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 anothers?

Question

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 anothers?

Answer 1

To determine if the ratios are equivalent, we need to compare the amounts of blue and red used in each mixture.

For Aria's purple paint:
Blue: 7 tbsp
Red: 2 tbsp

For Cody's purple paint:
Blue: 21 tbsp
Red: 6 tbsp

To simplify the ratios, we can divide both sides by the greatest common divisor, which in this case is 1.

Aria's ratio:
Blue: 7 tbsp
Red: 2 tbsp

Cody's ratio:
Blue: 21 tbsp
Red: 6 tbsp

Since the ratios are already simplified, we can see that the ratio of blue to red is the same for both Aria and Cody: 7:2. Therefore, their ratios of purple mixture are equivalent to one another.

Answer 2

To determine if Cody and Aria's ratios of purple mixtures are equivalent, we can compare the ratios of blue to red in each mixture.

Aria's ratio: 7 tbsp. of blue to 2 tbsp. of red.
Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red.

First, we can simplify both ratios by dividing both the blue and red amounts by their greatest common factor.

Aria's simplified ratio: 7/1 tbsp. of blue to 2/1 tbsp. of red.
Cody's simplified ratio: 21/3 tbsp. of blue to 6/3 tbsp. of red.

Now, let's compare the simplified ratios:

Aria's ratio: 7/1 tbsp. of blue to 2/1 tbsp. of red.
Cody's ratio: 7/1 tbsp. of blue to 2/1 tbsp. of red.

Since the simplified ratios are equal, it means that Cody and Aria's ratios of purple mixtures are equivalent.

Answer 3

To determine if the ratios of the purple mixtures used by Cody and Aria are equivalent, we need to compare the ratios of blue to red in their mixtures.

Let's start with Aria's ratio: 7 tbsp. of blue to 2 tbsp. of red.

To find the equivalent ratio, we need to multiply both sides of the ratio by the same number:
7 tbsp. of blue * 3 = 21 tbsp. of blue
2 tbsp. of red * 3 = 6 tbsp. of red

So, Aria's equivalent ratio is 21 tbsp. of blue to 6 tbsp. of red.

Now let's look at Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red.

Comparing the two ratios side by side:
Aria's ratio: 21 tbsp. of blue to 6 tbsp. of red
Cody's ratio: 21 tbsp. of blue to 6 tbsp. of red

Since the ratios are the same, we can conclude that Cody's and Aria's ratios of the purple mixture are equivalent to each other.