document.write( "Question 147291: How many gallons of 50% antifreeze must be mixed with 80 gallons of 20% antifreeze to get a mixture that is 40% antifreeze? \n" ); document.write( "

Algebra.Com's Answer #107663 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"x\"$ = gallons of 50% antifreeze to be added
\n" ); document.write( "How much antifreeze is in it?
\n" ); document.write( " $\".5x\"$ gallons
\n" ); document.write( "How much antifreeze is in the 20% solution?
\n" ); document.write( " $\".2%2A80+=+16\"$ gallons
\n" ); document.write( "What,s the total amount of solution you end up with?
\n" ); document.write( " $\"x+%2B+80\"$
\n" ); document.write( "In words:
\n" ); document.write( "(amount of antifreeze) / (total amount of solution) = % antifreeze
\n" ); document.write( " $\"%28.5x+%2B+16%29+%2F+%28x+%2B+80%29+=+.4\"$
\n" ); document.write( "multiply both sides by $\"x+%2B+80\"$
\n" ); document.write( " $\".5x+%2B+16+=+.4%2A%28x+%2B+80%29\"$
\n" ); document.write( " $\".5x+%2B+16+=+.4x+%2B+32\"$
\n" ); document.write( " $\".1x+=+16\"$
\n" ); document.write( " $\"x+=+160\"$
\n" ); document.write( "160 gallons of the 50% antifreeze must be added
\n" ); document.write( "check answer:
\n" ); document.write( " $\"%28.5x+%2B+16%29+%2F+%28x+%2B+80%29+=+.4\"$
\n" ); document.write( " $\"%28.5%2A160+%2B+16%29+%2F+%28160+%2B+80%29+=+.4\"$
\n" ); document.write( " $\"%2880+%2B+16%29+%2F+240+=+.4\"$
\n" ); document.write( " $\"96+%2F+240+=+.4\"$
\n" ); document.write( " $\"96+=+.4%2A240\"$
\n" ); document.write( " $\"96+=+96\"$
\n" ); document.write( "OK \n" ); document.write( "

\n" );