1. **State the problem:** We want to find how many moving boxes of dimensions 620 mm x 300 mm x 330 mm can fit inside a van with internal dimensions 2.50 m (length) x 1.26 m (width) x 1.22 m (height). 2. **Convert all dimensions to the same units:** - Box dimensions: 620 mm = 0.62 m, 300 mm = 0.30 m, 330 mm = 0.33 m - Van dimensions are already in meters. 3. **Calculate the volume of one box and the volume of the van:** $$\text{Volume of box} = 0.62 \times 0.30 \times 0.33 = 0.06138 \text{ m}^3$$ $$\text{Volume of van} = 2.50 \times 1.26 \times 1.22 = 3.8475 \text{ m}^3$$ 4. **Calculate the maximum number of boxes by volume:** $$\frac{3.8475}{0.06138} \approx 62.68$$ So, by volume alone, about 62 boxes could fit. 5. **Check fitting by dimensions (length, width, height):** We need to see how many boxes fit along each dimension. Since boxes can be oriented differently, we try all permutations of box dimensions to maximize count. Possible box dimension permutations (length x width x height): - 0.62 x 0.30 x 0.33 - 0.62 x 0.33 x 0.30 - 0.30 x 0.62 x 0.33 - 0.30 x 0.33 x 0.62 - 0.33 x 0.62 x 0.30 - 0.33 x 0.30 x 0.62 Calculate how many boxes fit along each van dimension for each permutation by integer division: For example, for 0.62 x 0.30 x 0.33: - Along length: $\left\lfloor \frac{2.50}{0.62} \right\rfloor = 4$ - Along width: $\left\lfloor \frac{1.26}{0.30} \right\rfloor = 4$ - Along height: $\left\lfloor \frac{1.22}{0.33} \right\rfloor = 3$ Total boxes = $4 \times 4 \times 3 = 48$ Calculate similarly for all permutations: - 0.62 x 0.33 x 0.30: $\lfloor 2.50/0.62 \rfloor=4$, $\lfloor 1.26/0.33 \rfloor=3$, $\lfloor 1.22/0.30 \rfloor=4$; total $4 \times 3 \times 4=48$ - 0.30 x 0.62 x 0.33: $\lfloor 2.50/0.30 \rfloor=8$, $\lfloor 1.26/0.62 \rfloor=2$, $\lfloor 1.22/0.33 \rfloor=3$; total $8 \times 2 \times 3=48$ - 0.30 x 0.33 x 0.62: $\lfloor 2.50/0.30 \rfloor=8$, $\lfloor 1.26/0.33 \rfloor=3$, $\lfloor 1.22/0.62 \rfloor=1$; total $8 \times 3 \times 1=24$ - 0.33 x 0.62 x 0.30: $\lfloor 2.50/0.33 \rfloor=7$, $\lfloor 1.26/0.62 \rfloor=2$, $\lfloor 1.22/0.30 \rfloor=4$; total $7 \times 2 \times 4=56$ - 0.33 x 0.30 x 0.62: $\lfloor 2.50/0.33 \rfloor=7$, $\lfloor 1.26/0.30 \rfloor=4$, $\lfloor 1.22/0.62 \rfloor=1$; total $7 \times 4 \times 1=28$ 6. **Find the maximum number of boxes that fit:** The maximum is 56 boxes with the orientation 0.33 m (length) x 0.62 m (width) x 0.30 m (height). **Final answer:** $$\boxed{56}$$ So, a maximum of 56 boxes can fit inside the van when arranged optimally.