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

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

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

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

Yes, they are equivalent.

Answer 1

To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of blue to red in both cases.

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 the same, we conclude:

Yes, they are equivalent.