Cody and Aria are painting a mural they decide they want part of the morals 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?

Question

Cody and Aria are painting a mural they decide they want part of the morals 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?

Answer 1

To compare the ratios, we need to simplify them.

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

To simplify Aria's ratio, we divide both sides by the greatest common factor, which is 1 in this case:
7/1 = 7
2/1 = 2

So Aria's simplified ratio is 7:2.

To simplify Cody's ratio, we divide both sides by the greatest common factor, which is 3 in this case:
21/3 = 7
6/3 = 2

So Cody's simplified ratio is 7:2 as well.

Since both ratios are simplified to the same values, Aria and Cody's purple mixtures are equivalent to each other.

Answer 2

To determine if Cody and Aria's ratios of purple mixture are equivalent, we need to compare the ratios of blue to red used by both of them.

First, let's find Cody's ratio of blue to red:
Cody used 21 tbsp of blue and 6 tbsp of red, so the ratio of blue to red is 21:6.

Next, let's find Aria's ratio of blue to red:
Aria used 7 tbsp of blue and 2 tbsp of red, so the ratio of blue to red is 7:2.

To check if the ratios are equivalent, we can simplify them by finding the greatest common divisor (GCD) of the numbers involved.

The GCD of 21 and 6 is 3.
So, Cody's simplified ratio of blue to red is 7:2.

The GCD of 7 and 2 is 1.
So, Aria's simplified ratio of blue to red is 7:2.

Both ratios are now simplified to 7:2, which means Cody and Aria's ratios of purple mixture are equivalent to one another's.

Answer 3

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

For Aria:
Blue:Red = 7 tbsp : 2 tbsp

For Cody:
Blue:Red = 21 tbsp : 6 tbsp

To simplify the ratios, we can divide both sides by their greatest common divisor (GCD) to obtain the simplest form of the ratio.

For Aria's ratio:
GCD(7, 2) = 1

So, Aria's simplified ratio is:
Blue:Red = 7/1 : 2/1 = 7 : 2

For Cody's ratio:
GCD(21, 6) = 3

So, Cody's simplified ratio is:
Blue:Red = 21/3 : 6/3 = 7 : 2

Comparing both simplified ratios, we can see that Aria's and Cody's ratios are indeed equivalent. Both ratios are 7:2, which means they used the same proportion of blue and red to create their purple paint mixture.