Question

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) 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 if Aria's and Cody's ratios are equivalent, we can simplify both mixtures to see if they result in the same ratio of blue to red.

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 equivalent, the answer is Yes, they are equivalent.