SOLUTION: The capacity of a car radiator is 18 quarts. If it is currently filled with a 20% antifreeze solution, how many quarts must be drained and replaced with a 100% antifreeze solution

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: The capacity of a car radiator is 18 quarts. If it is currently filled with a 20% antifreeze solution, how many quarts must be drained and replaced with a 100% antifreeze solution       Log On

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Question 972698: The capacity of a car radiator is 18 quarts. If it is currently filled with a 20% antifreeze solution, how many quarts must be drained and replaced with a 100% antifreeze solution to give 18 quarts of a 39% antifreeze solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.2%2A18+=+3.6+ quarts of antifreeze at beginning
Let +x+ = quarts of antifreeze solution to be drained off
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Note that you start with +18+ quarts
and you end up with +18+ quarts
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You are draining off a 20% solution, so you are
draining off +.2x+ quarts of the pure antifreeze
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You replace the solution drained off with +x+
quarts of pure antifreeze
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I can now say:
+%28+3.6+-+.2x+%2B+x+%29+%2F+18+=+.39+
+%28+3.6+%2B+.8x+%29+%2F+18+=+.39+
+3.6+%2B+.8x+=+.39%2A18+
+.8x+=+7.02+-+3.6+
+.8x+=+3.42+
+x+=+4.275+
4.275 quarts of solution must be drained off and replaced
with 100% pure antifreeze
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check:
+%28+3.6+%2B+.8x+%29+%2F+18+=+.39+
+%28+3.6+%2B+.8%2A4.275+%29+%2F+18+=+.39+
+%28+3.6+%2B+3.42+%29+%2F+18+=+.39+
+7.02+=+.39%2A18+
+7.02+=+7.02+
OK