document.write( "Question 419887: A chemist has one solution that is 80% acid and another solution that is 30% acid. How much of the first (80%) solution is needed to make a 400 L solution that is 62% acid? \n" ); document.write( "

Algebra.Com's Answer #293520 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"a\"$ = liters of 80% solution needed
\n" ); document.write( "Let $\"b\"$ = liters of 30% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"a+%2B+b+=+400\"$ L
\n" ); document.write( "acid in final solution is $\".62%2A400+=+248\"$ L
\n" ); document.write( "(2) $\".8a+%2B+.3b+=+248\"$
\n" ); document.write( "----------------
\n" ); document.write( "Multiply both sides of (1) by $\"3\"$
\n" ); document.write( "and subtract from (2)
\n" ); document.write( "----------------
\n" ); document.write( "(2) $\"+8a+%2B++3b+=+2480\"$
\n" ); document.write( "(1) $\"-3a+-+3b+=+-1200\"$
\n" ); document.write( " $\"+5a+=+1280+\"$
\n" ); document.write( " $\"+a+=+256+\"$
\n" ); document.write( "256 L of 80% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\".8a+%2B+.3b+=+248\"$
\n" ); document.write( "(2) $\".8%2A256+%2B+.3b+=+248\"$
\n" ); document.write( " $\"+204.8+%2B+.3b+=+248+\"$
\n" ); document.write( " $\".3b+=+43.2+\"$
\n" ); document.write( " $\"b+=+144\"$
\n" ); document.write( "and
\n" ); document.write( " $\"a+%2B+b+=+400\"$
\n" ); document.write( " $\"256+%2B+144+=+400\"$
\n" ); document.write( " $\"+400+=+400+\"$
\n" ); document.write( "OK \n" ); document.write( "

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