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?(1 point)
Responses
Yes, they are equivalent.
Yes, they are equivalent.
No, Cody’s has more red.
No, Cody’s has more red.
No, Aria’s has more blue.
No, Aria’s has more blue.
No, Cody’s has more blue.
No, Cody’s has more blue.
No, Cody’s has more blue.
No, Cody’s has more blue.
To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the quantities of blue and red used in their respective mixtures.
Aria uses 7 tbsp. of blue to 2 tbsp. of red to make her purple paint.
Cody uses 21 tbsp. of blue to 6 tbsp. of red to make his purple paint.
To simplify the comparison, we can divide the quantities of blue and red used in each mixture by the smallest quantity of that color used.
For Aria's mixture:
Blue ratio = 7 tbsp. / 2 tbsp. = 3.5
Red ratio = 2 tbsp. / 2 tbsp. = 1
For Cody's mixture:
Blue ratio = 21 tbsp. / 6 tbsp. = 3.5
Red ratio = 6 tbsp. / 2 tbsp. = 3
Comparing the ratios, we see that both Aria and Cody have the same blue-to-red ratio of 3.5. Therefore, their ratios of purple mixture are equivalent.
So, the correct response is: Yes, they are equivalent.