SOLUTION: A car radiator holds 2 gallons of fluid and initially is empty. If a mixture of water and antifreeze contains 70% antifreeze and another mixture contains 20% antifreeze, how much o

Algebra ->  Customizable Word Problem Solvers  -> Mixtures -> SOLUTION: A car radiator holds 2 gallons of fluid and initially is empty. If a mixture of water and antifreeze contains 70% antifreeze and another mixture contains 20% antifreeze, how much o      Log On

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Question 711002: A car radiator holds 2 gallons of fluid and initially is empty. If a mixture of water and antifreeze contains 70% antifreeze and another mixture contains 20% antifreeze, how much of each should be combined to fill the radiator with a 50% antifreeze mixture?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 70% antifreeze to be added
+2+-+x+ = gallons of 20% antifreeze to be added
+.7x+ = pure antifreeze in 70% mixture
+.2%2A%28+2+-+x+%29+ = pure antifreeze in 20% mixture
given:
+%28+.7x+%2B+.2%2A%28+2+-+x+%29+%29+%2F+2+=+.5+
+%28+.7x+%2B+.4+-+.2x+%29+%2F+2+=+.5+
+.5x+%2B+.4+=+1+
+.5x+=+.6+
+x+=+1.2+
+2+-+x+=+.8+
1.2 gallons of 70% antifreeze needs to be added
.8 gallons of 20% antifreeze needs to be added
check:
+%28+.7x+%2B+.2%2A%28+2+-+x+%29+%29+%2F+2+=+.5+
+%28+.7%2A1.2+%2B+.2%2A%28+2+-+1.2+%29+%29+%2F+2+=+.5+
+%28+.84+%2B+.2%2A.8+%29+%2F+2+=+.5+
+%28+.84+%2B+.16+%29+%2F+2+=+.5+
+1%2F2+=+.5+
+.5+=+.5+
OK