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)

Question

Responses

Yes, they are equivalent.
Yes, they are equivalent.

No, Cody’s has more red.
No, Cody’s has more red.

No, Cody’s has more blue.
No, Cody’s has more blue.

No, Aria’s has more blue.

Answer 1

To determine if the ratios of purple mixture used by Cody and Aria are equivalent, we need to compare the ratios of blue to red for both.

Aria's mixture:

• Blue: 7 tbsp
• Red: 2 tbsp
• Ratio: \( \frac{7}{2} \)

Cody's mixture:

• Blue: 21 tbsp
• Red: 6 tbsp
• Ratio: \( \frac{21}{6} \)

Next, we simplify Cody's ratio:

• \( \frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \)

Now we can compare:

• Aria's ratio: \( \frac{7}{2} \)
• Cody's ratio: \( \frac{7}{2} \)

Since both ratios are equal, we conclude that:

Yes, they are equivalent.