\[ 3: 4 \] a) If you have 10 cups of lemonade mix, how much water would you need for pitcher B? Draw a model (table, tape diagram, double number line).

To solve this problem, we need to determine how much water is needed for pitcher B when we have 10 cups of lemonade mix. Given: - 3 cups of lemonade mix for pitcher A - 4 cups of lemonade mix for pitcher B We are asked to find out how much water is needed for pitcher B when we have 10 cups of lemonade mix. Let's assume the amount of water needed for pitcher B is x cups. Since the ratio of lemonade mix to water is the same for both pitchers, we can set up a proportion: \[ \frac{3}{4} = \frac{10}{x} \] Now, we can solve for x to find out how much water is needed for pitcher B. Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{3}{4}=\frac{10}{x}\) - step1: Find the domain: \(\frac{3}{4}=\frac{10}{x},x\neq 0\) - step2: Swap the sides: \(\frac{10}{x}=\frac{3}{4}\) - step3: Rewrite the expression: \(x=\frac{10\times 4}{3}\) - step4: Divide the terms: \(x=\frac{40}{3}\) - step5: Check if the solution is in the defined range: \(x=\frac{40}{3},x\neq 0\) - step6: Find the intersection: \(x=\frac{40}{3}\) The amount of water needed for pitcher B when we have 10 cups of lemonade mix is \( \frac{40}{3} \) cups or approximately 13.33 cups. Therefore, to make pitcher B, you would need approximately 13.33 cups of water.