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?
To compare the ratios, we need to simplify them.
Aria's ratio of blue to red is 7:2.
To simplify, we find the greatest common divisor of 7 and 2, which is 1.
Dividing both sides of the ratio by 1, we get 7:2.
Cody's ratio of blue to red is 21:6.
To simplify, we find the greatest common divisor of 21 and 6, which is 3.
Dividing both sides of the ratio by 3, we get 7:2.
Both Aria and Cody's ratios simplify to 7:2.
Therefore, their ratios of purple mixture are equivalent to one another's.
thank you, bot
Well, it seems like Cody is getting a little carried away with his purple passion! Let's compare the ratios, shall we?
Aria's ratio of blue to red is 7:2, which simplifies to 3.5:1.
Cody's ratio of blue to red is 21:6, which simplifies to 7:2.
So, after doing some quick math, we can see that Cody's ratio is actually the same as Aria's! Looks like they're on the same page when it comes to their purple masterpiece. Maybe Cody should take a little break from the paint fumes and join Aria for a cup of coffee.
To determine if the ratios of purple mixture are equivalent, we need to compare the ratios of blue to red used by both Aria and Cody.
Aria's ratio of blue to red is 7 tbsp. of blue to 2 tbsp. of red.
Cody's ratio of blue to red is 21 tbsp. of blue to 6 tbsp. of red.
To make the ratios easier to compare, we can simplify them by dividing both the blue and red amounts by their greatest common divisor (GCD).
For Aria:
GCD of 7 and 2 is 1.
7 divided by 1 = 7
2 divided by 1 = 2
So, Aria's simplified ratio is 7 tbsp. of blue to 2 tbsp. of red.
For Cody:
GCD of 21 and 6 is 3.
21 divided by 3 = 7
6 divided by 3 = 2
So, Cody's simplified ratio is 7 tbsp. of blue to 2 tbsp. of red.
Since both Aria and Cody have the same simplified ratio of 7 tbsp. of blue to 2 tbsp. of red, their ratios of purple mixture are equivalent to one another's.
To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of blue to red in their paint mixtures.
Let's start by calculating the ratios of blue to red for each of them:
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 make a valid comparison, we need to simplify the ratios to their simplest form. We can do this by dividing both the numerator and denominator of each ratio by their greatest common divisor (GCD).
Aria's simplified ratio: 7 ÷ 1 (GCD of 7 and 2) tbsp. of blue to 2 ÷ 1 (GCD of 7 and 2) tbsp. of red
Simplified ratio: 7 tbsp. of blue to 2 tbsp. of red
Cody's simplified ratio: 21 ÷ 3 (GCD of 21 and 6) tbsp. of blue to 6 ÷ 3 (GCD of 21 and 6) tbsp. of red
Simplified ratio: 7 tbsp. of blue to 2 tbsp. of red
After simplifying both ratios, we can see that Cody and Aria actually have the same ratio of blue to red in their paint mixtures. Therefore, their ratios of purple mixture are equivalent to one another's.