1. **State the problem:** Doug has already saved $1200 and wants to save a total of $2800. He saves $200 each week. We need to find how many weeks it will take for him to reach $2800. 2. **Set up the equation:** Let $w$ be the number of weeks needed. The total amount saved after $w$ weeks is the initial amount plus the weekly savings multiplied by $w$: $$1200 + 200w = 2800$$ 3. **Solve for $w$:** Subtract 1200 from both sides: $$\cancel{1200} + 200w - \cancel{1200} = 2800 - 1200$$ $$200w = 1600$$ Divide both sides by 200: $$\frac{200w}{\cancel{200}} = \frac{1600}{\cancel{200}}$$ $$w = 8$$ 4. **Interpretation:** It will take Doug 8 weeks to save the remaining amount to reach $2800. **Final answer:** $w = 8$ weeks.