Question

As part of a chemistry experiment, Barry is making a mixture of two solutions. He uses 4 cups of solution A for every 2 cups of solution B. The table below shows the number of cups he uses of solution A and solution B.

Solution A
(cups) Solution B
(cups)
4 2
8 4
12 6
16 8

Using the information from the table, choose the correct statement.
A.
There are 3 cups of solution A for every 6 cups of the mixture.
B.
For each cup of solution A, there are 2 cups of solution B.
C.
The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.
D.
The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.

Answer 1

To determine the correct statement, let's analyze the given data and ratios.

The mixtures consist of:

- **Solution A** and **Solution B** in the ratio of 4:2. This simplifies to 2:1.

Calculating the total mixture for the examples in the table:

1. **For 4 cups of Solution A and 2 cups of Solution B:**
- Total mixture = 4 + 2 = 6 cups
- Ratio of Solution A to the total mixture = 4:6, which simplifies to 2:3.

2. **For 8 cups of Solution A and 4 cups of Solution B:**
- Total mixture = 8 + 4 = 12 cups
- Ratio of Solution A to the total mixture = 8:12, which simplifies to 2:3.

3. **For 12 cups of Solution A and 6 cups of Solution B:**
- Total mixture = 12 + 6 = 18 cups
- Ratio of Solution A to the total mixture = 12:18, which simplifies to 2:3.

4. **For 16 cups of Solution A and 8 cups of Solution B:**
- Total mixture = 16 + 8 = 24 cups
- Ratio of Solution A to the total mixture = 16:24, which simplifies to 2:3.

Now, let's evaluate each statement:

A. There are 3 cups of solution A for every 6 cups of the mixture.
- **False** (as we found the ratio A to mixture is 2:3, not 3:6).

B. For each cup of solution A, there are 2 cups of solution B.
- **False** (the ratio is actually 2 cups of A for every 1 cup of B).

C. The ratio of the number of cups of solution A to the total number of cups of the mixture is 3:2.
- **False** (it's actually 2:3).

D. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.
- **True** (as demonstrated by our calculations).

Therefore, the correct statement is:

**D. The ratio of the number of cups of solution A to the total number of cups of the mixture is 2:3.**