The box is only 2 inches deep, so the watch cases must be oriented such that the 2-inch dimension corresponds to the height of the box. Thus, there will only be 1 layer of watch cases.
Now think about the other two dimensions. The length and width of the box are divisible by the length and width of the watch cases respectively, so orient the cases such that the side of length 4 lies along the 16-inch length of the box and the side of length 3 lies along the 12-inch width of the box.
| The number of cases that lie along the 16-inch length of the box |
| will be |
16 |
÷ |
4 |
= |
4 |
, and the number of cases that lie along the |
| width of the box will be |
12 |
÷ |
3 |
= |
4 |
. So the box is filled with 4 |
| rows of 4 cases stacked 1 deep for a total of |
4 |
× |
4 |
× |
1 |
= |
16 |
Since each case holds 1 watch, the box can hold 16 watches.
