document.write( "Question 512137: A chemist is mixing three chemicals to get 15 liters of a 6% solution. How much of each of 3%, 7%, and 9% solutions should he use if he must use twice as much of the 3% as the 9% solution? \n" ); document.write( "

Algebra.Com's Answer #342557 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 3% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 7% solution needed
\n" ); document.write( "Let $\"c\"$ = liters of 9% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+15+\"$
\n" ); document.write( "(2) $\"+%28++.03a+%2B+.07b+%2B+.09c+%29+%2F+15+=+.06+\"$
\n" ); document.write( "(3) $\"+a+=+2c+\"$
\n" ); document.write( "----------
\n" ); document.write( "There are 3 equations and 3 unknowns, so it's solvable
\n" ); document.write( "(2) $\"+.03a+%2B+.07b+%2B+.09c++=+.06%2A15+\"$
\n" ); document.write( "(2) $\"+.03a+%2B+.07b+%2B+.09c++=+.9+\"$
\n" ); document.write( "(2) $\"+3a+%2B+7b+%2B+9c++=+90+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"7\"$
\n" ); document.write( "and subtract (2) from (1)
\n" ); document.write( "(1) $\"+7a+%2B+7b+%2B+7c+=+105+\"$
\n" ); document.write( "(2) $\"+-3a+-+7b+-+9c++=+-90+\"$
\n" ); document.write( "(4) $\"+4a+-+2c+=+15+\"$
\n" ); document.write( "Substitute (3) into (4)
\n" ); document.write( "(4) $\"+8c+-+2c+=+15+\"$
\n" ); document.write( "(4) $\"+6c+=+15+\"$
\n" ); document.write( "(4) $\"+c+=+2.5+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(3) $\"+a+=+2c+\"$
\n" ); document.write( "(3) $\"+a+=+5+\"$
\n" ); document.write( "and
\n" ); document.write( "(1) $\"+a+%2B+b+%2B+c+=+15+\"$
\n" ); document.write( "(1) $\"+5+%2B+b+%2B+2.5+=+15+\"$
\n" ); document.write( "(1) $\"+b+=+15+-+7.5+\"$
\n" ); document.write( "(1) $\"+b+=+7.5+\"$
\n" ); document.write( "5 liters of 3% solution are needed
\n" ); document.write( "7.5 liters of 7% solution are needed
\n" ); document.write( "2.5 liters of 9% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28++.03%2A5+%2B+.07%2A7.5+%2B+.09%2A2.5+%29+%2F+15+=+.06+\"$
\n" ); document.write( "(2) $\"+%28+.15+%2B+.525+%2B+.225+%29+%2F+15+=+.06+\"$
\n" ); document.write( "(2) $\"++.15+%2B+.525+%2B+.225++=+.06%2A15+\"$
\n" ); document.write( "(2) $\"+.9+=+.9+\"$
\n" ); document.write( "OK \n" ); document.write( "

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