document.write( "Question 713127: a laboratory needs to make 135 litter batch of a 20% acid solution. How can the laboratory combine a batch of acid solution the is pure acid with another that is 10%to get the desired concentration \n" ); document.write( "

Algebra.Com's Answer #438300 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = liters of pure acid needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 10% solution needed
\n" ); document.write( " $\"+.1b+\"$ = liters of pure acid in 10% solution
\n" ); document.write( "-------------
\n" ); document.write( "(1) $\"+a+%2B+b+=135+\"$
\n" ); document.write( "(2) $\"+%28+a+%2B+.1b+%29+%2F+135+=+.2+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(2) $\"+a+%2B+.1b+=+.2%2A135+\"$
\n" ); document.write( "(2) $\"+a+%2B+.1b+=+27+\"$
\n" ); document.write( "(2) $\"+10a+%2B+b+=+270+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+10a+%2B+b+=+270+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-135+\"$
\n" ); document.write( " $\"+9a+=+135+\"$
\n" ); document.write( " $\"+a+=+15+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=135+\"$
\n" ); document.write( "(1) $\"+15+%2B+b+=135+\"$
\n" ); document.write( "(1) $\"+b+=+135+-+15+\"$
\n" ); document.write( "(1) $\"+b+=+120+\"$
\n" ); document.write( "15 liters of pure acid are needed
\n" ); document.write( "120 liters of 10% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+a+%2B+.1b+%29+%2F+135+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+15+%2B+.1%2A120+%29+%2F+135+=+.2+\"$
\n" ); document.write( "(2) $\"+%28+15+%2B+12+%29+%2F+135+=+.2+\"$
\n" ); document.write( "(2) $\"+27+=+.2%2A135+\"$
\n" ); document.write( "(2) $\"+27+=+27+\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );