Cody and Aria are painting a mural. They decide they want part of mural to have a purple background. Marisa 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 ratio of purple mixture equvalent to one another's?

Question

Yes, they are equivalent

No, Arias has more blue

No, Codys has more blue

No, Codys has more red

Answer 1

To determine whether Cody and Aria's purple mixtures are equivalent, we can compare the ratios of blue to red in both mixtures.

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: \[ \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]

Since both Aria and Cody have the same ratio of blue to red, which is \(\frac{7}{2}\), their purple mixtures are equivalent.

Therefore, the correct answer is: Yes, they are equivalent.