document.write( "Question 617776: A chemist needs 12 liters of a 36% acid solution. How many liters of 18% acid should be combined with a 45% acid solution to obtain the proper mixture?\r
\n" ); document.write( "\n" ); document.write( "My teacher didn't teach us this at all. Please, provide an explanation. \n" ); document.write( "

Algebra.Com's Answer #388549 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a\"$ = liters of 18% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 45% solution needed
\n" ); document.write( " $\"+.18a+\"$ = liters of acid in 18% solution
\n" ); document.write( " $\"+.45b+\"$ = liters of acid in 45% solution
\n" ); document.write( "------------------
\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) $\"+a+=+4+\"$
\n" ); document.write( "4 liters of 18% solution are needed
\n" ); document.write( "12 liters of 45% solution are needed \n" ); document.write( "

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