1. **State the problem:** Alejandro sells tacos and burritos. He sold 43 tacos and wants to sell a total of 111 tacos and burritos combined. Each taco costs 4.50 and each burrito costs 7.25. He wants to make at least 670 in total sales. We need to find all possible numbers of burritos he must sell to meet these requirements. 2. **Define variables:** Let $b$ be the number of burritos sold. 3. **Write the constraints:** - Total tacos and burritos: $$43 + b \leq 111$$ - Total sales: $$4.50 \times 43 + 7.25 \times b \geq 670$$ 4. **Simplify the total tacos and burritos inequality:** $$b \leq 111 - 43$$ $$b \leq 68$$ 5. **Calculate the sales from tacos:** $$4.50 \times 43 = 193.5$$ 6. **Write the sales inequality for burritos:** $$193.5 + 7.25b \geq 670$$ 7. **Isolate $b$:** $$7.25b \geq 670 - 193.5$$ $$7.25b \geq 476.5$$ 8. **Divide both sides by 7.25:** $$b \geq \frac{476.5}{7.25}$$ $$b \geq \cancel{7.25} \frac{476.5}{\cancel{7.25}}$$ $$b \geq 65.72$$ 9. **Interpret the inequalities:** - Burritos sold must be at least 66 (since $b$ must be an integer and $b \geq 65.72$) - Burritos sold must be at most 68 10. **Final answer:** $$66 \leq b \leq 68$$ Alejandro must sell between 66 and 68 burritos inclusive to meet the requirements.