SOLUTION: need help solving this problem please. A tank contains 55 gallons of a 55% solution of antifreeze. How much solution needs to be drained out and replaced with pure antifreeze to

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Question 749685: need help solving this problem please.
A tank contains 55 gallons of a 55% solution of antifreeze. How much solution needs to be drained out and replaced with pure antifreeze to obtain a 70% solution?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The key here is to realize that you start with
55 gallons and end up with 55 gallons
Let +x+ = gallons of solution to be drained
and replaced with pure antifreeze
+.55x+ = gallons of antifreeze removed
+.55%2A55+=+30.25+ gallons of antifreeze
in original mixture
----------------------------
+%28+30.25+-+.55x+%2B+x+%29+%2F+55+=+.7+
+%28+30.25+%2B+.45x+%29+%2F+55+=+.7+
+30.25+%2B+.45x+=+.7%2A55+
+30.25+%2B+.45x+=+38.5+
+.45x+=+8.25+
+x+=+18.333+
18.333 gallons of solution must be drained and
replaced with pure antifreeze
check:
+%28+30.25+%2B+.45x+%29+%2F+55+=+.7+
+%28+30.25+%2B+.45%2A18.333+%29+%2F+55+=+.7+
+38%2C5+%2F+55+=+.7+
+38.5+=+.7%2A55+
+38.5+=+38.5+
OK