SOLUTION: How many mL of water should you add to 275 mL of a 9% solution to dilute it down to a 5% solution?

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Question 763119: How many mL of water should you add to 275 mL of a 9% solution to dilute it down to a 5% solution?
Answer by DrBeeee(684) About Me  (Show Source):
You can put this solution on YOUR website!
The initial solution contains 9% chemical, C, and 91% water, W, or
(1) C = 0.09*275 or
(2) C = 24.75 mL and
(1) W = .91*275 or
(2) W = 250.25 mL
Now we add some water, w, to yield a solution that is 95% water or
(3) 0.95 = (250.25 + w)/(275 + w)
Remember to add w to both the numerator and denominator.
Cross multiplying (3) gives us
(4) 0.95*(275+w) = 250.25 + w or
(5) 261.25 + 0.95*w = 250.25 + w or
(6) 11 = 0.05*w or
(7) w = 220 mL
Let's check this with chemical of (2) and the total solution.
Is (24.75/(275+220) = 0.05)?
Is (24.75/495 = 0.05)?
Is (0.05 = 0.05)? Yes
Answer: Add 220 mL of water.