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

No, Cody’s has more blue.

Answer 1

To determine if the ratios of purple paint made by Aria and Cody are equivalent, we can simplify both ratios.

Aria's mixture consists of:

• 7 tbsp. of blue
• 2 tbsp. of red

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

Cody's mixture consists of:

• 21 tbsp. of blue
• 6 tbsp. of red

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

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

Now we can compare the two ratios:

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

Since both ratios simplify to the same value, we conclude that:

Yes, they are equivalent.