First of all, let's review the relevant formulas of the profit problem:

Price-purchase price = profit;

Purchase price × profit rate = profit;

Profit rate = profit/purchase price × 100%= (selling price-purchase price)/purchase price ×100%;

List price = purchase price ×( 1+ as a percentage of the list price) (for example, if the purchase price is 100 yuan and the price is increased by 50%, the price will be =100× (1+50%) =150 yuan).

Note: the purchase price is also called cost; Sometimes the selling price is the marked price, and sometimes it is the marked price × discount.

Question 1:

How to solve the final profit and loss situation when two commodities with different purchase prices and the same selling price have the same profit and loss percentage?

Example: A store sells two different commodities at the price of 150 yuan, in which one gains 25% and the other loses 25%, then the profit and loss of the two commodities sold by the store is (a).

A. Loss of 20 yuan; B. Profitable 20 yuan; C. Loss of 50 yuan; Neither profit nor loss.

analyse

The thinking is clear. We must first calculate the respective purchase prices of two different commodities, then calculate their respective profits and losses, and then add up the profits of the two commodities to judge the total profits and losses. Formula selection: selling price-purchase price = purchase price × profit rate.

explain

(1) In the unfamiliar situation, the column equation is solved.

Let the purchase price of two pieces be x and y yuan respectively.

150-x=25%x, and the solution is x= 120.

Profit: 150- 120=30 yuan.

Y- 150=25%y, and the solution y=200.

Loss: 150-200=-50 yuan.

2 * * * Loss: 30+(-50)=-20 yuan.

If you are familiar with this kind of questions, you can do oral calculations directly without formulas.

Purchase price of profitable items = sales price ÷( 1+ profit percentage)

Buying price of loss = selling price ÷( 1- loss percentage)

You can calculate the profit and loss directly after you are familiar with it. This kind of questions are generally multiple-choice questions or fill-in-the-blank questions, so speed and accuracy are required.