Cody an 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?

Question

GPT 3.5 · Answer

To determine if the ratios of the purple mixture are equivalent, we need to compare the ratios of blue to red in their mixtures.

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

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

To simplify both ratios, we can divide both sides by the greatest common divisor.

For Aria's ratio:
7 ÷ gcd(7,2) = 7 ÷ 1 = 7
2 ÷ gcd(7,2) = 2 ÷ 1 = 2

So Aria's simplified ratio is 7:2.

For Cody's ratio:
21 ÷ gcd(21,6) = 21 ÷ 3 = 7
6 ÷ gcd(21,6) = 6 ÷ 3 = 2

So Cody's simplified ratio is 7:2.

Since the simplified ratios for both Aria and Cody are the same (7:2), their ratios of the purple mixture are equivalent.