SOLUTION: A radiator contains 13 quarts of fluid, 20% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 50% antifreeze? (R

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Question 511301: A radiator contains 13 quarts of fluid, 20% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 50% antifreeze? (Round your answer to two decimal places.)
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key is: you start with 13 quarts and you end up with
13 quarts.
Let +x+ = quarts of fluid to be drained
and replaced with pure antifreeze
given:
+.2%2A13+=+2.6+ quarts of original antifreeze
+.2x+ = quarts of antifreeze drained off
-----------------
+%28+2.6+-+.2x+%2B+x+%29+%2F+13+=+.5+
+%28+2.6+%2B+.8x+%29+%2F+13+=+.5+
+2.6+%2B+.8x+=+6.5+
+.8x+=+3.9+
+x+=+4.875+
4.88 quarts of fluid should be drained and replaced with pure antifreeze
check:
+%28+2.6+-+.2x+%2B+x+%29+%2F+13+=+.5+
+%28+2.6+%2B+.8%2A4.875+%29+%2F+13+=+.5+
+%28+2.6+%2B+3.9+%29+%2F+13+=+.5+
+6.5+%2F+13+=+.5+
+6.5+=+6.5+
OK