document.write( "Question 693621: How many liters of each of 20% acid solution and 45% acid solution must be used to produce 50 liters of a 40% acid solution? \n" ); document.write( "

Algebra.Com's Answer #427477 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = liters of 20% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 45% solution needed
\n" ); document.write( "-------
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.45b+%29+%2F+50+=+.4+\"$
\n" ); document.write( "---------------------------
\n" ); document.write( "(2) $\"+.2a+%2B+.45b+=+.4%2A50+\"$
\n" ); document.write( "(2) $\"+20a+%2B+45b+=+2000+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+20+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+20a+%2B+45b+=+2000+\"$
\n" ); document.write( "(1) $\"+-20a+-+20b+=+-1000+\"$
\n" ); document.write( " $\"+25b+=+1000+\"$
\n" ); document.write( " $\"+b+=+40+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+50+\"$
\n" ); document.write( "(1) $\"+a+%2B+40+=+50+\"$
\n" ); document.write( "(1) $\"+a+=+10+\"$
\n" ); document.write( "10 liters of 20% solution are needed
\n" ); document.write( "40 liters of 45% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.45b+%29+%2F+50+=+.4+\"$
\n" ); document.write( "(2) $\"+%28+.2%2A10+%2B+.45%2A40+%29+%2F+50+=+.4+\"$
\n" ); document.write( "(2) $\"+%28+2+%2B+18+%29+%2F+50+=+.4+\"$
\n" ); document.write( "(2) $\"+20%2F50+=+.4%0D%0A%282%29+%7B%7B%7B+20+=+.4%2A50+\"$
\n" ); document.write( "(2) $\"+20+=+20+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );