SOLUTION: how many gallons of a 12% salt solution should be added to 10 gallons of an 18% salt solution in order to produce a solution whose salt content is between 14% amd 16%

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Question 789282: how many gallons of a 12% salt solution should be added to 10 gallons of an 18% salt solution in order to produce a solution whose salt content is between 14% amd 16%
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = gallons of 12% solution needed
+.12x+ = gallons of salt in 12% solution
+.18%2A10+=+1.8+ gallons of salt in 18% solution
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First find for 14%
+%28+.12x+%2B+1.8+%29+%2F+%28+x+%2B+10+%29+=+.14+
+.12x+%2B+1.8+=+.14%2A%28+x+%2B+10+%29+
+.12x+%2B+1.8+=+.14x+%2B+1.4+
+.02x+=+.4+
+x+=+20+
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And find for 16%
+%28+.12x+%2B+1.8+%29+%2F+%28+x+%2B+10+%29+=+.16+
+.12x+%2B+1.8+=+.16%2A%28+x+%2B+10+%29+
+.12x+%2B+1.8+=+.16x+%2B+1.6+
+.04x+=+.2+
+x+=+5+
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between 5 gallons and 20 gallons of 12% salt
solution should be added