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 the purple mixture equivalent to one another's?

A. Yes, they are equivalent.
B. No, Aria's has more blue.
C. No, Cody's has more blue.
D. No, Cody's has more red.

Despite using larger quantities of paint, Cody's blue to red ratio for the purple paint mixture is the same as Aria's. Both have a ratio of 7 to 2, making their mixtures equivalent.

Explanation:

The question asks whether the purple paint mixtures prepared by Cody and Aria are equivalent, in terms of their blue to red paint ratio. Aria uses a ratio of 7 tbsp. of blue paint to 2 tbsp. of red paint, while Cody uses a ratio of 21 tbsp. of blue paint to 6 tbsp. of red paint. To determine if the ratios are equivalent, we simplify Cody's ratio by dividing both values by their greatest common factor, which in this case is 3. After simplifying, Cody's ratio becomes 7 to 2, which is identical to Aria's ratio. Therefore, yes, their ratios of purple mixture are equivalent to one another's.

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