SOLUTION: how many gallons of a 60% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 50% antifreeze? use the 6 step method

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Question 1030023: how many gallons of a 60% antifreeze solution must be mixed with 60 gallons of 20% antifreeze to get a mixture that is 50% antifreeze? use the 6 step method
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
I don't know the 6 step method, but
this is how I do it:
Let +x+ = gallons of 60% antifreeze solution needed
+.6x+ = gallons of pure antifreeze in the 60% solution
+.2%2A60+=+12+ gallons of pure antifreeze in 20% solution
----------------------------
+%28+.6x+%2B+12+%29+%2F+%28+x+%2B+60+%29+=+.5+
+.6x+%2B+12+=+.5%2A%28+x+%2B+60+%29+
+.6x+%2B+12+=+.5x+%2B+30+
+.1x+=+18+
+x+=+180+
180 gallons of 60% solution are needed
-----------------
check answer:
+%28+.6x+%2B+12+%29+%2F+%28+x+%2B+60+%29+=+.5+
+%28+.6%2A180+%2B+12+%29+%2F+%28+180+%2B+60+%29+=+.5+
+%28+108+%2B+12+%29+%2F+240+=+.5+
+120+=+.5%2A240+
+120+=+120+
OK