1. **State the problem:** We are given a ratio of flour to water as 9:4 and need to find how much water corresponds to 36 cups of flour. 2. **Formula and rules:** The ratio means $ \frac{\text{flour}}{\text{water}} = \frac{9}{4} $. 3. **Set up the proportion:** Let $ w $ be the cups of water needed. Then: $$ \frac{9}{4} = \frac{36}{w} $$ 4. **Solve for $ w $:** Cross multiply: $$ 9 \times w = 4 \times 36 $$ $$ 9w = 144 $$ Divide both sides by 9: $$ w = \frac{144}{9} = 16 $$ 5. **Interpretation:** The restaurant should use 16 cups of water to maintain the ratio. **Final answer:** 16 cups of water.