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

A. No, Cody’s has more red.

B. No, Cody’s has more blue.

C. No, Aria’s has more blue.

D. Yes, they are equivalent.

Answer 1

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

Aria's mixture is 7 tbsp. of blue to 2 tbsp. of red:

\[ \text{Ratio for Aria} = \frac{7 \text{ (blue)}}{2 \text{ (red)}} \]

Cody's mixture is 21 tbsp. of blue to 6 tbsp. of red:

\[ \text{Ratio for Cody} = \frac{21 \text{ (blue)}}{6 \text{ (red)}} \]

Now we simplify Cody's ratio:

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

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 their ratios are equivalent.

Thus, the answer is:

D. Yes, they are equivalent.