole solution and an 80% alocohol solution. How many liters of each solution should she mix to obtain 70 liters of wach solution should she mix to obtain 70 liters of a 50% alcohol solution? \n" ); document.write( "

Algebra.Com's Answer #421008 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 30% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 80% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+70+\"$
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.8b+%29+%2F+70+=+.5+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(2) $\"+.3a+%2B+.8b+=+.5%2A70+\"$
\n" ); document.write( "(2) $\"+.3a+%2B+.8b+=+35+\"$
\n" ); document.write( "(2) $\"+3a+%2B+8b+=+350+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+3+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+3a+%2B+8b+=+350+\"$
\n" ); document.write( "(1) $\"+-3a+-+3b+=+-210+\"$
\n" ); document.write( " $\"+5b+=+140+\"$
\n" ); document.write( " $\"+b+=+28+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+70+\"$
\n" ); document.write( "(1) $\"+a+%2B+28+=+70+\"$
\n" ); document.write( "(1) $\"+a+=+42+\"$
\n" ); document.write( "42 liters of 30% solution are needed
\n" ); document.write( "28 liters of 80% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+.3%2A42+%2B+.8%2A28+%29+%2F+70+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+12.6+%2B+22.4+%29+%2F+70+=+.5+\"$
\n" ); document.write( "(2) $\"+35+=+.5%2A70+\"$
\n" ); document.write( "(2) $\"+35+=+35+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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