SOLUTION: How many gallons of a 3.6% salt solution must be mixed with a 7% salt solution to obtain 25 gallons of a 4.5% salt solution

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Question 752248: How many gallons of a 3.6% salt solution must be mixed with a 7% salt solution to obtain 25 gallons of a 4.5% salt solution
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +a+ = gallons of 3.6% solution needed
Let +b+ = gallons of 7% solution needed
+.036a+ = gallons of salt in 3.6% solution
+.07b+ = gallons of salt in 7% solution
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(1) +a+%2B+b+=+25+
(2) +%28+.036a+%2B+.07b+%29+%2F+25+=+.045+
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(2) +%28+36a+%2B+70b+%29+%2F+25+=+45+
(2) +36a+%2B+70b+=+1125+
Multiply both sides of (1) by +36+
and subtract (1) from (2)
(2) +36a+%2B+70b+=+1125+
(1) +-36a+-+36b+=+-900+
+34b+=+225+
+b+=+6.618+
and
(1) +a+%2B+b+=+25+
(1) +a+=+18.382+
18.382 gallons of 3.6% solution are needed
6.618 gallons of 7% solution are needed
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check:
(2) +%28+.036a+%2B+.07b+%29+%2F+25+=+.045+
(2) +%28+.036%2A18.382+%2B+.07%2A6.618+%29+%2F+25+=+.045+
(2) +%28+.6618+%2B+.4633+%29+%2F+25+=+.045+
(2) +1.1251+=+.045%2A25+
(2) +1.1251+=+1.125+
close enough