document.write( "Question 648118: A chemist is mixing a 40% salt solution with a 20% salt solution to make 50 L of a new solution that will contain 25% salt. How much of the 40% solution should the chemist use? \n" ); document.write( "

Algebra.Com's Answer #406565 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 40% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 20% solution needed
\n" ); document.write( " $\"+.4a+\"$ = liters of salt in 40% solution
\n" ); document.write( " $\"+.2b+\"$ = liters of salt in 20% solution
\n" ); document.write( "------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(2) $\"+%28+.4a+%2B+.2b+%29+%2F+50+=+.25+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+.4a+%2B+.2b+=+.25%2A50+\"$
\n" ); document.write( "(2) $\"+.4a+%2B+.2b+=+12.5+\"$
\n" ); document.write( "(2) $\"+4a+%2B+2b+=+125+\"$
\n" ); document.write( "---------------------
\n" ); document.write( "Multiply both sides of (1) by $\"2\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+4a+%2B+2b+=+125+\"$
\n" ); document.write( "(1) $\"+-2a+-+2b+=+-100+\"$
\n" ); document.write( " $\"+2a+=+25+\"$
\n" ); document.write( " $\"+a+=+12.5+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+12.5+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+b+=+37.5+\"$
\n" ); document.write( "12.5 liters of the 40% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.4a+%2B+.2b+%29+%2F+50+=+.25+\"$
\n" ); document.write( "(2) $\"+%28+.4%2A12.5+%2B+.2%2A37.5+%29+%2F+50+=+.25+\"$
\n" ); document.write( "(2) $\"+%28+5+%2B+7.5+%29+%2F+50+=+.25+\"$
\n" ); document.write( "(2) $\"+12.5+=+.25%2A50+\"$
\n" ); document.write( "(2) $\"+12.5+=+12.5+\"$
\n" ); document.write( "OK
\n" ); document.write( " \n" ); document.write( "

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