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
To find out if the ratios of their purple mixture are equivalent, we need to compare the ratio of blue to red in each mixture.
For Aria's mixture, the ratio of blue to red is 7:2.
For Cody's mixture, the ratio of blue to red is 21:6.
We can simplify these ratios by dividing both numbers by their greatest common divisor.
For Aria's mixture, the greatest common divisor of 7 and 2 is 1. Dividing both numbers by 1, we get the simplified ratio of 7:2.
For Cody's mixture, the greatest common divisor of 21 and 6 is 3. Dividing both numbers by 3, we get the simplified ratio of 7:2.
Since both ratios simplify to the same ratio of 7:2, we can conclude that their ratios of purple mixture are equivalent to one another's.
To determine if their ratios of purple mixtures are equivalent, we need to simplify the ratios and see if they are equal.
Aria's ratio: 7 tbsp. of blue to 2 tbsp. of red = 7:2 (blue:red)
Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red = 21:6 (blue:red)
Let's simplify the ratios:
Aria's ratio: 7:2
Dividing both sides by the greatest common divisor (GCD), which is 1, we get: 7:2
Cody's ratio: 21:6
Dividing both sides by the GCD, which is 3, we get: 7:2
Both ratios simplify to 7:2, which means their ratios of purple mixtures are equivalent to one another's.
To determine if Cody's and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of blue to red in their paint mixtures.
Aria's ratio of blue to red is 7:2, which can also be written as 7/2.
Cody's ratio of blue to red is 21:6, which can be simplified to 7:2 (both numbers can be divided by 3).
Since both Cody's and Aria's ratios of blue to red are the same (7:2), their ratios of purple mixtures are indeed equivalent.
To calculate the ratio, you need to divide the amount of blue by the amount of red for each person's paint mixture. If the resulting ratios are the same, then the purple mixtures are equivalent.