SOLUTION: Find the amount of twenty five percent acid solution and the amount of a fifteen percent acid solution that combine to prepare fifty oz at an eighteen percent acid solution.

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Question 533457: Find the amount of twenty five percent acid solution and the amount of a fifteen percent acid solution that combine to prepare fifty oz at an eighteen percent acid solution.
Found 2 solutions by scott8148, josmiceli:
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
(x)(25%) + (50 - x)(15%) = (50)(18%)

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let a = ounces of 25% solution needed
Let b = ounces of 15% solution needed
given:
+.25a+ = ounces of acid in 25% solution
+.15b+ = ounces of acid in 15% solution
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given:
(1) +a+%2B+b+=+50+
(2) +%28+.25a+%2B+.15b+%29+%2F+50+=+.18+
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(2) +.25a+%2B+.15b+=+.18%2A50+
(2) +.25a+%2B+.15b+=+9+
(2) +25a+%2B+15b+=+900+
(2) +5a+%2B+3b+=+180+
Multiply both sides of (1) by 3, and
subtract (1) from (2)
(2) +5a+%2B+3b+=+180+
(1) +-3a+-+3b+=+-150+
+2a+=+30+
+a+=+15+
and, since
(1) +a+%2B+b+=+50+
(1) +15+%2B+b+=+50+
(1) +b+=+35+
15 ounces of 25% solution are needed
35 ounces of 15% solution are needed
check:
(2) +%28+.25%2A15+%2B+.15%2A35+%29+%2F+50+=+.18+
(2) +%28+3.75+%2B+5.25+%29+%2F+50+=+.18+
(2) +9%2F50+=+.18+
(2) +9+=+9+
OK