document.write( "Question 640216: What quantity of a 40% acid solution must be mixed with a 10% solution to produce 300 quarts of a 30% solution? \n" ); document.write( "

Algebra.Com's Answer #403064 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = quarts of 40% solution needed
\n" ); document.write( "Let $\"+b+\"$ = quarts of 10% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+300+\"$
\n" ); document.write( "(2) $\"+%28+.4a+%2B+.1b+%29+%2F+300+=+.3+\"$
\n" ); document.write( "------------------------
\n" ); document.write( "(2) $\"+.4a+%2B+.1b+=+.3%2A300+\"$
\n" ); document.write( "(2) $\"+.4a+%2B+.1b+=+90+\"$
\n" ); document.write( "(2) $\"+4a+%2B+b+=+900+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+4a+%2B+b+=+900+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-300+\"$
\n" ); document.write( " $\"+3a+=+600+\"$
\n" ); document.write( " $\"+a+=+200+\"$
\n" ); document.write( "and since
\n" ); document.write( "(1) $\"+a+%2B+b+=+300+\"$
\n" ); document.write( "(1) $\"+b+=+100+\"$
\n" ); document.write( "200 quarts of 40% solution is needed
\n" ); document.write( "100 quarts of 10% solution is needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.4%2A200+%2B+.1%2A100+%29+%2F+300+=+.3+\"$
\n" ); document.write( "(2) $\"+%28+80+%2B+10+%29+%2F+300+=+.3+\"$
\n" ); document.write( "(2) $\"+90+%2F+300+=+.3+\"$
\n" ); document.write( "(2) $\"+90+=+.3%2A300+\"$
\n" ); document.write( "(2) $\"+90+=+90+\"$
\n" ); document.write( "OK \n" ); document.write( "

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