1. **State the problem:** There are 30 bikers in total. Some ride bicycles (1 person each), others ride tandems (2 people each). The total number of bicycles and tandems combined is 23. We need to find how many tandems were used. 2. **Define variables:** Let $x$ be the number of bicycles and $y$ be the number of tandems. 3. **Write equations:** - Total bikes and tandems: $$x + y = 23$$ - Total bikers: $$1 \cdot x + 2 \cdot y = 30$$ 4. **Solve the system:** From the first equation, $$x = 23 - y$$. Substitute into the second: $$1 \cdot (23 - y) + 2y = 30$$ Simplify: $$23 - y + 2y = 30$$ $$23 + y = 30$$ 5. **Isolate $y$:** $$y = 30 - 23$$ $$y = 7$$ 6. **Answer:** There are **7 tandems** used on the trip.