1. **State the problem:** Troop Beverly Hills sold small boxes of donut holes for $1.25 each and cider for $2.50 per gallon. They need to raise at least $100 to cover expenses. 2. **Define variables:** Let $x$ be the number of small boxes of donut holes sold. Let $y$ be the number of gallons of cider sold. 3. **Write the inequality:** The total money raised from donut holes and cider must be at least 100. This can be written as: $$1.25x + 2.50y \geq 100$$ 4. **Explain the inequality:** The left side represents the total money raised from selling $x$ boxes and $y$ gallons. The right side is the minimum amount needed. 5. **Graphing the inequality:** - The boundary line is: $$1.25x + 2.50y = 100$$ - To graph, find intercepts: - When $x=0$, solve for $y$: $$2.50y = 100 \Rightarrow y = \frac{100}{2.50} = 40$$ - When $y=0$, solve for $x$: $$1.25x = 100 \Rightarrow x = \frac{100}{1.25} = 80$$ 6. **Shade the region:** Since the inequality is $\geq$, shade the region above or on the line. **Final inequality:** $$1.25x + 2.50y \geq 100$$