Cody and Aria are painting a mural. They decide they want part of the mural to have a purple background. Aria uses 7 tbsp. of blue to 2 tbsp. of red to make her purple paint. Cody is planning to use more and uses 21 tbsp. of blue to 6 tbsp. of red. Are their ratios of purple mixture equivalent to one another's?(1 point) Responses No, Cody’s has more blue. No, Cody’s has more blue. No, Aria’s has more blue. No, Aria’s has more blue. Yes, they are equivalent. Yes, they are equivalent. No, Cody’s has more red.

Answer 1

To compare the ratios, we can simplify both Aria's and Cody's mixtures.

Aria's ratio is:

• Blue : Red = 7 tbsp : 2 tbsp

To simplify, we can represent this as:

• \( \frac{7}{2} \)

Cody's ratio is:

• Blue : Red = 21 tbsp : 6 tbsp

To simplify, we can also represent this as:

• \( \frac{21}{6} \)

Now simplify \( \frac{21}{6} \):

• Divide both the numerator and the denominator by their greatest common divisor (GCD), which is 3:
• \( \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \)

Now we can see that both ratios simplify to \( \frac{7}{2} \).

Since both ratios are equivalent, the answer is: Yes, they are equivalent.