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.
images of kaylis mixture (5r:3b) and clintons mixture (4r:2b) are shown

Explanation:

Step1: Find the ratio of red to blue for Kayli

Kayli has 5 cups red (R) and 3 cups blue (B), so the ratio of R to B is $\frac{5}{3}$.

Step2: Find the ratio of red to blue for Clinton

Clinton has 4 cups red (R) and 2 cups blue (B), simplify $\frac{4}{2}=2$, or as a ratio of R to B it's $\frac{4}{2} = \frac{2}{1}$ (simplified). Wait, actually, let's simplify both ratios properly. Kayli's ratio: $\frac{5}{3} \approx 1.666...$. Clinton's ratio: $\frac{4}{2} = 2$. Wait, no, maybe I made a mistake. Wait, Clinton's ratio is 4R:2B, which simplifies to 2R:1B (dividing numerator and denominator by 2). Kayli's is 5R:3B, which is $\frac{5}{3} \approx 1.666$. Clinton's is $\frac{4}{2} = 2$. Wait, no, wait, maybe I should cross - multiply to check if the ratios are equal. If $\frac{5}{3}=\frac{4}{2}$, then cross - multiplying: $5\times2 = 10$ and $3\times4 = 12$. Since $10
eq12$, the ratios are not equal.

Wait, let's do it step by step.

Step1: Calculate Kayli's red - to - blue ratio

Kayli mixed 5 cups of red and 3 cups of blue. The ratio of red to blue is $\frac{\text{Red}}{\text{Blue}}=\frac{5}{3}\approx1.67$.

Step2: Calculate Clinton's red - to - blue ratio

Clinton mixed 4 cups of red and 2 cups of blue. The ratio of red to blue is $\frac{\text{Red}}{\text{Blue}}=\frac{4}{2} = 2$.

Step3: Compare the two ratios

Since $\frac{5}{3}\approx1.67$ and $2$ are not equal, the ratios of red to blue paint are different.

Answer:

No, Kayli’s and Clinton’s mixtures are not the same shade of purple. To determine this, we find the ratio of red paint to blue paint for each. For Kayli, the ratio of red to blue is $\frac{5}{3}\approx1.67$. For Clinton, the ratio of red to blue is $\frac{4}{2} = 2$. Since these ratios are not equal, the mixtures will have different shades of purple.