Cody and aria are painting a mural they decide they want part of the mural to have 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 anothers
To determine if the ratios of their purple mixtures are equivalent, we need to simplify both ratios.
Aria's ratio of blue to red is 7:2. This means that for every 7 tablespoons of blue, she uses 2 tablespoons of red.
Cody's ratio of blue to red is 21:6. This means that for every 21 tablespoons of blue, he uses 6 tablespoons of red.
To simplify Aria's ratio, we divide both numbers by their greatest common divisor (GCD), which is 1 in this case since 7 and 2 are prime numbers.
7 ÷ 1 = 7
2 ÷ 1 = 2
Therefore, Aria's simplified ratio is 7:2.
To simplify Cody's ratio, we divide both numbers by their GCD, which is 3 in this case.
21 ÷ 3 = 7
6 ÷ 3 = 2
Therefore, Cody's simplified ratio is 7:2, which is the same as Aria's simplified ratio.
Thus, their ratios of purple mixture are equivalent.
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To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the ratio of blue to red in both cases.
Aria's ratio: 7 tbsp blue to 2 tbsp red.
Cody's ratio: 21 tbsp blue to 6 tbsp red.
Now, let's simplify both ratios to their simplest form.
For Aria's ratio:
Divide both numbers (7 and 2) by their greatest common divisor, which is 1.
So, Aria's simplified ratio is 7:2.
For Cody's ratio:
Divide both numbers (21 and 6) by their greatest common divisor, which is 3.
21 ÷ 3 = 7
6 ÷ 3 = 2
So, Cody's simplified ratio is also 7:2.
Since both ratios are simplified to the same terms, Cody and Aria's ratios of purple mixture are equivalent.
To determine if the ratios of the purple mixture are equivalent, we need to compare the ratios of blue to red paint used by Aria and Cody.
Aria's ratio of blue to red paint is 7:2, which means for every 7 tablespoons of blue paint she uses, she uses 2 tablespoons of red paint.
Cody's ratio of blue to red paint is 21:6, meaning for every 21 tablespoons of blue paint he uses, he uses 6 tablespoons of red paint.
To see if their ratios are equivalent, we need to simplify both ratios to their simplest form.
For Aria's ratio, we can divide both the blue and red amounts by the greatest common divisor (GCD) of 7 and 2, which is 1. This gives us a simplified ratio of 7:2.
For Cody's ratio, we can divide both the blue and red amounts by the GCD of 21 and 6, which is 3. This results in a simplified ratio of 7:2 as well.
Therefore, both Aria's and Cody's ratios of blue to red paint are equivalent, indicating that their purple mixtures have the same ratio of blue to red paint.