A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as . Find . Round your answer to two decimal places.
A) 1.00 %
B) 0.17 %
C) 0.70 %
D) 0.67 %
E) 0.25 %

Question

A container holds 3 liters of a 25% brine solution. A model for the concentration C of the mixture after adding x liters of a 0.67 % brine solution to the container and then draining x liters of the well-mixed solution is given as  . Find  . Round your answer to two decimal places.
A) 1.00 % 
B) 0.17 % 
C) 0.70 % 
D) 0.67 % 
E) 0.25 %

Quizplus · Accepted Answer

We are given that the container initially has 3 liters of a 25% brine solution. This means that the container has 0.75 liters of salt (25% of 3 liters).

Next, we add x liters of a 0.67% brine solution. This means that we are adding (0.67/100)x liters of salt.

After this, we drain x liters of the well-mixed solution. This means that we are removing the same amount of brine solution (with the same concentration) and salt as we added earlier.

Therefore, the model for the new concentration can be written as:

C = (0.75 + 0.0067x)/(3 + x)

Now we can find the concentration when x = 1 liter (since we added and then drained 1 liter):

C = (0.75 + 0.0067(1))/(3 + 1) = 0.185/4 = 0.04625

Therefore, the concentration is 0.04625, which is equivalent to 0.04625 x 100% = 4.625%.

We must round our answer to two decimal places, which means that the answer is 4.63%. This corresponds to answer choice D: 0.67%.

A Container Holds 3 Liters of a 25% Brine Solution