To determine if Aria's and Cody's ratios are equivalent, we can simplify both mixtures to see if they result in the same ratio of blue to red.
Aria's mixture:
- Blue: 7 tbsp
- Red: 2 tbsp
The ratio of blue to red for Aria is: \[ \frac{7}{2} \]
Cody's mixture:
- Blue: 21 tbsp
- Red: 6 tbsp
The ratio of blue to red for Cody is: \[ \frac{21}{6} \] To simplify Cody's ratio, we can divide both the numerator and the denominator by 3: \[ \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]
Now, we compare the simplified ratios:
- Aria's ratio: \(\frac{7}{2}\)
- Cody's ratio: \(\frac{7}{2}\)
Since both ratios are equivalent, the answer is Yes, they are equivalent.