SOLUTION: A 3% saline solution is combined with a 5% saline solution to form 10 ounces of a 3.8% saline solution. How many ounces of the 3% solution are used?

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Question 996276: A 3% saline solution is combined with a 5% saline solution to form 10 ounces of a 3.8% saline solution. How many ounces of the 3% solution are used?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of the 3% solution needed
Let +b+ = ounces of the 5% solution needed
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(1) +a+%2B+b+=+10+
(2) +%28+.03a+%2B+.05b+%29+%2F+10+=+.038+
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(2) +.03a+%2B+.05b+=+.38+
(2) +3a+%2B+5b+=+38+
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Multiply both sides of (1) by +3+ and
subtract (1) from (2)
(2) +3a+%2B+5b+=+38+
(1) +-3a+-+3b+=+-30+
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+2b+=+8+
+b+=+4+
and
(1) +a+%2B+b+=+10+
(1) +a+%2B+4+=+10+
(1) +a+=+6+
6 ounces of the 3% solution are needed
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check:
(2) +%28+.03a+%2B+.05b+%29+%2F+10+=+.038+
(2) +%28+.03%2A6+%2B+.05%2A4+%29+%2F+10+=+.038+
(2) +%28+.18+%2B+.2+%29+%2F+10+=+.038+
(2) +.38+=+10%2A.038+
(2) +.38+=+.38+
OK