1. **Problem statement:** We need to find how many bags of fertilizer to buy so that the total weight of ammonium nitrate is at least 12 lb, phosphates at least 8 lb, and potash at least 11 lb. 2. **Given data:** - Each bag contains 7 lb ammonium nitrate, 4.6 lb phosphates, 3.8 lb potash. - Let $x$ be the number of bags. 3. **Set up inequalities:** $$7x \geq 12$$ $$4.6x \geq 8$$ $$3.8x \geq 11$$ 4. **Solve each inequality for $x$:** $$x \geq \frac{12}{7} \approx 1.714$$ $$x \geq \frac{8}{4.6} \approx 1.739$$ $$x \geq \frac{11}{3.8} \approx 2.895$$ 5. **Interpretation:** To satisfy all three conditions simultaneously, $x$ must be at least the maximum of these values: $$x \geq \max(1.714, 1.739, 2.895) = 2.895$$ 6. **Since $x$ must be an integer number of bags, round up:** $$x = 3$$ **Final answer:** The agency must purchase **3 bags** of fertilizer to meet the requirements.