document.write( "Question 475262: In testing gasohol mixtures, two mixtures are on hand: Mixture A (90% gasoline, 10% alcohol) and mixture B (80% gasoline, 20% alcohol). How much of each mixture must be combined to get 100 gallons of an 84% gasoline, 16% alcohol mixture. \n" ); document.write( "

Algebra.Com's Answer #325915 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = gallons of mixture A needed
\n" ); document.write( "Let $\"b\"$ = gallons of mixture B needed
\n" ); document.write( "In words:
\n" ); document.write( "(gallons of gasoline in final mixture) / (gallons of final mixture) = 84%
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(2) $\"+%28.9a+%2B+.8b%29+%2F+100+=+.84+\"$
\n" ); document.write( "-----------------
\n" ); document.write( "From (2),
\n" ); document.write( "(2) $\"+.9a+%2B+.8b+=+84+\"$
\n" ); document.write( "(2) $\"+9a+%2B+8b+=+840+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"8\"$ and subtract from (2)
\n" ); document.write( "(2) $\"+9a+%2B+8b+=+840+\"$
\n" ); document.write( "(1) $\"+-8a+-+8b+=+-800+\"$
\n" ); document.write( " $\"+a+=+40+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+=+100+\"$
\n" ); document.write( "(1) $\"+40+%2B+b+=+100+\"$
\n" ); document.write( "(1) $\"+b+=+60+\"$
\n" ); document.write( "40 gallons of mixture A must be added to 60 gallons of mixture B
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28.9a+%2B+.8b%29+%2F+100+=+.84+\"$
\n" ); document.write( "(2) $\"+%28.9%2A40+%2B+.8%2A60%29+%2F+100+=+.84+\"$
\n" ); document.write( "(2) $\"+%28+36+%2B+48+%29+%2F+100+=+.84+\"$
\n" ); document.write( "(2) $\"+84%2F100+=+.84+\"$
\n" ); document.write( "OK \n" ); document.write( "

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