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

No, Cody’s has more blue.
No, Cody’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 the ratios of Aria and Cody's purple paint mixtures are equivalent, we need to express each mixture's ratio in simplest form.

Aria's mixture:

• Blue: 7 tbsp
• Red: 2 tbsp

The ratio of blue to red is \( \frac{7}{2} \).

Cody's mixture:

• Blue: 21 tbsp
• Red: 6 tbsp

The ratio of blue to red is \( \frac{21}{6} \).

Now, let's simplify Cody's ratio:

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

Now we can see that:

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

Since both ratios simplify to \( \frac{7}{2} \), we can conclude that the ratios of their purple mixtures are indeed equivalent.

The correct response is: Yes, they are equivalent.