Question

Problem 9. (3 points) You are making a “Maracuja Schorle”, which is a mixture of pure

passion fruit juice and carbonated water. You have a 6 quart pitcher, which is currently a
mixture of 1/3 passion fruit juice, and 2/3 carbonated water, and you find it is too watered
down. How much of the mixture should you pour out, and replace with pure passion fruit
juice so that the new mixture is 1/2 passion fruit juice and 1/2 carbonated water?

Answer 1

Answer: 3/2 quarts

Explanation:

At the beginning, we have, if v represents the volume of the pitcher:

v/3 of passion fruit

2*v/3 of carbonated water.

Now, suppose that you pour out a volume x of the mixture.

Then now we have (v - x) left in the pitcher.

And as the mixture is homogeneous, we have:

(v - x)/3 of passion fruit juice.

2*(v - x)/3 of carbonated water.

Now yo add x of passion fruit juice, so the total volume of mixture in the pitcher is v again:

Now we have:

(v - x)/3 + x of passion fruit juice

2*(v - x)/3 of carbonated water.

If we want to have 1/2 of passion fruit juice, and 1/2 of carbonated water, then the above amounts must be equal:

(v - x)/3 + x = 2*(v - x)/3

And we know that v = 6 quart.

I will ignore the units in the math, so it is easier to read.

(6 - x)/3 + x = 2*(6 - x)/3

x = 2*(6 - x)/3 - (6 - x)/3 = (6 - x)/3 = 2 - x/3

x + x/3 = 2

x*(1 + 1/3) = 2

x*(4/3) = 2

x = 2*3/4 = 6/4 = 3/2

So the amount that you need to pour out, and replace with passion fruit juice, is 3/2 quarts.