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To find the ratios of the purple mixture, we need to simplify the ratios of blue to bread for both Ariel and Cody.
For Ariel, the ratio of blue to bread is 7:2.
To simplify this ratio, we divide both sides by the greatest common divisor of 7 and 2, which is 1:
7 ÷ 1 = 7
2 ÷ 1 = 2
So Ariel's simplified ratio is 7:2.
For Cody, the ratio of blue to bread is 21:6.
To simplify this ratio, we divide both sides by the greatest common divisor of 21 and 6, which is 3:
21 ÷ 3 = 7
6 ÷ 3 = 2
So Cody's simplified ratio is 7:2.
Thus, the ratios of their purple mixtures, equivalent to one another, are both 7:2.