2. You have a sugar solution (solution A) with concentration x. You pour one-fourth of this solution

into a beaker, and add an equivalent volume of water (solution B).
a) What is the ratio of sugar in solutions A and B?
b) Compare the volumes of soutions A and B.
c) What is the ratio of the concentrations of sugar in solutions A and B?

I will be happy too critique your thinking or work. This is straightforward thinking.

I still don't get it

a) The ratio of sugar in solutions A and B is 1:3. This is because when you pour one-fourth of solution A into the beaker, you are left with three-fourths of solution A and one part of water (solution B). Therefore, the sugar in solution A is divided into four equal parts, with one part remaining in solution A and three parts in solution B.

b) The volume of solution A is three-fourths of the original volume, while the volume of solution B is equal to the volume of solution A that was poured into the beaker. Therefore, the volume of solution A is three times larger than the volume of solution B.

c) The concentration of sugar in solution A is x, which is the original concentration. The concentration of sugar in solution B is reduced by one-fourth since one part of solution A was poured into the beaker and replaced with water. Therefore, the concentration of sugar in solution B is 3/4x. The ratio of the concentrations of sugar in solutions A and B is x:3/4x, which simplifies to 4:3.

a) To find the ratio of sugar in solutions A and B, we need to consider that when one-fourth of solution A is poured into the beaker, the remaining three-fourths of solution A is still in the original container. Therefore, the ratio of sugar in solutions A and B is 3:1.

b) Since one-fourth of solution A is poured into the beaker and an equivalent volume of water (solution B) is added, the volume of solution A in the beaker is one-fourth of the original volume of solution A. Therefore, the volume of solution B is equal to the volume of solution A in the beaker. So, the volumes of solutions A and B are equal.

c) The concentration of a solution is given by the ratio of the amount of solute (in this case, sugar) to the volume of the solution. Since the volumes of solutions A and B are equal, the ratio of their concentrations is also 3:1, which means the concentration of sugar in solution A is three times the concentration of sugar in solution B.

To solve this problem, we need to understand the process and make some calculations. Let's break down each question and explain how to find the answers.

a) What is the ratio of sugar in solutions A and B?

Let's assume the initial volume of solution A is V (unknown), and it has a concentration of x (given). After pouring one-fourth of solution A into the beaker, the remaining volume of solution A will be 3/4 V.

Since we add an equivalent volume of water (solution B) to the beaker, the volume of solution B is also 3/4 V.

Now, let's consider the sugar concentration.

The initial volume of sugar in solution A is V * x.

When one-fourth of solution A is poured into the beaker, the volume of sugar transferred to the beaker is (1/4) * V * x.

The remaining volume of sugar in solution A is V * x - (1/4) * V * x = (3/4) * V * x.

Since an equivalent volume of water was added to the beaker, the volume of sugar in solution B is 0.

Therefore, the ratio of sugar in solutions A and B is (3/4) * V * x : 0, which simplifies to 3x:0, or simply 3:0.

b) Compare the volumes of solutions A and B.

From our previous explanation, we know that the volume of solution A is 3/4 V, and the volume of solution B is also 3/4 V.

Therefore, the volumes of solutions A and B are equal.

c) What is the ratio of the concentrations of sugar in solutions A and B?

The concentration of a solution is defined as the amount of solute (sugar) dissolved in a given volume of solution.

The initial concentration of sugar in solution A is x.

After transferring one-fourth of solution A into the beaker, the concentration of sugar transferred to the beaker is (1/4) * x.

The remaining concentration of sugar in solution A is x - (1/4) * x = (3/4) * x.

Since an equivalent volume of water was added to the beaker, the concentration of sugar in solution B is 0.

Therefore, the ratio of the concentrations of sugar in solutions A and B is (3/4) * x : 0, which simplifies to 3x:0, or simply 3:0.

In summary:
a) The ratio of sugar in solutions A and B is 3:0.
b) The volumes of solutions A and B are equal.
c) The ratio of the concentrations of sugar in solutions A and B is 3:0.