document.write( "Question 770735: How much of 40% alcohol and how much of 80% solution should be mixed to give 40 gallons of 50% solution? \n" ); document.write( "

Algebra.Com's Answer #469745 by josmiceli(19441) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let $\"+a+\"$ = gallons of 40% solution needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 80% solution needed
\n" ); document.write( " $\"+.4a+\"$ = gallons of alcohol in 40% solution
\n" ); document.write( " $\"+.8b+\"$ = gallons of alcohol in 80% solution
\n" ); document.write( "----------------------
\n" ); document.write( "(1) $\"+a+%2B+b+=+40+\"$
\n" ); document.write( "(2) $\"+%28+.4a+%2B+.8b+%29+%2F+40+=+.5+\"$
\n" ); document.write( "--------------------------
\n" ); document.write( "(2) $\"+.4a+%2B+.8b+=+.5%2A40+\"$
\n" ); document.write( "(2) $\"+.4a+%2B+.8b+=+20+\"$
\n" ); document.write( "(2) $\"+4a+%2B+8b+=+200+\"$
\n" ); document.write( "(2) $\"+a+%2B+2b+=+50+\"$
\n" ); document.write( "Subtract (1) from (2)
\n" ); document.write( "(2) $\"+a+%2B+2b+=+50+\"$
\n" ); document.write( "(1) $\"+-a+-+b+=+-40+\"$
\n" ); document.write( " $\"+b+=+10+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+40+\"$
\n" ); document.write( "(1) $\"+a+=+30+\"$
\n" ); document.write( "30 gallons of 40% solution are needed
\n" ); document.write( "10 gallons of 80% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.4%2A30+%2B+.8%2A10+%29+%2F+40+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+12+%2B+8+%29+%2F+40+=+.5+\"$
\n" ); document.write( "(2) $\"+20+=+.5%2A40+\"$
\n" ); document.write( "(2) $\"+20+=+20+\"$
\n" ); document.write( "OK\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

\n" );