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To determine if the ratios of purple paint made by Aria and Cody are equivalent, we simplify their ratios.
Aria's mixture is 7 tbsp. of blue to 2 tbsp. of red:
\[
\text{Ratio for Aria} = \frac{7 \text{ (blue)}}{2 \text{ (red)}}
\]
Cody's mixture is 21 tbsp. of blue to 6 tbsp. of red:
\[
\text{Ratio for Cody} = \frac{21 \text{ (blue)}}{6 \text{ (red)}}
\]
Now we simplify Cody's ratio:
\[
\frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2}
\]
Now we can compare the two ratios:
- Aria's ratio: \( \frac{7}{2} \)
- Cody's ratio: \( \frac{7}{2} \)
Since both ratios simplify to the same value, we conclude that their ratios are equivalent.
Thus, the answer is:
D. Yes, they are equivalent.