document.write( "Question 891887: A pharmacist wants to prepare 300 ml of a 20 percent alcohol solution. How much of a 30 percent solution and a 15 percent solution can be used to form the desired mixture? \n" ); document.write( "

Algebra.Com's Answer #540129 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ml of 30% solution needed
\n" ); document.write( "Let $\"+b+\"$ = ml of 15% solution needed
\n" ); document.write( "-------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+300+\"$
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.15b+%29+%2F+300+=+.2+\"$
\n" ); document.write( "-------------------------------
\n" ); document.write( "(2) $\"+.3a+%2B+.15b+=+.2%2A300+\"$
\n" ); document.write( "(2) $\"++.3a+%2B+.15b+=+60+\"$
\n" ); document.write( "(2) $\"+30a+%2B+15b+=+6000+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+15+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+30a+%2B+15b+=+6000+\"$
\n" ); document.write( "(1) $\"+-15a+-+15b+=+4500+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( " $\"+15a+=+1500+\"$
\n" ); document.write( " $\"+a+=+100+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+300+\"$
\n" ); document.write( "(1) $\"+b+=+200+\"$
\n" ); document.write( "100 ml of 30% solution is needed
\n" ); document.write( "200 ml of 15% solution is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.15b+%29+%2F+300+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+.3%2A100+%2B+.15%2A200+%29+%2F+300+=+.2+\"$
\n" ); document.write( "(2) $\"+30+%2B+30+=+.2%2A300+\"$
\n" ); document.write( "(2) $\"+60+=+60+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );