A toy manufacturer produces action figures and packages them into small boxes. The distribution center then puts them in larger boxes to ship them to stores.

1.) Decide which box can ship the most action figures.
2.) How many action figures fit in the box?
3.) How can they be arranged to fit the maximum amount in the box?
Action figure box: 8"X4"X2"
Shipping Box A: 2ftX1ftX1 1/2ft
Shipping Box B: 2ftX2ftX3/4ft
Shipping Box C: 1ftX1ftX3ft
The volume of the toy box is 8x2x2+8x4x2+2x4x2=112 Using the same equation the volume of shipping box A is 1872, B is 2016, C is 2016. I drew out pictures of the boxes and I think I can get 72 action figures in each shipping container but I don't know how to figure that out using the volume.

To decide which box can ship the most action figures, you need to determine which box has the largest volume that can accommodate the action figures.

1.) Calculate the volume of each box:
- The volume of the action figure box is 8" x 4" x 2" = 64 cubic inches.
- The volume of shipping box A is 2 ft x 1 ft x 1.5 ft = 3 cubic feet = 5184 cubic inches.
- The volume of shipping box B is 2 ft x 2 ft x 0.75 ft = 3 cubic feet = 5184 cubic inches.
- The volume of shipping box C is 1 ft x 1 ft x 3 ft = 3 cubic feet = 5184 cubic inches.

2.) Divide the volume of each shipping box by the volume of the action figure box to find out how many action figures can fit in each box:
- Box A: 5184 cubic inches / 64 cubic inches = 81 action figures.
- Box B: 5184 cubic inches / 64 cubic inches = 81 action figures.
- Box C: 5184 cubic inches / 64 cubic inches = 81 action figures.

Therefore, all three shipping boxes can accommodate the same maximum number of 81 action figures.

3.) To figure out how the action figures can be arranged to fit the maximum amount in each box, you need to consider the dimensions of the action figure box and the orientation in which they can be packed efficiently. Based on the given dimensions of the action figure box (8" x 4" x 2"), we assume that the figures can be arranged in three rows with two figures in each row, resulting in a total of six figures per layer. The remaining depth allows for multiple layers to be stacked vertically:

- Box A: Since it has a height of 1.5 ft, which is taller than the others, you can stack the action figures vertically, maximizing the number in each box. Each layer would consist of six action figures, and you would have 81/6 = 13 layers. Thus, you can fit a total of 13 x 6 = 78 action figures in Box A.

- Box B: With a height of 0.75 ft, you can still stack the action figures vertically as in Box A. Similarly, each layer can hold six action figures, and you would have 81/6 = 13 layers. Therefore, Box B can also fit 13 x 6 = 78 action figures.

- Box C: As it has a height of 3 ft, the figures cannot be stacked vertically in this direction. However, you can arrange them in layers horizontally. With two action figures in each row and three rows per layer, you would have 2 x 3 = 6 action figures per layer. Thus, to fit 81 action figures, you would need 81/6 = 14 layers. Therefore, Box C can hold 14 x 6 = 84 action figures, which is the maximum capacity among the three boxes.

In conclusion, Box C can ship the most action figures with a capacity of 84, and the action figures in this box should be arranged in layers with two figures in each row and three rows per layer.