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 red to make her purple paint. cody is planning to use more and uses 21 tbsp. of blue to 6tbsp. of red. are their ratios of purple mixture equivalent to one another's?
To determine if their ratios of purple mixture are equivalent, we need to compare the ratio of red to blue in their mixtures.
For Aria, she uses 7 tbsp. of red to make her purple paint. Therefore, the ratio of red to blue in her mixture is 7:0 (since she does not use any blue).
For Cody, he uses 6 tbsp. of red to 21 tbsp. of blue in his mixture. To simplify the ratio, we divide both numbers by the greatest common divisor (GCD) of 6 and 21, which is 3.
So, Cody's ratio of red to blue is 6/3 : 21/3, which simplifies to 2:7.
Comparing the two ratios:
Aria's ratio of red to blue = 7:0
Cody's ratio of red to blue = 2:7
As we can see, the ratios are not equivalent. Therefore, their ratios of purple mixture are not equivalent to one another's.
To determine if Cody's and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of red to blue they used.
Aria used 7 tbsp. of red to make her purple paint.
Cody used 6 tbsp. of red to 21 tbsp. of blue.
To compare the ratios, we can simplify them by finding the greatest common divisor (GCD).
The GCD of 7 and 6 is 1.
By multiplying both ratios by the reciprocal of the other ratio's GCD, we can compare them:
Aria's Ratio: 7 tbsp. red : X tbsp. blue
Cody's Ratio: Y tbsp. red : 21 tbsp. blue
To get the equivalent ratios, we have:
Aria's Ratio: 7 tbsp. red : X tbsp. blue (multiply by 6):
42 tbsp. red : 6X tbsp. blue
Cody's Ratio: Y tbsp. red : 21 tbsp. blue (multiply by 7):
7Y tbsp. red : 147 tbsp. blue
Now, the ratios are:
Aria's Ratio: 42 tbsp. red : 6X tbsp. blue
Cody's Ratio: 7Y tbsp. red : 147 tbsp. blue
As you can see, the ratios are not equivalent. Aria used a higher proportion of red compared to Cody, resulting in a different purple color mixture.
To determine if the ratios of purple mixture are equivalent, we need to compare the amount of red to the amount of blue in each mixture.
Aria's mixture:
- 7 tbsp. of red
Cody's mixture:
- 6 tbsp. of red
- 21 tbsp. of blue
To find the ratio, we need to simplify the fractions by dividing both the red and blue amounts by their greatest common divisor (GCD).
For Aria's mixture, the GCD of 7 tbsp. is 7, so the simplified ratio is:
- 7 tbsp. of red / 7 = 1 tbsp. of red
For Cody's mixture, the GCD of 6 tbsp. of red and 21 tbsp. of blue is 3. Dividing by 3 gives:
- 6 tbsp. of red / 3 = 2 tbsp. of red
- 21 tbsp. of blue / 3 = 7 tbsp. of blue
Now, we can compare the simplified ratios:
- Aria's mixture: 1 tbsp. of red
- Cody's mixture: 2 tbsp. of red and 7 tbsp. of blue
Since the ratios have different amounts of blue, they are not equivalent.
Therefore, the ratios of purple mixture from Aria's and Cody's paints are not the same.