1. **Problem 2:** The heights of 2 poles are in a ratio of 9:5. The height of the shorter pole is 8 m. What is the height of the taller pole? 2. **Set up the proportion:** Let the height of the taller pole be $x$ meters. Since the ratio of heights is $9:5$, and the shorter pole corresponds to 5 parts, we write: $$\frac{9}{5} = \frac{x}{8}$$ 3. **Solve the proportion:** Cross-multiply: $$9 \times 8 = 5 \times x$$ $$72 = 5x$$ Divide both sides by 5: $$x = \frac{72}{5} = 14.4$$ 4. **Answer:** The height of the taller pole is $14.4$ meters. 5. **Problem 5:** A popular ratio of compounds of the chemicals nitrogen, phosphorus, and potassium in lawn fertilizer is 10:6:4. How much of each chemical is in the bag if the bag weighs 30L? 6. **Set up the problem:** Let the amounts of nitrogen, phosphorus, and potassium be $10k$, $6k$, and $4k$ liters respectively. The total weight is 30L, so: $$10k + 6k + 4k = 30$$ $$20k = 30$$ 7. **Solve for $k$:** $$k = \frac{30}{20} = 1.5$$ 8. **Find each amount:** - Nitrogen: $10k = 10 \times 1.5 = 15$ L - Phosphorus: $6k = 6 \times 1.5 = 9$ L - Potassium: $4k = 4 \times 1.5 = 6$ L 9. **Answer:** The bag contains 15 L nitrogen, 9 L phosphorus, and 6 L potassium.