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?
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
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.
To determine whether the ratios of purple mixture are equivalent, we need to compare the amounts of blue and red used by each person.
Aria's ratio: 7 tbsp. of blue to 2 tbsp. of red.
Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red.
To compare the ratios, we need to find a common factor for the blue and red amounts in both ratios.
For Aria's ratio:
- The common factor for blue is 7.
- Multiplying 7 by 3 gives us 21 as the equivalent amount of blue in Cody's ratio.
- Multiplying 2 by 3 gives us 6 as the equivalent amount of red in Cody's ratio.
Now we can compare the equivalent 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.
The equivalent ratios show that Cody used the same amount of red and three times the amount of blue compared to Aria. Therefore, the answer is:
C. no, Cody's has more blue.
To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the amounts of blue and red they used in their respective ratios.
Aria used 7 tbsp. of blue and 2 tbsp. of red to make her purple paint.
Cody used 21 tbsp. of blue and 6 tbsp. of red to make his purple paint.
First, let's compare the amounts of blue used:
Aria: 7 tbsp. of blue
Cody: 21 tbsp. of blue
Since 21 is three times larger than 7, Cody used three times more blue than Aria.
Next, let's compare the amounts of red used:
Aria: 2 tbsp. of red
Cody: 6 tbsp. of red
Since 6 is three times larger than 2, Cody used three times more red than Aria.
Based on our comparisons, we can conclude that Cody's ratio has three times more blue and three times more red than Aria's ratio. Therefore, the ratios are not equivalent.
The correct answer is:
C. no, Cody's has more blue