francoisph wrote:A certain quantity of 40% solution is replaced with 25% solution such that the new concentration is 35%. What is the fraction of the solution that was replaced?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 2/3
(E) 3/4
Use the answer choices.
The answer choices represent what fraction of the solution should be the 25% solution. Normally we'd start with C because it's right in the middle, but we know that the solution can't be half 40% and half 25% because then the resulting percentage would be (40+25)/2 = 32.5. So we need to use less of the 25% solution. The correct answer must be B or A.
Answer choice B:
Let's use a number for the solution that's divisible by 4 (since we'll need to take 40% and 25% of this number) and 3 (since we'll need to take 1/3 of it).
Say the solution = 300.
If 1/3 is the 25% solution, then (1/3)(300) = 100 of the 25% solution, leaving us 200 of the 40% solution.
.25(100) = 25.
.4(200) = 80.
So the solution contains 25 + 80 = 105.
Since 105/300 = 35/100, the resulting solution is 35%. Success!
The correct answer is
B.
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