SOLUTION: 5 quart solution of 30% antifreeze plus how many quarts of 100% antifreeze to get a 40% antifreeze solution?

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Question 779613: 5 quart solution of 30% antifreeze plus how many quarts of 100% antifreeze to get a 40% antifreeze solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+.3%2A5+=+1.5+ quarts of antifreeze in 30% solution
Let +x+ = quarts of pure antifreeze to be added
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+%28+1.5+%2B+x+%29+%2F+%28+5+%2B+x+%29+=+.4+
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+1.5+%2B+x+=+.4%2A%28+5+%2B+x+%29+
+1.5+%2B+x+=+2+%2B+.4x+
+.6x+=+2+-+1.5+
+.6x+=+.5+
+x+=+5%2F6+
5/6 of a quart of 100% antifreeze must be added
check:
+%28%28+1.5+%2B+x+%29%29+%2F+%28%28+5+%2B+x+%29%29+=+.4+
+%28%28+1.5+%2B+5%2F6+%29%29+%2F+%28%28+5+%2B+5%2F6+%29%29+=+.4+
+%28%28+9%2F6+%2B+5%2F6+%29%29+%2F+%28%28+30%2F6+%2B+5%2F6+%29%29+=+.4+
+%28%28+14%2F6+%29%29+%2F+%28%28+35%2F6+%29%29+=+.4+
+14%2F35+=+.4+
+2%2F5++=+.4+
+.4+=+.4+
OK