SOLUTION: How many pints of 1% peroxide solution should be mixed with 4% peroxide solution to obtain 10 pints of 2% peroxide solution?

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Question 746115: How many pints of 1% peroxide solution should be mixed with 4% peroxide solution to obtain 10 pints of 2% peroxide solution?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = pints of 1% solution needed
Let +b+ = pints of 4% solution needed
+.01a+ = peroxide in 1% solution
+.04b+ = peroxide in 4% solution
--------------------------------
(1) +a+%2B+b+=+10+
(2) +%28+.01a+%2B+.04b+%29+%2F+10+=+.02+
-----------------------------
(2) +.01a+%2B+.04b+=+.2+
(2) +a+%2B+4b+=+20+
Subtract (1) from (2)
(2) +a+%2B+4b+=+20+
(1) +-a+-+b+=+-10+
+3b+=+10+
+b+=+3.333+
and, since
(1) +a+%2B+b+=+10+
(1) +a+%2B+3.333+=+10+
(1) +a+=+6.667+
6.667 pints of 1% solution are needed
3.333 pints of 4% solution are needed
check:
(2) +%28+.01%2A6.667+%2B+.04%2A3.333+%29+%2F+10+=+.02+
(2) +%28+.0667+%2B+.1333+%29+%2F+10+=+.02+
(2) +.2+=+10%2A.02+
(2) +.2+=+.2+
OK