document.write( "Question 598912: a worker needs to form 12 gallons of 70% ammonia solution to strip wax from some floors. He has one solution of 30% ammonia and another solution of 90% ammonia. How many gallons of the 90% solution should he use in the mixture? \n" ); document.write( "

Algebra.Com's Answer #378722 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = gallons of 30% mixture needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 90% mixture needed
\n" ); document.write( "given:
\n" ); document.write( " $\"+.3a+\"$ = gallons of ammonia in 30% mixture
\n" ); document.write( " $\"+.9a+\"$ = gallons of ammonia in 90% mixture
\n" ); document.write( "-----------
\n" ); document.write( "(1) $\"+a+%2B+b+=+12+\"$
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.9b+%29+%2F+12+=+.7+\"$
\n" ); document.write( "-----------
\n" ); document.write( "(2) $\"+.3a+%2B+.9b+=+.7%2A12+\"$
\n" ); document.write( "(2) $\"+.3a+%2B+.9b+=+8.4+\"$
\n" ); document.write( "(2) $\"+3a+%2B+9b+=+84+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+3+\"$ and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+3a+%2B+9b+=+84+\"$
\n" ); document.write( "(1) $\"+-3a+-+3b+=+-36+\"$
\n" ); document.write( " $\"+6b+=+48+\"$
\n" ); document.write( " $\"+b+=+8+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+12+\"$
\n" ); document.write( "(1) $\"+a+=+12+-+8+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "8 gallons of the 90% mixture are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.9b+%29+%2F+12+=+.7+\"$
\n" ); document.write( "(2) $\"+%28+.3%2A4+%2B+.9%2A8+%29+%2F+12+=+.7+\"$
\n" ); document.write( "(2) $\"+1.2+%2B+7.2+=+.7%2A12+\"$
\n" ); document.write( "(2) $\"+8.4+=+8.4+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );