document.write( "Question 570856: Gabe, a Nuclear Physicist, needs 90 liters of a 50% acid solution. He currently has a 30% solution and a 60% solution. How many liters of each does he need to make the needed 90 liters of 50% acid solution? \n" ); document.write( "

Algebra.Com's Answer #367810 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"+a+\"$ = liters of 30% solution needed
\n" ); document.write( "Let $\"+b+\"$ = liters of 60% solution needed
\n" ); document.write( "given:
\n" ); document.write( "(1) $\"+a+%2B+b+=+90+\"$
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.6b+%29+%2F+90+=+.5+\"$
\n" ); document.write( "----------
\n" ); document.write( "(2) $\"+.3a+%2B+.6b+=+.5%2A90+\"$
\n" ); document.write( "(2) $\"+.3a+%2B+.6b+=+45+\"$
\n" ); document.write( "(2) $\"+3a+%2B+6b+=+450+\"$
\n" ); document.write( "Multiply both sides of (1) by $\"+3+\"$
\n" ); document.write( "and subtract (1) from (2)
\n" ); document.write( "(2) $\"+3a+%2B+6b+=+450+\"$
\n" ); document.write( "(1) $\"+-3a+-+3b+=+-270+\"$
\n" ); document.write( " $\"+3b+=+180+\"$
\n" ); document.write( " $\"++b+=+60+\"$
\n" ); document.write( "and, since
\n" ); document.write( "(1) $\"+a+%2B+b+=+90+\"$
\n" ); document.write( "(1) $\"+a+%2B+60+=+90+\"$
\n" ); document.write( "(1) $\"+a+=+30+\"$
\n" ); document.write( "30 liters of 30% solution are needed
\n" ); document.write( "60 liters of 60% solution are needed
\n" ); document.write( "check:
\n" ); document.write( "(2) $\"+%28+.3a+%2B+.6b+%29+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+.3%2A30+%2B+.6%2A60+%29+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+%28+9+%2B+36+%29+%2F+90+=+.5+\"$
\n" ); document.write( "(2) $\"+45%2F90+=+.5+\"$
\n" ); document.write( "(2) $\"+45+=+45+\"$
\n" ); document.write( "OK \n" ); document.write( "

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