SOLUTION: How much pure sodium must be mixed with 5o quarts of a 65% sodium solution to get a 75% sodium solution?

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Question 765293: How much pure sodium must be mixed with 5o quarts of a 65% sodium solution to get a 75% sodium solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = quarts of pure sodium needed
+.65%2A50+=+32.5+ quarts of pure sodium in 65% solution
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+%28+x+%2B+32.5+%29+%2F+%28+x+%2B+50+%29++=+.75+
+x+%2B+32.5+=+.75%2A%28+x+%2B+50+%29+
+x+%2B+32.5+=+.75x+%2B+37.5+
+.25x+=+5+
+x+=+20+
20 quarts of pure sodium are needed
check:
+%28+x+%2B+32.5+%29+%2F+%28+x+%2B+50+%29++=+.75+
+%28+20+%2B+32.5+%29+%2F+%28+20+%2B+50+%29++=+.75+
+52.5+%2F+70+=+.75+
+52.5+=+.75%2A70+
+52.5+=+52.5+
OK