1. **State the problem:** We have a lilac paint mixture where 40% is white paint, 20% is blue paint, and the rest is red paint. Given 4 cups of blue paint, find: a. Cups of white paint used b. Cups of red paint used c. Total cups of lilac paint in the batch 2. **Define variables and percentages:** Let total cups of lilac paint be $T$. White paint = 40% of $T$ = $0.40T$ Blue paint = 20% of $T$ = $0.20T$ Red paint = remaining percentage = $100\%-40\%-20\%=40\%$ of $T$ = $0.40T$ 3. **Use given information:** Blue paint amount is 4 cups, so: $$0.20T = 4$$ 4. **Solve for $T$:** $$T = \frac{4}{0.20}$$ $$T = \frac{4}{\cancel{0.20}} \times \frac{1}{\cancel{1}} = 20$$ So, total lilac paint $T = 20$ cups. 5. **Find cups of white paint:** $$\text{White paint} = 0.40 \times 20 = 8 \text{ cups}$$ 6. **Find cups of red paint:** $$\text{Red paint} = 0.40 \times 20 = 8 \text{ cups}$$ 7. **Summary of answers:** a. White paint = 8 cups b. Red paint = 8 cups c. Total lilac paint = 20 cups