SOLUTION: how many gallons of 90 percent antifreeze solution must be mixed with 100 gallons of 10 percent antifreeze solution to get a mixture that is 80 percent antifreeze

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Question 515163: how many gallons of 90 percent antifreeze solution must be mixed with 100 gallons of 10 percent antifreeze solution to get a mixture that is 80 percent antifreeze
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 90% antifreeze needed
In words:
( gallons of antifreeze you end up with ) / ( total gallons of solution ) = 80%
+.1%2A100+=+10+ gallons of antifreeze in 10% solution
given:
+100+%2B+x+ = total solution
+%28+.9x+%2B+10+%29+%2F+%28+x+%2B+100+%29+=+.8+
+.9x+%2B+10+=+.8%2A%28+x+%2B+100+%29+
+.9x+%2B+10+=+.8x+%2B+80+
+.1x+=+80+-+10+
+.1x+=+70+
+x+=+700+
700 gallons of 90% antifreeze are needed
check answer:
+%28+.9%2A700+%2B+10+%29+%2F+%28+700+%2B+100+%29+=+.8+
+%28+630+%2B+10+%29+%2F+800+=+.8+
++640+%2F+800+=+.8+
+640+=+.8%2A800+
+640+=+640+
OK