Discount sales is one of the problems solved by linear equation of one variable. We have talked about the concepts of discount, cost price, marked price, selling price, profit, profit rate and profit. So, what is the relationship between these concepts? This is the mathematical formula we are going to talk about today, which is often used in discounting profit and loss problem.

Learning mathematical concepts, we focus on understanding. So what is a formula?

In my opinion, the so-called formula is a mathematical relationship, and formulas are used to explain the relationship between mathematical concepts. In this relationship, concepts complement each other, and no one can do without anyone. Once this relationship is broken, the formula does not exist.

So the relationship in mathematics is very important. It can be said that the relationship runs through the whole mathematics learning career. It can also be said that the formula is the expression of mathematical relations!

Well, after the formula is understood, let's talk about what formulas we need to master in discount sales.

Before I talk about formulas in detail, I will divide them into two categories: one is the basic formula, and the other is the deformation formula. So what is the basic formula? What is the deformation formula? What is the relationship between the basic formula and the deformation formula?

Basic formula: it is the most important formula in mathematics and the most important way to solve problems in mathematics. Invariance means the basic formula. In other words, no matter how to change it, it is all around the basic formula, and the ultimate goal is to apply the basic formula. For example, the area formula of triangle: triangle area = base x height ÷ 2, which is a basic formula. In the process of solving problems, no matter how to find the bottom, no matter what the bottom has to do with it, no matter how to find the height, no matter what the height has to do with it, the ultimate goal is to go for the basic formula of triangle area = bottom x height ÷ 2.

Deformation formula: the deformation formula evolved from the basic formula, but all other relations in the basic formula were written in, which is actually a simplified basic formula.

1. Relationship between profit and selling price, cost price (purchase price), marked price (original price) and discount:

Basic formula: profit = selling price-cost price

This formula is easy to understand. Profit is the money earned, the selling price, how much to sell, and the cost price is the purchase price of the goods. Therefore, profit is the money sold, MINUS the money bought, and naturally it is the money earned.

Deformation formula: profit = list price x discount-cost price:

This relationship is also easy to understand and close to life. Now merchants are willing to use discounts to promote sales. So the price becomes "list price x discount". As we know, the marked price, also called original price and fixed price, refers to the price that has not been sold in the store, and the actual transaction price is often a discount on this basis.

In fact, the formula "profit = list price x discount-cost price" evolved from "profit = selling price-cost price".

In short, Formula A and Formula B both express the meaning: "Money earned = money sold-money bought", which is Formula A.

2, the relationship between profit rate and profit, cost and price:

Basic formula: profit rate = (profit-cost price) x? 100%

This formula is easy to understand. The profit rate is the ratio of the money earned to the cost price. In other words, the profit rate is only related to "profit" and "cost price".

Deformation formula: profit rate = (selling price-cost price) ÷ cost price x? 100%

Or? Profit rate = (list price x discount-cost price) ÷ cost price x? 100%

……

In fact, no matter how it evolves, it is still the basic formula of that profit rate after simplification.

3. Sales price, cost price, profit, profit rate, price and discount

Basic formula: selling price = cost price+profit.

Selling price = cost price x (1+ profit rate)

This formula is easy to understand, that is, selling price, including buying price and money earned.

We should pay attention here, because profit or profit rate may be positive or negative, which means making money and negative means losing money. So the selling price may also be lower than the cost price.

Or: when there is no discount: selling price = list price.

This formula is easy to understand. In the case of no discount, the transaction price is equal to the unsold marked price in the store.

When discounting: selling price = list price x discount

Deformation formula: there are many. Substituting other relations of elements in the basic formula becomes the deformation formula. I won't give examples here.

At this point, we have completed the formulas involved in discount sales, including profit formula, profit rate formula and selling price formula, which are the master keys to solve the problem of sales.