rvc27 wrote:

Five gallons of a solution of vinegar and water with 8% vinegar is to be diluted with water to make a 4% vinegar mixture. How many gallons of water should be added?

A. 10

B. 5

C. 4

D. 2

E. 1

This is probably a very easy question but I have an extreme aversion to raitos, so any help is appreciated.

Source: Bell Curves

Let x = amount of water to be added

A = solution with 8% vinegar

B = water, which 0.0 percent vinegar

(% A)(Vol A) + (% B)(Vol B) = (% of A+B)(Vol A+B)You do not need the 0x on LHS. It's a reminder that water IS being added, but that its concentration /percent vinegar has no weight.

\(.08(5) + 0.0(x) = .04(5 + x)\)

\(.40 + 0x = .20 + .04x\)

\(.20 = .04x\)

\(x = \frac{.20}{.04}=\frac{20}{5}=5\)

Answer B

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