document.write( "Question 1094740: a laboratory needs to make a 21-liter batch of a 40% acid solution. how can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration? \n" ); document.write( "
Algebra.Com's Answer #709311 by josmiceli(19441)\"\" \"About 
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Let \"+a+\" = liters of pure acid needed
\n" ); document.write( "Let \"+b+\" = liters of 10% solution needed
\n" ); document.write( "----------------------------------------
\n" ); document.write( "(1) \"+a+%2B+b+=+21+\"
\n" ); document.write( "(2) \"+%28+a+%2B+.1b+%29+%2F+21+=+.4+\"
\n" ); document.write( "------------------------------
\n" ); document.write( "(2) \"+a+%2B+.1b+=+8.4+\"
\n" ); document.write( "(2) \"+10a+%2B+b+=+84+\"
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) \"+10a+%2B+b+=+84+\"
\n" ); document.write( "(1) \"+-a+-+b+=+21+\"
\n" ); document.write( "------------------------
\n" ); document.write( "\"+9a+=+63+\"
\n" ); document.write( "\"+a+=+7+\"
\n" ); document.write( "and
\n" ); document.write( "(1) \"+7+%2B+b+=+21+\"
\n" ); document.write( "(1) \"+b+=+14+\"
\n" ); document.write( "------------------------
\n" ); document.write( "7 liters of pure acid are needed
\n" ); document.write( "14 liters of 10% solution are needed
\n" ); document.write( "----------------------------------
\n" ); document.write( "check:
\n" ); document.write( "(2) \"+%28+a+%2B+.1b+%29+%2F+21+=+.4+\"
\n" ); document.write( "(2) \"+%28+7+%2B+.1%2A14+%29+%2F+21+=+.4+\"
\n" ); document.write( "(2) \"+%28+7+%2B+1.4+%29+%2F+21+=+.4+\"
\n" ); document.write( "(2) \"+8.4+%2F+21+=+.4+\"
\n" ); document.write( "(2) \"+8.4+=+8.4+\"
\n" ); document.write( "OK
\n" ); document.write( "
\n" );