document.write( "Question 658021: A CHEMIST NEEDS TO MIX AN 18% ACID SOLUTION WITH A 45% ACID SOLUTION TO OBTAIN 12 GALLONS OF A 36% ACID SOLUTION. HOW MANY GALLONS OF EACH OF THE ACID SOLUTIONS MUST HE USE?
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Algebra.Com's Answer #410113 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = gallons of 18% solution needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 45% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+12+\"$
\n" ); document.write( "(2) $\"+%28+.18a+%2B+.45b+%29+%2F+12+=+.36+\"$
\n" ); document.write( "-----------------------------
\n" ); document.write( "(2) $\"+.18a+%2B+.45b+=+.36%2A12+\"$
\n" ); document.write( "(2) $\"+.18a+%2B+.45b+=+4.32+\"$
\n" ); document.write( "(2) $\"+18a+%2B+45b+=+432+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+18+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+18a+%2B+45b+=+432+\"$
\n" ); document.write( "(1) $\"+-18a+-+18b+=+-216+\"$
\n" ); document.write( " $\"+27b+=+216+\"$
\n" ); document.write( " $\"+b+=+8+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+12+\"$
\n" ); document.write( "(1) $\"+a+=+12+-+8+\"$
\n" ); document.write( "(1) $\"+a+=+4+\"$
\n" ); document.write( "-------------
\n" ); document.write( "4 gallons of 18% solution are needed
\n" ); document.write( "8 gallons of 45% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.18%2A4+%2B+.45%2A8+%29+%2F+12+=+.36+\"$
\n" ); document.write( "(2) $\"+%28+.72+%2B+3.6+%29+%2F+12+=+.36+\"$
\n" ); document.write( "(2) $\"+4.32+=+.36%2A12+\"$
\n" ); document.write( "(2) $\"+4.32+=+4.32+\"$
\n" ); document.write( "OK \n" ); document.write( "

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