1. **State the problem:** We have 11 ducks, each having either 8 or 9 ducklings. The total number of ducklings is 92. We need to find how many ducks had 8 ducklings. 2. **Define variables:** Let $x$ be the number of ducks with 8 ducklings, and $y$ be the number of ducks with 9 ducklings. 3. **Set up equations:** Since there are 11 ducks total, we have: $$x + y = 11$$ The total number of ducklings is 92, so: $$8x + 9y = 92$$ 4. **Solve the system:** From the first equation, express $y$ as: $$y = 11 - x$$ Substitute into the second equation: $$8x + 9(11 - x) = 92$$ Simplify: $$8x + 99 - 9x = 92$$ $$-x + 99 = 92$$ $$-x = 92 - 99$$ $$-x = -7$$ $$x = 7$$ 5. **Interpret the result:** The number of ducks with 8 ducklings is $7$. **Final answer:** 7 ducks had 8 ducklings.