document.write( "Question 451165: Theresa Yee, a chemist, has 25% hydrochloric acid solution and a 50% hydrochloric acid solution. How many liters of each should she mix to get 10 liters of a hydrochloric acid solution with a 40% acid concentration? \n" ); document.write( "

Algebra.Com's Answer #310259 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 25% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 50% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$ liters
\n" ); document.write( "(2) $\"+%28.25a+%2B+.5b%29+%2F+10+=+.4+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "(2) $\"+.25a+%2B+.5b+=+4+\"$
\n" ); document.write( "(2) $\"+25a+%2B+50b+=+400+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"25\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+25a+%2B+50b+=+400+\"$
\n" ); document.write( "(1) $\"+-25a+-+25b+=+-250+\"$
\n" ); document.write( " $\"+25b+=+150+\"$
\n" ); document.write( " $\"+b+=+6+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+10+\"$
\n" ); document.write( " $\"+a+=+4+\"$
\n" ); document.write( "4 liters of 25% solution are needed
\n" ); document.write( "6 liters of 50% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28.25a+%2B+.5b%29+%2F+10+=+.4+\"$
\n" ); document.write( "(2) $\"+%28.25%2A4+%2B+.5%2A6%29+%2F+10+=+.4+\"$
\n" ); document.write( "(2) $\"+%281+%2B+3%29%2F10+=+.4+\"$
\n" ); document.write( "(2) $\"+4%2F10+=+.4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );