1. **State the problem:** Leo is building a rectangular garden bed. Each side requires $2 \frac{3}{4}$ meters of wood per layer, and he plans $1 \frac{2}{3}$ layers in height. Each plank is $1.8$ meters long and costs $11.70$ each. We need to find how many planks he must buy and the total cost. 2. **Convert mixed numbers to improper fractions:** - $2 \frac{3}{4} = \frac{11}{4}$ meters per side per layer. - $1 \frac{2}{3} = \frac{5}{3}$ layers. 3. **Calculate total wood length per side:** $$\text{Length per side} = \frac{11}{4} \times \frac{5}{3} = \frac{55}{12} \approx 4.5833 \text{ meters}$$ 4. **Calculate total wood length for all four sides:** $$4 \times \frac{55}{12} = \frac{220}{12} = \frac{55}{3} \approx 18.3333 \text{ meters}$$ 5. **Calculate number of planks needed:** Each plank is $1.8$ meters long, so $$\text{Number of planks} = \frac{18.3333}{1.8} \approx 10.185$$ Since he cannot buy a fraction of a plank, he must buy $11$ planks. 6. **Calculate total cost:** $$11 \times 11.70 = 128.7$$ **Final answer:** Leo must buy **11 planks** and the total cost is **128.7**.