Systematic Treatise on Arithmetic: Scroll 1

Page 11

Two hundred thirty-six piculs of cargo; the boat fare is debated based on the distance of the journey.

Ninety-five piculs are calculated at six cents; eighty-five piculs are paid back at four cents.

There are also fifty-six piculs of cargo; two cents and five mills are calculated first.

Simply because the boat grounded in the shallows, the boat price was contested, and two taels, five mace, and two cents were added.

May I ask the brilliant and capable scholars: how much should each person be assigned so they are free from distress?

Explanation: Suppose there are three people—Zhao three, Qian three, and Sun three These are the three most common Chinese surnames, used here as placeholders like "Person A, B, and C"—whose cargo totals two hundred thirty-six piculs dan (担): a unit of weight, also called a picul, approximately 60kg. They hire one boat. Originally, because the distances of their journeys were unequal, the shipping costs differed.

Within this group:
1. Zhao’s six cargo is ninety-five piculs. The unloading point is very eighty This likely refers to a distance of 80 li far. Each picul costs six cents five 0.065 taels in boat fare.
2. The second person's cargo is eighty-five piculs. The unloading point is quite near. Each picul costs four cents 0 0.04 taels in boat fare.
3. Sun’s cargo is fifty-six piculs. The journey is even nearer. Each picul costs two cents and five mills 0.025 taels in boat fare.

After these amounts were paid in full, the boat grounded in the shallows mid-journey boqian (剥淺): the process of unloading cargo into smaller barges to lighten a ship so it can pass through shallow water. An additional two taels, five mace, and two cents 2.52 taels must be paid. This cost should be apportioned among them based on their original fare ratios. How much does each person owe?