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
No, Cody’s has more red.
No, Cody’s has more red.
Yes, they are equivalent.
Yes, they are equivalent.
No, Aria’s has more blue.
No, Aria’s has more blue.
No, Cody’s has more blue.
Yes, they are equivalent.
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 mixtures.
Aria's mixture has a ratio of 7 tbsp. of blue to 2 tbsp. of red.
Cody's mixture has a ratio of 21 tbsp. of blue to 6 tbsp. of red.
To make a comparison, we can simplify both ratios by dividing both the number of blue tablespoons and the number of red tablespoons by the greatest common divisor (GCD) of both numbers.
For Aria's mixture:
The GCD of 7 and 2 is 1.
Divide both numbers by 1.
The simplified ratio is 7 tbsp. of blue to 2 tbsp. of red.
For Cody's mixture:
The GCD of 21 and 6 is 3.
Divide both numbers by 3.
The simplified ratio is 7 tbsp. of blue to 2 tbsp of red.
Both simplified ratios are the same: 7 tbsp. of blue to 2 tbsp. of red.
Therefore, the answer is:
Yes, they are equivalent.
Cody's and Aria's ratios of purple mixture are equivalent since they both have the same ratio of blue to red.