A few minutes later, a group of people from the competition class came to the restaurant happily, sat down together at a big table, picked up the menu and started ordering.

This restaurant is well-known, the taste is very good, and the price is higher than the canteen. Many students are here for the first time, but there is no need to be polite when the coach treats you.

Li Xuan picked up the menu and looked at it, and found that this store mainly sold set meals for two, and there were no separate dishes. The menu read:

"Pork trotters, chicken legs, add two vegetarian dishes, add soup, 41 yuan."

“Braised pork ribs, golden egg roll, two vegetarian dishes, plus soup, 44 yuan.”

“Pork trotters, braised pork, two vegetarian dishes, soup, 42 yuan.”

"Braised pork ribs, seafood, two vegetarian dishes, soup, 45 yuan."

"Golden egg roll, pig's feet, two vegetarian dishes, soup, 42 yuan."

…

There are dozens of dishes in total, and there are various combinations of double set meals with different prices, ranging from high to low, for guests to choose from.

Liang Zhihui had been silent on the road, but when he looked at the menu, he suddenly frowned and said, "Do you think it's weird?"

What was going on? Everyone turned to Liang Zhihui, confused.

Liang Zhihui said seriously: "Look at the menu, the price of the set meal is clearly stated, but the price of each specific dish is unknown. I want to find the unit price of a pig's trotter. Let's set the price of pig's trotter as x and establish a linear equation system.

, I feel like I have no idea at all. Is there something wrong with the price of this package? Did I make a miscalculation?"

Everyone was stunned for a moment, Liang Zhihui kept saying one thing after another, ordered a meal and returned the equation with no solution. It was so serious, so funny.

After hearing this, Yan Pengfei couldn't help complaining and said: "It's so tiring to be with you academic masters. Let's just have a meal and stop thinking about math problems."

When Li Xuan heard what Liang Zhihui said, he was stunned for a moment, silently looked at the menu, did some mental calculations, and nodded: "Liang Zhihui is right. There is no solution for asking for the unit price of this set meal."

Xu Lingchu heard this and stared at the menu, feeling stunned.

Li Xuan just looked at the menu and calculated in his head that the linear equations had no solution. The key was that he didn't need to write. This was a bit incredible.

She could also calculate the unit price of pig's feet by writing, but mental calculation was impossible. She couldn't figure out how Li Xuan calculated it, and the speed was too fast. Because she couldn't figure it out, her eyes when she looked at Li Xuan were filled with admiration unconsciously.

Because both Li Xuan and Liang Zhihui said so, everyone looked at the menu and began to do mental calculations silently.

Lin Xuerui just nodded and smiled, turning to Li Xuan: "Classmate Li Xuan, your mental arithmetic is very strong. In fact, whether the equation has a solution can be judged simply like this. If there are three unknowns, the three equations can find a finite solution or

There is no solution. If there are only two equations less than the number of unknowns, it is an infinite solution. The calculation is a little more complicated. Either elementary mathematics elimination method is used to calculate it, or knowledge about determinants is required. Li Xuan, how did you calculate it? Have you learned it?

Linear algebra?”

Li Xuan nodded: "Coach, I replaced the constant term coefficient with one column of the coefficients of the linear equation system to get the determinant. Because the determinant is not 0, I judge that the equation has no solution."

Lin Xuerui sighed for a while. She was surprised at Li Xuan's learning progress and laughed: "You have learned more knowledge than many college students."

Liang Zhihui also widened his eyes and looked at Li Xuan. He used the elimination method to calculate mentally, step by step. In fact, it took him a long time to reach this conclusion, but Li Xuan calculated it in one step?

What kind of computing power is this?

Li Xuan could only say that he couldn't do it before, but because his mental arithmetic ability has greatly improved now, he can do very complex calculations mentally.

The other students looked confused and looked at Li Xuan in shock. They had no idea what a determinant was. After all, this solution was something that could only be mastered after in-depth study of linear algebra in college.

Yan Pengfei was confused after hearing this: "Coach, what is a determinant?"

Lin Xuerui explained: "The determinant is a general method that can solve a system of linear equations. There is a Clem's law, which gives a more general method for the existence and uniqueness of the solution of a system of linear equations. Of course, there are many systems of equations.

If so, the amount of calculation will be huge. Whether the equation has a solution can be simply judged according to the method Li Xuan just said."

The students were confused when they heard it.

Lin Xuerui smiled and said: "What is Clem's law? Don't be intimidated by the strange term. To put it simply, Clem's law is to find out whether two straight lines are different and intersect at a point in plane analytic geometry.

problem."

Yan Pengfei was annoyed by the incomprehensible terms in mathematics and made the mathematics more and more complicated. He couldn't help but said: "Coach, this is a very simple problem of solving whether a system of linear equations has a solution. There is no need to make it so complicated. Junior high school students can do it."

Let’s solve a system of linear equations.”

"You are right, the elimination method is a good method." Lin Xuerui showed a smile on her face, "But in fact, the method you learned in junior high school for solving linear equations is the original source of the determinant.

Solving systems of linear equations was later extended to solving systems of higher-order equations.”

"Determinants can be extended to n vectors in n-dimensional Euclidean space, and even functions are useful. Mathematics is all common. When you learn advanced mathematics, many of the knowledge you have learned will be connected."

