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 use 21 tbsp.of blue to 6 tbsp.of red. Are their ratios of purple mixture equivalent to on another's?
A. Yes, they are equivalent
B. No, Cody's has more red
C. No, Cody's has more blue
D. No, Aries has more blue
C. No, Cody's has more blue.
To compare the ratios of blue and red in their purple mixtures, we can simplify their respective ratios:
Aria's ratio: 7 tbsp of blue to 2 tbsp of red
Cody's ratio: 21 tbsp of blue to 6 tbsp of red
We can simplify these ratios by dividing both sides by their greatest common divisor.
Aria's simplified ratio: 7 tbsp of blue to 2 tbsp of red
Cody's simplified ratio: 7 tbsp of blue to 2 tbsp of red
From this, we can see that their simplified ratios are equivalent, indicating that they have the same ratios of blue and red in their purple mixtures. Therefore, the correct answer is:
A. Yes, they are equivalent.
To determine if Cody's and Aria's ratios of purple mixture are equivalent, we need to compare the amounts of blue and red used in each mixture.
Aria's ratio of blue to red is 7 tbsp. to 2 tbsp.
Cody's ratio of blue to red is 21 tbsp. to 6 tbsp.
To compare the ratios, we need to find the lowest common denominator.
For Aria's ratio:
Multiply both parts by 3: 7 tbsp. x 3 = 21 tbsp. and 2 tbsp. x 3 = 6 tbsp.
So, Aria's ratio becomes 21 tbsp. of blue to 6 tbsp. of red.
Now, we can directly compare the ratios:
- Aria's ratio: 21 tbsp. of blue to 6 tbsp. of red
- Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red
The ratios of blue to red in both mixtures are the same, so the answer is:
A. Yes, they are equivalent
To determine if the ratios of the purple mixtures are equivalent, we need to compare the amount of blue to the amount of red used in each mixture.
For Aria's purple mixture, she uses 7 tbsp of blue to 2 tbsp of red. This can be expressed as a ratio of 7:2 in its simplest form.
For Cody's purple mixture, he uses 21 tbsp of blue to 6 tbsp of red. This can be simplified to a ratio of 7:2 as well.
Since both ratios simplify to the same ratio of 7:2, the answer is:
A. Yes, they are equivalent.