Question 444701: how many gallons of a 5% salt solution must be mixed with 40 gallons of a 9% solution to obtain a 7% solution? Answer by oberobic(2304) (Show Source):
You can put this solution on YOUR website! The key to solution/mixture problems is to figure out how much "pure" stuff you need.
x = unknown gallons of 5% salt solution that you can add
40 = gallons of 9% salt solution you started with
40+x = gallons of 7% salt solution that is the final result
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.07(40+x) = .05x + .09(40)
Multiply through by 100 to get rid of decimals.
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7(40+x) = 5x + 9(40)
280 +7x = 5x +360
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Subtract 5x from both sides.
280 +2x = 360
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Subtract 280 from both sides.
2x = 80
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Divide both sides by 2
x = 40
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Hmmm. That suggests 40 gallons of 5% solution added to 40 gallons of 9% solution will produce 80 gallons of 7% solution.
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Always check your answer.
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80*.07 = 5.6 gallons of salt
40*.05 = 2.0 gallons of salt
40*.09 = 3.6 gallons of salt
5.6 = 2.0 + 3.6
Checks.
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Answer: Add 40 gallons of 5% solution to 40 gallons of 9% solution to obtain a 7% solution.
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