SOLUTION: A radiator contains 14 quarts of fluid, 35% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?

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Question 952633: A radiator contains 14 quarts of fluid, 35% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A radiator contains 14 quarts of fluid, 35% of which is antifreeze. How much fluid should be drained and replaced with pure antifreeze so that the new mixture is 40% antifreeze?
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Equation:
alch - alch + alch = alcohol
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0.35*14 - 0.35x + 1*x = 0.40*14
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35*14 - 0 + 100x = 40*14
100x = 5*14
x = 0.7 quarts (amt of fluid to remove and replace with pure antifreeze)
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Cheers,
Stan H.
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = quarts of fluid to be
drained off
+.35x+ = quarts of antifreeze drained off
In words:
( quarts of antifreeze ) / ( total quarts ) = 40%
+%28+x+%2B+.35%2A%28+14+-+x+%29+%29+%2F+14+=+.4+
+%28+x+%2B+4.9+-+.35x+%29+%2F+14+=+.4+
+%28+.65x+%2B+4.9+%29+%2F+14+=+.4+
+.65x+%2B+4.9+=+5.6+
+.65x+=+.7+
+x+=+1.077+
1.077 quarts should be drained off & replaced
with pure antifreeze
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check:
+%28+x+%2B+.35%2A%28+14+-+x+%29+%29+%2F+14+=+.4+
+%28+1.077+%2B+.35%2A%28+14+-+1.077+%29+%29+%2F+14+=+.4+
+%28+1.077+%2B+.35%2A12.923+%29+%2F+14+=+.4+
+%28+1.077+%2B+4.523+%29+%2F+14+=+.4+
+5.6+=+.4%2A14+
+5.6+=+5.6+
OK