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.

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

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

No, Cody’s has more red.

Answer 1

To determine whether Cody's and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of blue to red in each case.

Aria's mixture:

• Blue: 7 tbsp
• Red: 2 tbsp

The ratio of blue to red for Aria is: \[ \text{Ratio}_\text{Aria} = \frac{7}{2} \]

Cody's mixture:

• Blue: 21 tbsp
• Red: 6 tbsp

The ratio of blue to red for Cody is: \[ \text{Ratio}_\text{Cody} = \frac{21}{6} \]

Now, we can simplify Cody's ratio by dividing both the numerator and denominator by their greatest common divisor (which is 3): \[ \frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]

Since both ratios simplify to \(\frac{7}{2}\), the ratios are equivalent.

Thus, the correct response is: Yes, they are equivalent.