1. **State the problem:** We want to find how many boxes of size 100 cm by 120 cm by 150 cm can fit on a pallet of size 40 inches by 48 inches, stacked up to 15 feet high. 2. **Convert all dimensions to the same unit:** - Pallet size: 40 inches by 48 inches - Stack height: 15 feet - Box size: 100 cm by 120 cm by 150 cm Convert pallet dimensions from inches to centimeters (1 inch = 2.54 cm): $$40 \times 2.54 = 101.6\text{ cm}$$ $$48 \times 2.54 = 121.92\text{ cm}$$ Convert stack height from feet to centimeters (1 foot = 30.48 cm): $$15 \times 30.48 = 457.2\text{ cm}$$ 3. **Determine how many boxes fit on the pallet surface:** We can place boxes in two orientations on the pallet surface: - Orientation A: box length 100 cm along pallet length 101.6 cm, box width 120 cm along pallet width 121.92 cm - Orientation B: box length 120 cm along pallet length 101.6 cm, box width 100 cm along pallet width 121.92 cm Calculate how many boxes fit in each orientation: - Orientation A: $$\text{boxes along length} = \left\lfloor \frac{101.6}{100} \right\rfloor = 1$$ $$\text{boxes along width} = \left\lfloor \frac{121.92}{120} \right\rfloor = 1$$ Total boxes on surface = $1 \times 1 = 1$ - Orientation B: $$\text{boxes along length} = \left\lfloor \frac{101.6}{120} \right\rfloor = 0$$ $$\text{boxes along width} = \left\lfloor \frac{121.92}{100} \right\rfloor = 1$$ Total boxes on surface = $0 \times 1 = 0$ So only Orientation A fits 1 box on the pallet surface. 4. **Determine how many boxes can be stacked vertically:** Box height = 150 cm Stack height = 457.2 cm $$\text{boxes stacked} = \left\lfloor \frac{457.2}{150} \right\rfloor = 3$$ 5. **Calculate total number of boxes:** $$\text{total boxes} = \text{boxes on surface} \times \text{boxes stacked} = 1 \times 3 = 3$$ **Final answer:** You can fit **3** boxes of size 100x120x150 cm on the pallet stacked 15 feet high.