document.write( "Question 720623: Gus has on hand 5% alcohol solution and a 20% alcohol solution. He needs 30 liters of 10% alcohol solution. How many liters of each solution should he mix together to obtain the mixture he needs? \n" ); document.write( "

Algebra.Com's Answer #441897 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 5% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 20% solution needed
\n" ); document.write( "-----------
\n" ); document.write( "(1) $\"+a+%2B+b+=+30+\"$
\n" ); document.write( "(2) $\"+%28+.05a+%2B+.2b+%29+%2F+30+=+.1+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+.05a+%2B+.2b+=+3+\"$
\n" ); document.write( "(2) $\"+5a+%2B+20b+=+300+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+5+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+20b+=+300+\"$
\n" ); document.write( "(1) $\"+-5a+-+5b+=+-150+\"$
\n" ); document.write( " $\"+15b+=+150+\"$
\n" ); document.write( " $\"+b+=+10+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+30+\"$
\n" ); document.write( "(1) $\"+a+=+20+\"$
\n" ); document.write( "20 liters of 5% solution are needed
\n" ); document.write( "10 liters of 20% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+.05%2A20+%2B+.2%2A10+%29+%2F+30+=+.1+\"$
\n" ); document.write( "(2) $\"+%28+1%2B+2+%29+%2F+30+=+.1+\"$
\n" ); document.write( "(2) $\"+3%2F30+=+.1+\"$
\n" ); document.write( "(2) $\"+3+=+3+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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