Question

kayli and clinton each made a batch of purple paint.

• kayli mixed 5 cups of red paint with 3 cups of blue paint.
• clinton mixed 4 cups of red paint with 2 cups of blue paint.

are kayli’s and clinton’s mixtures the same shade of purple? describe the method you use to find your answer.
kayli’s mixture: 5 red (r) cups, 3 blue (b) cups, labeled 5r:3b; clinton’s mixture: 4 red (r) cups, 2 blue (b) cups, labeled 4r:2b

Explanation:

Step1: Find Kayli's ratio

Kayli's red to blue ratio is \( \frac{5}{3} \approx 1.67 \)

Step2: Find Clinton's ratio

Clinton's red to blue ratio is \( \frac{4}{2} = 2 \)

Step3: Compare ratios

Since \( 1.67
eq 2 \), the ratios are different.

Answer:

The two batches are the different. I decided this by calculating the ratio of red paint to blue paint for each mixture. Kayli's ratio of red to blue paint is \( \frac{5}{3} \) (or approximately 1.67) and Clinton's ratio is \( \frac{4}{2}=2 \). Since these ratios are not equal, the mixtures will be different shades of purple.