document.write( "Question 292646: how many quarts of 30% soap solution and 60% soap solution should be mixed to obtain 60 quarts of 50 % soap solution? \n" ); document.write( "

Algebra.Com's Answer #211369 by josmiceli(19441) $\"\"$ $\"About$

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In words:
\n" ); document.write( "(total quarts of soap)/(total quarts of solution) = 50%
\n" ); document.write( "Let $\"a\"$ = quarts of 30% solution
\n" ); document.write( "Let $\"b\"$ = quarts of 60% solution
\n" ); document.write( "------------------------------------
\n" ); document.write( "given:
\n" ); document.write( " $\"a+%2B+b+=+60\"$
\n" ); document.write( " $\"b+=+60+-+a\"$
\n" ); document.write( "----------------
\n" ); document.write( " $\"%28.3a+%2B+.6b%29%2F60+=+.5\"$
\n" ); document.write( " $\".3a+%2B+.6b+=+30\"$
\n" ); document.write( " $\"3a+%2B+6b+=+300\"$
\n" ); document.write( " $\"a+%2B+2b+=+100\"$
\n" ); document.write( "By substitution:
\n" ); document.write( " $\"a+%2B+2%2A%2860+-+a%29+=+100\"$
\n" ); document.write( " $\"a+%2B+120+-+2a+=+100\"$
\n" ); document.write( " $\"-a+=+-20\"$
\n" ); document.write( " $\"a+=+20\"$
\n" ); document.write( "and, since
\n" ); document.write( " $\"a+%2B+b+=+60\"$
\n" ); document.write( " $\"b+=+60+-+20\"$
\n" ); document.write( " $\"b+=+40\"$
\n" ); document.write( "20 quarts of 30% solution and 40 quarts of 60% solution are needed
\n" ); document.write( "check:
\n" ); document.write( " $\"%28.3a+%2B+.6b%29%2F60+=+.5\"$
\n" ); document.write( " $\"%28.3%2A20+%2B+.6%2A40%29%2F60+=+.5\"$
\n" ); document.write( " $\"%286+%2B+24%29%2F60+=+.5\"$
\n" ); document.write( " $\"30%2F60+=+.5\"$
\n" ); document.write( " $\".5+=+.5\"$
\n" ); document.write( "OK \n" ); document.write( "

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