1. A clothing store sells 50 yuan underwear from 30 yuan at an average price of 300 pieces per month. After the trial sale, it is found that the price of each underwear will increase by 10 yuan, and its sales will decrease by 10. In order to achieve a daily sales profit of 8700 yuan, if you are a seller, how would you arrange the purchase?

Solution: If the price of 10a is increased on the basis of 59 yuan, 10a will be sold less.

According to the meaning of the question

(50+ 10a-30)×(300- 10a)= 8700

(20+ 10a)×(30-a)=870

(a+2)(a-30)=-87

Answer? -28a+27=0

(a- 1)(a-27)=0

A= 1 or a=27

When a= 1, the price increases by 10 yuan, and 300- 10× 1=290 pieces are sold.

When a=27, the price will increase by 27× 10=270 yuan, and 300- 10×27=30 pieces will be sold (this price is unrealistic).

Belonging to theoretical calculation

2. A company produces a certain commodity. The cost of each product is 3 yuan and the price is 4 yuan. The annual sales volume is 654.38+ten thousand pieces. In order to cope with the global economic crisis in 2009, the company is going to spend some money on advertising. According to experience, the annual advertising investment is X (10,000 yuan), and the product sales will be Y times of the original, while

y=-x？ /10+7/10x+7/10IF: annual profit = total sales-cost-advertising fee.

(1) Can the company's annual profit reach 1.5 million? Can it reach 1.6 million?

(2) Can the company's annual profit reach 6.5438+0.7 million? If yes, please calculate how much the advertisement should be at this time. If not; Please provide a justification for the answer.

Solution: Suppose the annual profit is one million yuan,

a=4× 10y-3× 10y-x

=40y-30y-x= 10y-x

= 10×(-x？ / 10+7/ 10x+7/ 10)-x

=-x？ +7x+7x

=-x？ +6x+7

When a= 15

-x？ +6x+7= 15

x？ -6x+8=0

(x-2)(x-4)=0

X=2 or 4

When the advertising fee is 20,000 yuan or 40,000 yuan, the profit will reach 6.5438+0.5 million yuan.

When a= 16

-x？ +6x+7= 16

x？ -6x+9=0

(x-3)？ =0

x 1=x2=3

When the advertising fee is 30,000 yuan, the profit will reach 6.5438+0.6 million yuan.

When a= 17

-x？ +6x+7= 17

x？ -6x+ 10=0

Discriminant = 36-40 =-4

So the profit can't reach 1.7 million.

3. Several people in an interest group send each other a greeting card during the New Year. It is known that the whole group has issued a 132 card. Please find out the number of people in this group.

Solution: Suppose there is a person in this group.

According to the meaning of the question

a×(a- 1)= 132

Answer? -a- 132=0

(a- 12)(a+ 1 1)= 0

A= 12 or a=- 1 1 (omitted)

There were 12 people, and each person received12-1=11card.