document.write( "Question 551101: A chemist has one solution that is 20% acid and a second that is 65% acid. How many gallons of each should be mixed together to get 120 gallons of a solution that is 50% acid? \n" ); document.write( "

Algebra.Com's Answer #359380 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = gallons of 20% solution needed
\n" ); document.write( "Let $\"+b+\"$ = gallons of 65% solution needed
\n" ); document.write( " $\"+.2a+\"$ = gallons of acid in 20% solution
\n" ); document.write( " $\"+.65b+\"$ = gallons of acid in 65% solution
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=120+\"$
\n" ); document.write( "(2) $\"+%28+.2a+%2B+.65b+%29+%2F+120+=+.5+\"$
\n" ); document.write( "-------------------------
\n" ); document.write( "(2) $\"+.2a+%2B+.65b+=+.5%2A120+\"$
\n" ); document.write( "(2) $\"+.2a+%2B+.65b+=+60+\"$
\n" ); document.write( "(2) $\"+20a+%2B+65b+=+6000+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+20+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+20a+%2B+65b+=+6000+\"$
\n" ); document.write( "(1) $\"+-20a+-+20b+=+-2400+\"$
\n" ); document.write( " $\"+45b+=+3600+\"$
\n" ); document.write( " $\"+b+=+80+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=120+\"$
\n" ); document.write( "(1) $\"+a+%2B+80+=120+\"$
\n" ); document.write( "(1) $\"+a+=+120+-+80+\"$
\n" ); document.write( "(1) $\"+a+=+40+\"$
\n" ); document.write( "40 gallons of 20% solution are needed
\n" ); document.write( "80 gallons of 65% solution are needed
\n" ); document.write( "check answer:
\n" ); document.write( "(2) $\"+%28+.2%2A40+%2B+.65%2A80+%29+%2F+120+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+8+%2B+52+%29+%2F+120++=+.5+\"$
\n" ); document.write( "(2) $\"+60+%2F+120+=+.5+\"$
\n" ); document.write( "(2) $\"+60+=+.5%2A120+\"$
\n" ); document.write( "(2) $\"+60+=+60+\"$
\n" ); document.write( "OK \n" ); document.write( "

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