document.write( "Question 533457: Find the amount of twenty five percent acid solution and the amount of a fifteen percent acid solution that combine to prepare fifty oz at an eighteen percent acid solution. \n" ); document.write( "

Algebra.Com's Answer #351092 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = ounces of 25% solution needed
\n" ); document.write( "Let $\"b\"$ = ounces of 15% solution needed
\n" ); document.write( "given:
\n" ); document.write( " $\"+.25a+\"$ = ounces of acid in 25% solution
\n" ); document.write( " $\"+.15b+\"$ = ounces of acid in 15% solution
\n" ); document.write( "----------------------------------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(2) $\"+%28+.25a+%2B+.15b+%29+%2F+50+=+.18+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(2) $\"+.25a+%2B+.15b+=+.18%2A50+\"$
\n" ); document.write( "(2) $\"+.25a+%2B+.15b+=+9+\"$
\n" ); document.write( "(2) $\"+25a+%2B+15b+=+900+\"$
\n" ); document.write( "(2) $\"+5a+%2B+3b+=+180+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"3\"$ , and
\n" ); document.write( "subtract (1) from (2)
\n" ); document.write( "(2) $\"+5a+%2B+3b+=+180+\"$
\n" ); document.write( "(1) $\"+-3a+-+3b+=+-150+\"$
\n" ); document.write( " $\"+2a+=+30+\"$
\n" ); document.write( " $\"+a+=+15+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+15+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+b+=+35+\"$
\n" ); document.write( "15 ounces of 25% solution are needed
\n" ); document.write( "35 ounces of 15% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.25%2A15+%2B+.15%2A35+%29+%2F+50+=+.18+\"$
\n" ); document.write( "(2) $\"+%28+3.75+%2B+5.25+%29+%2F+50+=+.18+\"$
\n" ); document.write( "(2) $\"+9%2F50+=+.18+\"$
\n" ); document.write( "(2) $\"+9+=+9+\"$
\n" ); document.write( "OK \n" ); document.write( "

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