document.write( "Question 401189: A car radiator has a 16 quart capacity and is currently filled with a 40% antifreeze solution. How many quarts of this solution must be drained off and replaced with 100% antifreeze to create a 50% antifreeze solution? \n" ); document.write( "

Algebra.Com's Answer #283868 by josmiceli(19441) $\"\"$ $\"About$

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In words:
\n" ); document.write( "(quarts of antifreeze started with (-) quarts of antifreeze drained off (+) quarts of antifreeze added) / ( final quarts of solution) = 50%
\n" ); document.write( "Let $\"x\"$ = quarts of solution drained off
\n" ); document.write( "Then $\"x\"$ = quarts of 100% antifreeze added
\n" ); document.write( "given:
\n" ); document.write( " $\"16\"$ = final quarts of solution
\n" ); document.write( " $\".4%2A16+=+6.4\"$ = quarts of antifreeze to start with
\n" ); document.write( " $\".4x\"$ = quarts of antifreeze drained off
\n" ); document.write( "------------------------------------------
\n" ); document.write( " $\"%286.4+-.4x+%2B+x%29+%2F+16+=+.5\"$ (note: $\"16\"$ is really $\"16+-+x+%2B+x\"$ )
\n" ); document.write( " $\"6.4+-+.4x+%2B+x+=+16%2A.5\"$
\n" ); document.write( " $\".6x+=+8+-+6.4\"$
\n" ); document.write( " $\".6x+=+1.6\"$
\n" ); document.write( " $\"x+=+2.667\"$ quarts
\n" ); document.write( "2.667 quarts of 40% solution must be removed and 2.667 quarts of
\n" ); document.write( "antifreeze must be added
\n" ); document.write( "check answer:
\n" ); document.write( " $\"%286.4+-.4%2A%288%2F3%29+%2B+8%2F3%29+%2F+16+=+.5\"$
\n" ); document.write( " $\"6.4+-+3.2%2F3++%2B+8%2F3+=+8\"$
\n" ); document.write( " $\"3%2A6.4+-+3.2+%2B+8+=+24\"$
\n" ); document.write( " $\"19.2+-+3.2+%2B+8+=+24\"$
\n" ); document.write( " $\"16+=+16\"$
\n" ); document.write( "OK \n" ); document.write( "

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