1. **State the problem:** Emily wants to buy turquoise stones priced at 4 or 6 each, spending no more than 30 total, and wants to give stones to at least 4 friends. 2. **Define variables:** Let $x$ be the number of 4-dollar stones and $y$ be the number of 6-dollar stones. 3. **Write the inequality for the budget:** $$4x + 6y \leq 30$$ 4. **Condition for friends:** Emily wants to give stones to at least 4 friends, so total stones must be at least 4: $$x + y \geq 4$$ 5. **Graphing constraints:** - $x$ (4-dollar stones) on horizontal axis from 0 to 7 - $y$ (6-dollar stones) on vertical axis from 0 to 6 6. **Rewrite budget inequality to express $y$ in terms of $x$ for graphing:** $$6y \leq 30 - 4x$$ $$y \leq \frac{30 - 4x}{6} = 5 - \frac{2x}{3}$$ 7. **Plot the line $y = 5 - \frac{2x}{3}$ and shade below it (budget constraint). Also plot the line $x + y = 4$ and shade above it (friends constraint). The feasible region is where both conditions hold. 8. **List three possible integer solutions $(x,y)$ satisfying both constraints:** - $(3,2)$: $4(3) + 6(2) = 12 + 12 = 24 \leq 30$ and $3 + 2 = 5 \geq 4$ - $(5,1)$: $4(5) + 6(1) = 20 + 6 = 26 \leq 30$ and $5 + 1 = 6 \geq 4$ - $(1,4)$: $4(1) + 6(4) = 4 + 24 = 28 \leq 30$ and $1 + 4 = 5 \geq 4$ Final answer: Possible solutions include $(3,2)$, $(5,1)$, and $(1,4)$.