Question

Cody and Ariel are painting a mural they decide they want part of the mirror to have a purple background area uses seven tablespoons of blue to two tablespoons of red to make her purple paint code is planning to use more and uses 21 tablespoons of blue to six tablespoons of red are there ratios a purple mixture equivalent to one another's a no Cody says more red be no Eris has more blue see yes they are equivalent D no code is has more blue

Answer 1

To determine if the ratios of purple mixtures created by Cody and Ariel are equivalent, we can compare the ratios of blue to red in each of their mixtures.

Cody's mixture:

• Blue: 7 tablespoons
• Red: 2 tablespoons

The ratio of blue to red in Cody's mixture is: \[ \text{Ratio for Cody} = \frac{7 \text{ (blue)}}{2 \text{ (red)}} = \frac{7}{2} \]

Ariel's mixture:

• Blue: 21 tablespoons
• Red: 6 tablespoons

The ratio of blue to red in Ariel's mixture is: \[ \text{Ratio for Ariel} = \frac{21 \text{ (blue)}}{6 \text{ (red)}} \]

To simplify Ariel's ratio, we can divide both the numerator and the denominator by 3: \[ \frac{21}{6} = \frac{21 \div 3}{6 \div 3} = \frac{7}{2} \]

Now, we can compare the two ratios:

• Cody's ratio: \( \frac{7}{2} \)
• Ariel's ratio: \( \frac{7}{2} \)

Since both ratios simplify to \( \frac{7}{2} \), we conclude that the mixtures are equivalent.

The correct answer is: C: Yes, they are equivalent.