1. **State the problem:** We are given that the total number of residents in two neighboring barangays is 3,200. We want to understand how to represent and solve problems involving totals. 2. **Set variables:** Let $x$ be the number of residents in the first barangay and $y$ be the number of residents in the second barangay. 3. **Write the equation:** Since the total number of residents is 3,200, we have the equation: $$x + y = 3200$$ 4. **Explain the equation:** This equation means that when you add the residents of the first barangay ($x$) and the second barangay ($y$), the sum is 3,200. 5. **Example solution:** If we know one barangay's population, we can find the other. For example, if the first barangay has 1,200 residents, then: $$x + y = 3200$$ $$1200 + y = 3200$$ 6. **Isolate $y$:** $$\cancel{1200} + y = 3200$$ $$y = 3200 - 1200$$ $$y = 2000$$ 7. **Interpretation:** The second barangay has 2,000 residents. This method can be used to find the population of one barangay if the other is known, or to set up problems involving totals.