The warehouse at the edge of the market has one old balance, and it will take a pallet but not a single crate: the platform is too wide to hold one steady.
So when a delivery arrived as one large crate and several identical small ones, the storekeeper could not simply weigh them one at a time. He weighed them in groups instead, and wrote two lines in the book.
The large crate together with one small crate came to 42 kilograms. The large crate together with two small ones came to 59.
Look at what changed between the two weighings. The large crate was on the platform both times, so it cannot explain the difference. Only one extra small crate was added — and the reading went up by 17 kilograms. That is the weight of a small crate, and it was found without opening anything.
The rest follows in one step. If the large crate and one small crate are 42, and the small crate is 17, then the large crate is 25 kilograms.
The storekeeper does this so often that he has stopped thinking of it as arithmetic. He calls it taking the first weighing away from the second, and the phrase is exactly right: the load that appears in both measurements cancels, and what is left is the thing you wanted to know.