1. **State the problem:** We have two pumpkins. The larger pumpkin weighs $x$ pounds. The smaller pumpkin weighs 3.2 pounds less than the larger pumpkin, so its weight is $x - 3.2$ pounds. 2. **Write the equation for the combined weight:** The total weight of both pumpkins is 17.4 pounds. So, $$x + (x - 3.2) = 17.4$$ 3. **Simplify the equation:** $$x + x - 3.2 = 17.4$$ $$2x - 3.2 = 17.4$$ 4. **Isolate the variable term:** Add 3.2 to both sides: $$2x - 3.2 + 3.2 = 17.4 + 3.2$$ $$2x = 20.6$$ 5. **Solve for $x$ by dividing both sides by 2:** $$x = \frac{20.6}{2}$$ 6. **Show cancellation explicitly:** $$x = \frac{\cancel{20.6}}{\cancel{2}} = 10.3$$ 7. **Answer:** The larger pumpkin weighs **10.3 pounds**.