document.write( "Question 798711: A hospital staff mixed a 75% disinfectant solution with a 25% disinfectant solution. How many liters of each were used to make 30 L of a 45% disinfectant solution? \n" ); document.write( "

Algebra.Com's Answer #482360 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 75% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 25% solution needed
\n" ); document.write( "--------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+30+\"$
\n" ); document.write( "(2) $\"+%28+.75a+%2B+.25b+%29+%2F+30+=+.45+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+.75a+%2B+.25b+=+.45%2A30+\"$
\n" ); document.write( "(2) $\"+.75a+%2B+.25b+=+13.5+\"$
\n" ); document.write( "(2) $\"+75a+%2B+25b+=+1350+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+25+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+75a+%2B+25b+=+1350+\"$
\n" ); document.write( "(1) $\"+-25a+-+25b+=+-750+\"$
\n" ); document.write( " $\"+50a+=+600+\"$
\n" ); document.write( " $\"+a+=+12+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+30+\"$
\n" ); document.write( "(1) $\"+b+=+18+\"$
\n" ); document.write( "12 liters of 75% solution are needed
\n" ); document.write( "18 liters of 25% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.75a+%2B+.25b+%29+%2F+30+=+.45+\"$
\n" ); document.write( "(2) $\"+%28+.75%2A12+%2B+.25%2A18+%29+%2F+30+=+.45+\"$
\n" ); document.write( "(2) $\"+%28+9+%2B+4.5+%29+%2F+30+=+.45+\"$
\n" ); document.write( "(2) $\"+13.5+=+.45%2A30+\"$
\n" ); document.write( "(2) $\"+13.5+=+13.5+\"$
\n" ); document.write( " \n" ); document.write( "

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