Example 1 The shopping mall sells a batch of famous brand shirts, with an average of 20 shirts sold every day, each of which makes a profit in 40 yuan. In order to expand sales and increase profits, the mall decided to take appropriate price reduction measures. According to the survey, if the price of each shirt is reduced by 1 yuan, the mall can sell an average of two more shirts every day. If the mall wants to make a profit every day 1200 yuan, how much will the price of each shirt be reduced?

Solution: the price of each piece is reduced by X yuan, the profit of each piece is 40-X, and it can be sold by 20+2x every day. Then (40-x) (20+2x) = 1200, you will get x=20, x= 10.

That is, when the price of each commodity is reduced by 10 yuan and 20 yuan, the daily profit of the shopping mall can be 1200 yuan.

Example 2: After two price adjustments, a shopping mall adjusted the price of a commodity from the original 40 yuan to 32.4 yuan per piece.

(1). If the price reduction of the mall is the same twice, find this price reduction.

(2) According to the survey, every time the price of this commodity is reduced by 0.2 yuan, it can sell 10. If this commodity can sell 500 pieces per month, how many pieces can this commodity sell per month after two price adjustments?

Solution: (1) Let this price reduction rate be X.

Judging from the meaning of the question: 40( 1-X)2=32.4.

The solution is X=0. 1= 10%.

(2) Monthly sales = 500+(40-32.4) *10/0.2 = 880 pieces.

Answer: (1) The price reduction range is 10%.

(2) After these two price adjustments, the commodity can sell 880 pieces per month.