1. **State the problem:** Sara is making 3 batches of chocolate chip cookies and 3 batches of oatmeal cookies. Each batch of chocolate chip cookies uses $2 \frac{1}{4}$ cups of flour. The total flour used for all six batches is $12 \frac{3}{4}$ cups. We need to find how many cups of flour are needed for each batch of oatmeal cookies. 2. **Write the known quantities and variables:** - Flour per chocolate chip batch: $2 \frac{1}{4} = \frac{9}{4}$ cups - Number of chocolate chip batches: 3 - Number of oatmeal batches: 3 - Total flour used: $12 \frac{3}{4} = \frac{51}{4}$ cups - Let $x$ = cups of flour per oatmeal batch 3. **Set up the equation:** $$3 \times \frac{9}{4} + 3x = \frac{51}{4}$$ 4. **Simplify the equation:** $$\frac{27}{4} + 3x = \frac{51}{4}$$ 5. **Isolate $3x$ by subtracting $\frac{27}{4}$ from both sides:** $$3x = \frac{51}{4} - \frac{27}{4}$$ $$3x = \frac{24}{4}$$ $$3x = 6$$ 6. **Divide both sides by 3 to solve for $x$:** $$x = \frac{6}{3}$$ $$x = 2$$ 7. **Interpret the result:** Each batch of oatmeal cookies requires 2 cups of flour. **Final answer:** $$\boxed{2}$$ cups of flour per oatmeal batch.