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?

Question

A. yes, they are equivalent
B. no, Cody's has more red
C. no, Cody's has more blue
D. no, Aria has more blue

Answer 1

To compare the ratios of purple mixture, we need to simplify the ratios by finding the greatest common factor (GCF) between the amounts of blue and red used.

For Aria's mixture:
GCF of 7 and 2 is 1.

For Cody's mixture:
GCF of 21 and 6 is 3.

Simplifying the ratios:

Aria's mixture: 7/1 blue to 2/1 red
Cody's mixture: 21/3 blue to 6/3 red

After simplifying, the ratios are not equivalent because they have different GCFs. Therefore, the answer is:
C. no, Cody's has more blue.