To determine whether Cody and Aria's ratios of purple paint are equivalent, we can simplify both of their mixtures and compare them.
Aria’s mixture:
- Blue = 7 tbsp
- Red = 2 tbsp
The ratio of blue to red in Aria's mixture is: \[ \frac{7}{2} \]
Cody’s mixture:
- Blue = 21 tbsp
- Red = 6 tbsp
The ratio of blue to red in Cody's mixture is: \[ \frac{21}{6} \]
Now, we can simplify Cody's ratio: \[ \frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]
Both Aria's and Cody's mixtures simplify to the same ratio: \[ \frac{7}{2} \]
Since both ratios are equivalent, the correct response is:
Yes, they are equivalent.