"It doesn't matter if you don't understand. There is an elective textbook in high school that contains knowledge about determinants. When you get to college, many majors will also learn linear algebra. You will understand it then. Now you can do the calculations and use the elimination method you learned in junior high school.

Let’s see if we can calculate the unit price of pig’s feet. The time limit is two minutes.”

The coach said this, and everyone began to calculate silently.

Xu Lingchu hesitated to speak. She really wanted to say forget it and order the food first. She was almost starving to death, but seeing that everyone was meditating, she was too embarrassed to say it.

Yan Pengfei just happened to bring a pen, and he started doing calculations in the restaurant's menu book: "I calculated, the price of each dish is unknown, only the total price of the set meal is known, it seems that the linear equation system has too many unknowns, right?"

Jiang Shu looked at Yan Pengfei and said, "Idiot, just include the set meal related to pig's feet. Moreover, the set meal includes two vegetarian dishes and soup. You can set the total price of vegetarian dishes and soup to an unknown quantity.

In this way, there is one less unknown quantity. The process of calculating the price of pig's feet and solving a system of linear linear equations is much simpler, and even junior high school students can calculate it."

Many students came over to watch Yan Pengfei's calculations. Mental calculations were too difficult, but calculations on paper were easier.

Yan Pengfei listed the package prices related to pig's feet on the paper.

"Pork trotters, chicken legs, add two vegetarian dishes, add soup, 41 yuan."

"Pork trotters, braised pork, add two vegetarian dishes, add soup, 42 yuan."

"Pork trotters, golden egg roll, add two vegetarian dishes, add soup, 42 yuan."

"Braised pork, golden egg roll, add two vegetarian dishes, add soup, 43 yuan."

"Chicken legs, golden egg roll, add two vegetarian dishes, add soup, 43 yuan."

"..."

Simultaneous equations, elimination, Yan Pengfei discovered that there are two unit price possibilities for pig's feet in different combinations of equations.

"It seems so, the system of linear equations has no solution."

Now it is confirmed that there is really no solution.

When the boss was called, Yan Pengfei became very rude and took the lead and said: "Boss, what the hell? Can you tell me why there are two results when you calculate the price of pig's feet? Is it 15 yuan or 16 yuan, you give

Is there a specific value?"

The boss came over and didn’t understand at first. After listening to the explanations from the students, he suddenly understood and explained with a smile: “Classmates, this is a promotional method. Let me explain the reason. After running the store for a while, I found that the egg rolls are very good.

It is difficult to sell pig's feet, but our store has a lot of pig's feet. In order to sell more pig's feet, we bundled pig's feet with golden egg rolls and lowered the price of the set meal to attract customers.

Yan Pengfei understood, "Boss, are you saying that some packages are discounted and some packages are not discounted?"

The boss nodded and said: "Yes. Doing business requires careful budgeting. Customers can't see the price of pig's feet, but they can also tell which set meal is cheaper from the price. This will attract customers to order... Students, in short, different set meals

The discount coefficient is different, and mathematics cannot be viewed with static thinking."

Yan Pengfei: "..."

Li Xuan: "..."

Other students: “…”

The boss smiled and asked again: "Students, do you have any other questions?"

Yan Pengfei was scared and found that there was something in his boss's head. He didn't dare to question it and shook his head: "No..."

The students sitting aside looked confused and even a little unbelievable when they heard the boss say this.

"I wonder, are all store owners so good at math these days?"

"Don't make trouble, this is just a discount and promotion issue and has little to do with pure mathematics."

"If you are good at mathematics, many people work in insurance. Actuarial science in insurance also requires mathematics ability."

"I heard that the small employees who run errands on Wall Street are all top international Mathematical Olympiad experts. They don't know math and don't have the ability to do finance."

"Restaurant, insurance, finance... they all have a bad reputation. When you say that, I feel so worried. I suddenly don't want to participate in the math competition."

…

At this time, Li Xuan picked up the menu, glanced at it, and suddenly discovered something.

"Pork trotters, chicken legs, add two vegetarian dishes, add soup, 41 yuan."

"Pork trotters, braised pork, add two vegetarian dishes, add soup, 42 yuan."

"Pork trotters, golden egg roll, add two vegetarian dishes, add soup, 42 yuan."

According to the information provided by the boss, Li Xuan suddenly said: "Boss, in addition to golden egg rolls, your chicken legs are very popular? I see that the prices of pig feet and chicken legs have also been reduced.

Promotion. Hmm... after all, braised pork is cheaper than other meats, but pork trotters and braised pork are not on sale together. Does this mean that braised pork is not easy to sell? Pork trotters are not easy to sell. This pig's trotters and braised pork are not sold together.

The meat set meal means giving up treatment. Don’t you want customers to order it? It’s the boss. Your store doesn’t buy much braised pork..."

The boss was stunned and looked at Li Xuan, a little surprised.

He said that golden egg rolls are easy to sell, but pig's feet are not. From this information alone, Li Xuan just looked at the prices on the menu and immediately inferred that chicken legs are also easy to sell, and there may not be many in the braised pork shop. It can be seen that

The mathematical operation ability is quite strong.

In other words, he is a master of reasoning.

The boss likes children who are good at math very much and nods appreciatively: "Classmate, your math skills are very good. I'm going to treat you to lunch today. Just this time, it's free."
Chapter completed!