document.write( "Question 658959: Suppose that you have a supply of a 40% solution of alcohol and a 60% solution of alcohol. How many quarts of each should be mixed to produce 90 quarts that is 50% alcohol?
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Algebra.Com's Answer #410571 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = quarts of 40% solution needed
\n" ); document.write( "Let $\"b\"$ = quarts of 60% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+90+\"$
\n" ); document.write( "(2) $\"+%28+.4a+%2B+.6b+%29+%2F+90+=+.5+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+.4a+%2B+.6b+=+.5%2A90+\"$
\n" ); document.write( "(2) $\"+.4a+%2B+.6b+=+45+\"$
\n" ); document.write( "(2) $\"+4a+%2B+6b+=+450+\"$
\n" ); document.write( "--------------------
\n" ); document.write( "Multiply both sides of (1) by $\"+4+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+4a+%2B+6b+=+450+\"$
\n" ); document.write( "(1) $\"+-4a+-+4b+=+-360+\"$
\n" ); document.write( " $\"+2b+=+90+\"$
\n" ); document.write( " $\"+b+=+45+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+90+\"$
\n" ); document.write( "(1) $\"+a+%2B+45+=+90+\"$
\n" ); document.write( "(1) $\"+a+=+45+\"$
\n" ); document.write( "45 quarts of 40% solution are needed
\n" ); document.write( "45 quarts of 60% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.4%2A45+%2B+.6%2A45+%29+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+18+%2B+27+%29+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+45+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+45+=+.5%2A90+\"$
\n" ); document.write( "(2) $\"+45+=+45+\"$
\n" ); document.write( "OK \n" ); document.write( "

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