1. **State the problem:** We want to find how many boxes of size 29 inches by 20 inches by 15 inches 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 units:** - Pallet base: 40 inches by 48 inches - Box base: 29 inches by 20 inches - Maximum stack height: 15 feet = $15 \times 12 = 180$ inches 3. **Calculate how many boxes fit on the pallet base:** We can arrange boxes in two orientations on the pallet base: - Orientation A: box length 29" along pallet length 40", box width 20" along pallet width 48" - Orientation B: box length 20" along pallet length 40", box width 29" along pallet width 48" Calculate number of boxes per layer for each orientation: - Orientation A: - Along length: $\left\lfloor \frac{40}{29} \right\rfloor = 1$ - Along width: $\left\lfloor \frac{48}{20} \right\rfloor = 2$ - Total per layer: $1 \times 2 = 2$ - Orientation B: - Along length: $\left\lfloor \frac{40}{20} \right\rfloor = 2$ - Along width: $\left\lfloor \frac{48}{29} \right\rfloor = 1$ - Total per layer: $2 \times 1 = 2$ Both orientations fit 2 boxes per layer. 4. **Calculate how many layers can be stacked:** - Box height: 15 inches - Max stack height: 180 inches - Number of layers: $\left\lfloor \frac{180}{15} \right\rfloor = 12$ 5. **Calculate total number of boxes:** - Total boxes = boxes per layer $\times$ number of layers = $2 \times 12 = 24$ **Final answer:** You can fit **24** boxes of size 29 x 20 x 15 inches on a 40 x 48 inch pallet stacked 15 feet high.