1. **State the problem:** We need to find the weight of the larger pumpkin given that the smaller pumpkin weighs 3.2 pounds less than the larger one, and their combined weight is 17.4 pounds. 2. **Define variables:** Let $x$ be the weight of the larger pumpkin in pounds. 3. **Express the smaller pumpkin's weight:** Since the smaller pumpkin weighs 3.2 pounds less, its weight is $x - 3.2$. 4. **Write the equation for combined weight:** The total weight is the sum of both pumpkins: $$x + (x - 3.2) = 17.4$$ 5. **Simplify the equation:** $$2x - 3.2 = 17.4$$ 6. **Isolate $x$:** Add 3.2 to both sides: $$2x - \cancel{3.2} + 3.2 = 17.4 + 3.2$$ $$2x = 20.6$$ 7. **Solve for $x$ by dividing both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{20.6}{\cancel{2}}$$ $$x = 10.3$$ 8. **Interpret the result:** The larger pumpkin weighs **10.3 pounds**. **Final answer:** $$\boxed{10.3}$$