Chapter 28 Section 4 Profit and Loss Technique
Profit and loss technique is a method of building equations by transposing terms. The Equation Chapter of "Nine Chapters" says: "The loss is the gain, and the benefit is the loss." In today's words, the loss at one end of the equation is equivalent to the gain at the other end; the gain at one end of the equation is equivalent to the loss at the other end. .Sometimes it is a constant item of profit and loss, such as the second question in the Equation Chapter: "Today, there are seven packs of up-grain crops, one bucket of real crops, two packs of lower crops, and ten buckets of real crops; There are two packs of upper grain, and ten buckets of real grain. Ask the geometry of one pack of upper grain and lower grain?" The first equation is:
After profit and loss, it is transformed into:
Sometimes there are both constant items of profit and loss, and unknowns of profit and loss.For example, the fourth question: "Today, there are five packs of up grain, one bucket and one liter of lost grain, and seven packs of current grain; seven packs of up grain, two buckets and five liters of lost grain, five packs of current grain. Geometries?" The equation begins with:
After profit and loss, it is transformed into:
The profit and loss method also includes the current consolidated similar items.The 11th question is: "Today, there are two horses and one ox that cost more than 10,000, such as the price of half a horse; the price of one horse and two oxen is less than 10,000, such as the price of half a ox. What are the prices of ox and horse?" The first is:
After profit and loss, we get:
Sometimes there are both constant items of profit and loss, and unknowns of profit and loss.For example, the fourth question: "Today, there are five packs of up grain, one bucket and one liter of lost grain, and seven packs of current grain; seven packs of up grain, two buckets and five liters of lost grain, five packs of current grain. Geometries?" The equation begins with:
After profit and loss, it is transformed into:
The profit and loss method also includes the current consolidated similar items.The 11th question is: "Today, there are two horses and one ox that cost more than 10,000, such as the price of half a horse; the price of one horse and two oxen is less than 10,000, such as the price of half a ox. What are the prices of ox and horse?" The first is:
After profit and loss, we get: