1. **Problem Statement:** We are given two tables showing ratios of paint quantities (white paint to red paint, and white paint to purple paint) and need to find the missing values. 2. **Understanding Ratios:** A ratio compares two quantities and can be written as $\frac{a}{b}$. If the ratio is constant, then $\frac{a_1}{b_1} = \frac{a_2}{b_2}$. 3. **First Table (White Paint and Red Paint):** Given: - White paint: 2, 6, 8, ? - Red paint: 3, ?, ?, 36 Step 1: Find the constant ratio using known values: $$\frac{2}{3} = \frac{6}{x}$$ Solve for $x$: $$x = \frac{6 \times 3}{2} = 9$$ Step 2: Use the ratio to find the next missing red paint value: $$\frac{8}{y} = \frac{2}{3} \Rightarrow y = \frac{8 \times 3}{2} = 12$$ Step 3: Find the missing white paint value corresponding to red paint 36: $$\frac{w}{36} = \frac{2}{3} \Rightarrow w = \frac{2 \times 36}{3} = 24$$ 4. **Second Table (White Paint and Purple Paint):** Given: - White paint: 1, 3, ?, ? - Purple paint: ?, 30, 40, 60 Step 1: Find the constant ratio using known values: $$\frac{3}{30} = \frac{1}{p} \Rightarrow p = \frac{1 \times 30}{3} = 10$$ Step 2: Use the ratio to find the missing white paint value for purple paint 40: $$\frac{w}{40} = \frac{1}{10} \Rightarrow w = \frac{1 \times 40}{10} = 4$$ Step 3: Find the missing white paint value for purple paint 60: $$\frac{w}{60} = \frac{1}{10} \Rightarrow w = \frac{1 \times 60}{10} = 6$$ **Final answers:** - First table missing values: Red paint 9, 12; White paint 24 - Second table missing values: White paint 10, 4, 6; Purple paint 10 These values maintain the constant ratios in each table.