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.
Yes, they are equivalent.

Answer 1

To determine whether Cody and Aria's ratios of purple paint are equivalent, we can simplify both of their mixtures and compare them.

Aria’s mixture:

• Blue = 7 tbsp
• Red = 2 tbsp

The ratio of blue to red in Aria's mixture is: \[ \frac{7}{2} \]

Cody’s mixture:

• Blue = 21 tbsp
• Red = 6 tbsp

The ratio of blue to red in Cody's mixture is: \[ \frac{21}{6} \]

Now, we can simplify Cody's ratio: \[ \frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]

Both Aria's and Cody's mixtures simplify to the same ratio: \[ \frac{7}{2} \]

Since both ratios are equivalent, the correct response is:

Yes, they are equivalent.