SOLUTION: a beaker contains 30 oz of an acid solution. A second beaker contains 35 oz of an acid solution, which has a concentration which is twice the concentration of the acid solution in

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Question 842196: a beaker contains 30 oz of an acid solution. A second beaker contains 35 oz of an acid solution, which has a concentration which is twice the concentration of the acid solution in the first beaker. The contents of these 2 beakers are poured into a third beaker. The acid solution in this 3rd beaker has a concentration of 17%. Find the concentrations of the acid solutions in the first 2 containers
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = ounces of acid in 30 ounces of solution
Let +b+ = ounces of acid in 35 ounces of solution
+30+%2B+35+=+65+ = ounces of solution in 3rd beaker
---------------------------------------------
(1) +b%2F35+=+2%2A%28+a%2F30+%29+
(2) +%28+a+%2B+b+%29+%2F+65+=+.17+
--------------------------
(1) +b%2F35+=+2%2A%28+a%2F30+%29+
(1) +b%2F35+=+a%2F15+
Multiply both sides by +15%2A35+
(1) +15b+=+35a+
(1) +b+=+%287%2F3%29%2Aa+
and
(2) +a+%2B+b+=+.17%2A65+
(2) +a+%2B+%287%2F3%29%2Aa+=+11.05+
(2) +%28+10%2F3+%29%2Aa+=+11.05+
(2) +a+=+.3%2A11.05+
(2) +a+=+3.315+
and
(1) +b+=+%287%2F3%29%2Aa+
(1) +b+=+%287%2F3%29%2A3.315+
(1) +b+=+7.735+
---------------------
The concentration of the 30 ounce solution is:
+a%2F30+=+3.315%2F30+
+a%2F30+=+.1105+ = 11.05%
The concentration of the 35 ounce solution is:
+b%2F35+=+7.735%2F35+
+b%2F35+=+.221+ = 22.1%
---------------------------
check answers:
(1) +b%2F35+=+2%2A%28+a%2F30+%29+
(1) +7.735%2F35+=+2%2A%28+3.315%2F30+%29+
(1) +.221+=+.221+
and
(2) +%28+a+%2B+b+%29+%2F+65+=+.17+
(2) +%28+3.315+%2B+7.735+%29+%2F+65+=+.17+
(2) +.17+=+.17+
OK