Chapter 189 Linear Equations in One Variable

Cheng Wanwan is decorating her new home.

She had already bought many bed sheets and duvet covers at the mall and put them in trunks. Now she asked Wu Huiniang and Cao Yingying to take them out and put them in each room.

This is linen, a material that many people in modern society like. It feels similar to coarse linen, but it is softer and more comfortable to sleep on.

The standard setup for everyone's room in the house is a bed, a wardrobe, and a table; you can make your own room for anything else you need.

Cheng Wanwan took some time to decorate her room. Instead of a bed, her room had a kang (a heated brick bed) that took up most of the space. She laid a cotton quilt on the kang, then a sheet on top, and lay down. It was extremely comfortable.

It wasn't that she was selfish, but rather that her children were all incredibly intelligent, and she dared not take out anything of dubious origin.

This is her room. Without her permission, no child would dare to enter, let alone lie down on her bed.

She also bought herself a latex pillow, put on a linen pillowcase, and it didn't look very nice, but once she slept on it, she realized how comfortable it was.

The walls of the room were made of adobe bricks, with visible straw stalks and yellow mud. If you scratched them with your hand, yellow mud would fall off, which really affected the visual experience.

Cheng Wanwan bought some thin, silky fabric from the mall and carefully hung it down from the ceiling, just like wallpaper.

The pink and white fabrics hung on the four walls, which greatly enhanced the light in the room.

She laid a tablecloth on the table in the room, bought an antique brown porcelain jar, and put a few wildflowers from her front door into the jar, instantly elevating the style of the entire room.

Cheng Wanwan let out a comfortable sigh. After being in Dahe Village for so long, she finally had her own private space and could finally get a good night's sleep.

From now on, their family's life will definitely get better and better.

She walked out of the room and closed the door, glancing around casually. The other rooms were all the same, except for Cao Yingying's room, which had an extra touch of color: a bunch of small purple flowers on the table.

Seeing Cheng Wanwan's gaze fall on the little flower, Cao Yingying said somewhat shyly, "I think this flower is quite pretty, and it would look even better in the room."

Cheng Wanwan laughed: "I also put a bouquet of flowers in my room. We really thought of the same thing."

She plans to buy some hardy flower seeds from the mall and scatter them along the courtyard wall. Then, the wall will be covered with all sorts of flowers. In spring and summer, she can sit in the courtyard drinking tea, surrounded by birdsong and fragrant flowers – that's true enjoyment of life!

Without hesitation, she immediately went into the yard.

As soon as I stepped outside, I bumped into Zhao Ergou, who was holding a piece of paper and looking thoughtful.

He helped Cheng Wanwan up and asked, "Mother, is my eldest cousin here?"

"I'm reading," Cheng Wanwan said casually. "What do you want with your older cousin?"

Zhao Ergou went inside and walked to the door of Cheng Zhao's room. The door was ajar, and he saw Cheng Zhao writing with his head down.

When his older cousin was studying hard, he didn't dare to disturb him, so he quietly slipped away.

Cheng Wanwan glanced at the thing he was holding, which was covered in traditional Chinese characters. She frowned and asked, "What is this?"

"After the abacus class, my older cousin started teaching me and Si Dan the 'Nine Chapters on the Mathematical Art.' There are some problems I really don't understand, so I came to ask him." Zhao Ergou folded the paper. "I'll ask my older cousin again when class starts tonight."

"etc!"

Cheng Wanwan took the paper from his hand.

The above is a math problem, probably taken from "Nine Chapters on the Mathematical Art," a book considered a culmination of ancient mathematics, containing many problems that are quite relevant to real life.

"A certain county has seven large villages and two small villages. One large village plus two small villages can accommodate 1,680 villagers, and two large villages plus one small village can accommodate 2,280 villagers. How many villagers can each of the large and small villages accommodate?"

Zhao Ergou was scratching his head so hard he was almost bald: "This question is so difficult. I've been thinking about it since yesterday, but I still can't figure it out."

He's quite proficient with the abacus now, but when he holds it, he doesn't know where to start; his mind is a complete mess.

While the two of them were talking, Cheng Zhao also came out at some point and said, "This question is like this..."

He studied it for a long time yesterday, found the direction to solve the problem, and calculated that the result was correct.

He explained carefully: "Let's assume all the villagers live in the big village, then..."

Cheng Wanwan listened from the side. It was a very simple linear equation in one variable, but she insisted on using the assumption method, going around in circles, which made everyone's head spin.

She saw that Zhao Ergou's confused expression grew deeper and deeper, and he was pulling his hair out.

She sighed; it seemed she was the only one who could do it.

“Zhao’er, I think there might be a simpler way,” she said. “Let’s change the assumption. Let’s say a small village can accommodate A villagers…”

Zhao Ergou, humbly asking, "What does 'A' mean?"

“This represents a number we don’t know yet. A small village is called a Jia, so 1,680 minus 2 Jia is the number of people a large village can accommodate.” Cheng Wanwan spoke slowly to make it easier for the two to understand. “According to the assumption, two 1,680 minus 2 Jia plus 1 Jia equals 2,280. Then we can calculate what Jia is.”

She reached out and took the calligraphy brush.

That's the downside of ancient times. Instead of Arabic numerals, they used traditional Chinese characters, which took a long time to write a single number. Seeing these uppercase numbers made it difficult to form an immediate intuition. You had to mentally convert them to 2 (1680 - 2甲) + 甲 = 2280, which made it much more intuitive and gave you the answer instantly.

She smiled and said, "A is three hundred and sixty."

Multiplication tables existed in ancient times as well. Zhao Ergou had already learned the simple multiplication table and could calculate it clearly, but very slowly.

He went through the process in his mind, his eyes widening in disbelief, and said, "Mom, you're so smart! I actually understood it! I know how to calculate it! It's so simple!"

Cheng Zhao also looked incredulous: "Second Aunt, how did you come up with this method?"

The teachers at Nanfu Academy hadn't covered this topic, but he had read some related books. They all used the assumption method or the counting rods to arrange and count. Regardless of the method, it was very slow, taking at least the time it takes to brew a cup of tea. But with Second Aunt's method, once the principle was understood, he could write down the answer in an instant when he encountered similar problems in the future.

Cheng Wanwan coughed and said, "Our family runs a business, and we have to calculate income and expenses every day. Gradually, we've developed our own methods."

"Hey, what are you guys talking about? I've been calling you for ages and you haven't answered." Shen Zheng came over. "Seriously? Why are you talking about arithmetic? It gives me a headache. I'm leaving!"

He took off running.

Cheng Zhao grabbed him by the back of his collar: "Brother Chen, come here, I'll tell you a way to solve arithmetic problems."

Shen Zheng was on the verge of tears: "The imperial examinations don't test this, I'm not going to study it."

"The imperial examinations just didn't emphasize arithmetic, not that they didn't test it. Every year, the last question on the exam was an arithmetic problem." Cheng Zhao pulled him into the room. "Sit down and listen carefully as I explain it to you. Er Gou, you come in too. Let's go through it again and record this problem-solving method."

Cheng Wanwan smiled and continued with her work.

Cao Yingying, who had been standing not far away, had an extremely complicated expression. From the first day she came to this family, she knew that this family was different from ordinary farmers.

But at this moment she clearly realized that the biggest reason why this place was different from other villagers was because of Aunt Zhao.

Aunt Zhao was literate, could do arithmetic, and was very gentle. She seemed to know everything and was not like an ordinary peasant woman at all. Instead, she seemed like a well-educated lady from a prominent family who had attended school.

I always felt that Aunt Zhao was not a simple person.