Splitting a Bulk Order Into Equal Crates
A warehouse receives 1,872 identical parts packed in bulk. The crew must ship them in crates holding exactly 36 parts each, and every crate must be completely full before it leaves. The supervisor also wants 5 spare parts held back in the office for quality checks, so those must be removed from the shipping total first. A crew member estimates they will need about 50 crates. Before ordering crates, the supervisor asks for the exact crate count and a check that the arithmetic is right, since a miscount means either wasted crates or a partial shipment that gets rejected at the dock.
1. How many full crates can be shipped, and how many parts (if any) are left over after the 5 spare parts are set aside?
Read the worked answer
Set aside spares: 1,872 − 5 = 1,867 parts for shipping.
Divide: 1,867 ÷ 36.
- 36 × 50 = 1,800, remainder 67.
- 36 × 1 = 36, so 51 crates gives 1,836, remainder 31.
- 36 × 52 = 1,872, which is more than 1,867.
So 51 full crates with 31 parts left over. The leftover 31 parts cannot fill a 52nd crate, so they stay behind or are reworked.
Check: 51 × 36 = 1,836; 1,836 + 31 = 1,867. Correct.
2. The crew member's estimate of 50 crates is off. By how many crates does the true full-crate count differ from the estimate, and does the leftover change whether 50 crates could ever hold everything?
Read the worked answer
True full crates = 51; estimate = 50; difference = 1 crate.
Capacity of 50 crates: 50 × 36 = 1,800 parts. We have 1,867 to ship, so 50 crates fall short by 1,867 − 1,800 = 67 parts - more than one crate's worth (36), confirming at least 51 are needed.
The leftover of 31 parts does not rescue the estimate: even with 51 crates, 31 parts remain unshipped, and 50 crates leave 67 unshipped. So the estimate is short by exactly one full crate plus a partial, and 50 crates can never hold everything.