In a Wisconsin dairy, the number six has special significance for the dairy workers. When they prepare
the cartons of milk for shipping, they put six cartons in a box, six boxes in a crate, six crates in a flat,
and six flats on a pallet.
6 cartons = 1 box
6 boxes = 1 crate
6 crates = 1 flat
6 flats = 1 pallet
So that they know how many more cartons of milk are needed to complete a pallet, the dairy workers
have developed a system for describing the status of a pallet at any point during the packing process.
Their notation is:
(# of flats)(# of crates)(# of boxes)(# of cartons)
For example, a 4312 is a partially filled pallet that has 4 flats, 3 crates, 1 box and 2 cartons on it. Using
this notation, 10000 is a completed, ready-to-ship pallet.
(a) While you were on a field trip to the dairy, you counted 321 cartons of milk that were ready to be
placed on a pallet. How would you represent that amount of cartons in the dairy's notation? Show
all your work.
(b) As you were walking out the door, you heard someone yell, \"I have a 2045 that needs filling!\" How
many milk cartons, in dairy notation, do they need to complete the pallet? Show all your work.