document.write( "Question 696425: A chemist mixes one solution that is 10% alcohol with a solution that is 15% alcohol to make 100 milliliters of a solution that is 12% alcohol. How many milliliters of liquid was in the first solution? \n" ); document.write( "

Algebra.Com's Answer #429048 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = ml of 10% solution
\n" ); document.write( "Let $\"+b+\"$ = ml of 15% alcohol
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(2) $\"+%28+.1a+%2B+.15b+%29+%2F+100+=+.12+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+.1a+%2B+.15b+=+.12%2A100+\"$
\n" ); document.write( "(2) $\"+.1a+%2B+.15b+=+12+\"$
\n" ); document.write( "(2) $\"+10a+%2B+15b+=+1200+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+10+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+10a+%2B+15b+=+1200+\"$
\n" ); document.write( "(1) $\"+-10a+-+10b+=+-1000+\"$
\n" ); document.write( " $\"+5b+=+200+\"$
\n" ); document.write( " $\"+b+=+40+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(1) $\"+a+=+100+-+b+\"$
\n" ); document.write( "(1) $\"+a+=+100+-+40+\"$
\n" ); document.write( "(1) $\"+a+=+60+\"$
\n" ); document.write( "60 ml of 10% solution is needed
\n" ); document.write( "40 ml of 15% alcohol is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.1a+%2B+.15b+%29+%2F+100+=+.12+\"$
\n" ); document.write( "(2) $\"+%28+.1%2A60+%2B+.15%2A40+%29+%2F+100+=+.12+\"$
\n" ); document.write( "(2) $\"+%28+6+%2B+6+%29+%2F+100+=+.12+\"$
\n" ); document.write( "(2) $\"+12+=+.12%2A100+\"$
\n" ); document.write( "(2) $\"+12+=+12+\"$
\n" ); document.write( "OK\r
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