Let's analyze the proportional relationship between red paint and yellow paint based on the given table.
The table shows:
| Red (mL) | Yellow (mL) |
|----------|-------------|
| 10.5 | 28 |
| 7.5 | 20 |
| 9 | 24 |
| ? | ? |
Step 1: Calculate the ratio of red paint to yellow paint for each given pair:
1. For 10.5 mL of red paint and 28 mL of yellow paint:
[tex]\[
\text{Ratio} = \frac{10.5}{28} = 0.375
\][/tex]
2. For 7.5 mL of red paint and 20 mL of yellow paint:
[tex]\[
\text{Ratio} = \frac{7.5}{20} = 0.375
\][/tex]
3. For 9 mL of red paint and 24 mL of yellow paint:
[tex]\[
\text{Ratio} = \frac{9}{24} = 0.375
\][/tex]
We can observe that the ratios are all equal to 0.375, which confirms that the paints are in a proportional relationship.
Step 2: Verify that the missing pair also follows this proportional relationship:
Let's find possible values for the missing pair.
Method 1: Assume a value for red paint and find the corresponding yellow paint:
Suppose we have 6 mL of red paint.
To find the corresponding yellow paint:
[tex]\[
\text{Yellow (mL)} = \frac{\text{Red (mL)}}{\text{Ratio}} = \frac{6}{0.375} = 16 \text{ mL}
\][/tex]
So, one possible pair is [tex]\( (6, 16) \)[/tex].
Method 2: Assume a value for yellow paint and find the corresponding red paint:
Suppose we have 16 mL of yellow paint.
To find the corresponding red paint:
[tex]\[
\text{Red (mL)} = \text{Yellow (mL)} \times \text{Ratio} = 16 \times 0.375 = 6 \text{ mL}
\][/tex]
So, another possible pair is [tex]\( (6, 16) \)[/tex].
Therefore, the valid paint mixtures that could fit the missing values in the table, maintaining the proportional relationship, are:
1. 6 mL of red paint and 16 mL of yellow paint.
2. 6 mL of red paint and 16 mL of yellow paint.
Since both steps give the same mixture, the missing values that fit the proportional relationship are:
[tex]\((6 \text{ mL of red}, 16 \text{ mL of yellow})\)[/tex].
