Walkabout wrote:
A tank contains 10,000 gallons of a solution that is 5 percent sodium chloride by volume. If 2,500 gallons of water evaporate from the tank, the remaining solution will be approximately what percent sodium chloride?
(A) 1.25%
(B) 3.75%
(C) 6.25%
(D) 6.67%
(E) 11.7%
Conceptually, it helps to remember that unless told otherwise, water is assumed to have zero percent sodium chloride (or zero percent alcohol, etc.).
The prompt refers to a
solution that is 5 percent sodium chloride by volume. It's part water, part sodium chloride.
To make these numbers easier to work with, divide each original volume total by 100.
Let A = 100 gallons of 5 percent (=.05) sodium chloride solution
Let B = 25 gallons of water with zero percent (=0.0) sodium chloride
Resultant solution is A - B
(Concentration A)(Volume A) - (Concentration B)(Volume B) = (Resultant concentration of A - B)(Volume of resultant solution A - B)
In the equation below, arithmetically, LHS doesn't need the second term. It's just there to show that, in weighted average terms, it
is being subtracted (it evaporates).
(.05)(100) - (0.0)(25) = \(\frac{x}{100}\)(100 - 25)
5 - 0 = \(\frac{75}{100}\)x
5 = \(\frac{3}{4}\)x
\(\frac{4}{3}\)*(5) = x
x = \(\frac{20}{3}\) = 6.67
Answer D
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