When a shopping mall sells a certain commodity, it will increase the purchase price of the commodity by 25% as the sales price in the first month, making a total profit of 6000 yuan. In the second month, the shopping mall will carry out promotional activities, and increase the purchase price of the commodity by 10% as the sales price. In the second month, it will increase 80 pieces compared with the first month, and make a profit of 400 yuan more than the first month? How many items are sold in the second month?

When a shopping mall sells a certain commodity, it will increase the purchase price of the commodity by 25% as the sales price in the first month, making a total profit of 6000 yuan. In the second month, the shopping mall will carry out promotional activities, and increase the purchase price of the commodity by 10% as the sales price. In the second month, it will increase 80 pieces compared with the first month, and make a profit of 400 yuan more than the first month? How many items are sold in the second month?

Let the purchase price of this commodity be x yuan. According to the meaning of the question, we can get: 600025% · x = 6000 + 40010% · x-80. The solution is: x = 500. It is tested that x = 500 is the root of the original equation.. 6000 + 40010% · x = 6400500 × 10% = 128 (pieces). Answer: the purchase price of this commodity is 500 yuan, and 128 pieces are sold in the second month

Two
1. For a travel club, the unit price of a group of 30 people is 800 yuan per person. For more than 30 people, the unit price will be reduced by 10 yuan per person for each additional person in the group. When the number of people in a group is, can the travel agency get the maximum profit?
2. If a store buys a batch of goods with a unit price of 8 yuan and sells them at 10 yuan per piece, it can sell 100 pieces per day. After investigation, it is found that when the unit price of this kind of goods increases by 1 yuan, the sales volume will decrease by 10 pieces correspondingly. What is the maximum profit when the sales price is set?
(let's set the price down or up. Quadratic function)

1. The number of tour groups is x, and the maximum profit of travel agency is y yuan
Y=[800-10（X-30）]X=-10X^2+1100X
Because - B / 2A = - 1100 / 2 * (- 10) = 55 (4ac-b ^ 2) / 4A = - 1100 ^ 2 / [4 * (- 10)] = 30250
A: the number of tour groups is 55, and the maximum profit the travel agency can make is 30250 yuan
2. Suppose the selling price is increased by X Yuan and the maximum profit is y yuan
y=(100-10x)(x+10-8)=-10x^2+80x+200
Because - B / 2A = - 80 / 2 * (- 10) = 4 (4ac-b ^ 2) / 4A = [4 * (- 10) * 200-80 ^ 2] / [4 * (- 10)] = 360
So the selling price is 4 + 10 = 14 yuan
A: if the selling price is set at 14 yuan, the maximum profit will be 360 yuan

1. It is reported that the resources of crop straw in China are huge, but the rational utilization is very limited. The utilization rate in 2006 is only 30%. Assuming that the total amount of straw produced in our province every year remains unchanged, but the growth rate of rational utilization is the same, if the utilization rate in 2008 is increased to 60%, the annual growth rate? Root 2 is taken as 1.41
formulation of equation
2. Xiaodao A is 40 nautical miles to the west of wharf B. at 9 a.m., a fishing boat and a yacht set out at the same time. The fishing boat sailed due north from B at the speed of 20 nautical miles per hour, and the yacht sailed from a to B at the speed of 25 nautical miles per hour, After a period of time, the fishing boat broke down and stopped at C to serve the signal. The yacht directly sailed to the fishing boat after receiving the signal at D. when did the yacht receive the signal at 11 a.m

(1) 0.3*(1+x)^2=0.6
1 + x = root 2 = 1.41
x=0.41
41% growth rate
(2) Set cruise ship x to receive signal
(40-25*（x-9）)^2+(20*（x-9）)^2=（25*（9-x）)^2
x=10
10 am