SOLUTION: how many pints of disinfectant that is 74% alcohol must be mixed with 5 pints of one that is 90% alcohol to obtain a disinfectant that contains 84% alcohol?

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Question 978701: how many pints of disinfectant that is 74% alcohol must be mixed with 5 pints of one that is 90% alcohol to obtain a disinfectant that contains 84% alcohol?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +x+ = pints of 74% disinfectant needed
+.74x+ = pints of alcohol in 74% disinfectant
+.9%2A5+=+4.5+ = pints of alcohol in 90% diinfectant
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+%28+.74x+%2B+4.5+%29+%2F+%28+x+%2B+5+%29+=+.84+
+.74x+%2B+4.5+=+.84%2A%28+x+%2B+5+%29+
+.74x+%2B+4.5+=+.84x+%2B+4.2+
+.1x+=+.3+
+x+=+3+
3 pints of 74% disinfectant are needed
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check:
+%28+.74x+%2B+4.5+%29+%2F+%28+x+%2B+5+%29+=+.84+
+%28+.74%2A3+%2B+4.5+%29+%2F+%28+3+%2B+5+%29+=+.84+
+%28+2.22+%2B+4.5+%29+%2F+8+=+.84+
+6.72+%2F+8+=+.84+
+6.72+=+6.72+
OK