Practical problems and quadratic equations of one variable 1. To make a product, the original cost price of each product is 500 yuan, and the sales price is 625 yuan. According to the market forecast, the sales price of the product will decrease by 20% in the first month, and increase by 6% in the second month. In order to make the sales profit after two months be the same as the original sales profit, what percentage of the average monthly cost price of the product should be reduced? 2. When a shopping mall sells a certain commodity, the purchase price of each product is 2500 yuan. When the sales price is 2900 yuan, it can sell 8 units per day on average. When the sales price is reduced by 50 yuan, it can sell 4 more units per day on average. If the shopping mall wants to make the sales profit of this product reach 5000 yuan per day on average, how much should the price of each product be

Practical problems and quadratic equations of one variable 1. To make a product, the original cost price of each product is 500 yuan, and the sales price is 625 yuan. According to the market forecast, the sales price of the product will decrease by 20% in the first month, and increase by 6% in the second month. In order to make the sales profit after two months be the same as the original sales profit, what percentage of the average monthly cost price of the product should be reduced? 2. When a shopping mall sells a certain commodity, the purchase price of each product is 2500 yuan. When the sales price is 2900 yuan, it can sell 8 units per day on average. When the sales price is reduced by 50 yuan, it can sell 4 more units per day on average. If the shopping mall wants to make the sales profit of this product reach 5000 yuan per day on average, how much should the price of each product be

1. To make a product, the original cost price of each product is 500 yuan, and the sales price is 625 yuan. According to the market forecast, the sales price of the product will decrease by 20% in the first month, and increase by 6% in the second month. In order to make the sales profit after two months be the same as the original sales profit, what percentage of the average monthly cost price of the product should be reduced?
The selling price in the first month is 500, and that in the second month is 500 × 106% = 530
If the cost price is X after 2 months, then 530-x = 625-500, so x = 405
Let the percentage of monthly decrease be y, then [500 (1-y)] (1-y) = 405
Y = 10%
2. When a shopping mall sells a certain commodity, the purchase price of each product is 2500 yuan. When the sales price is 2900 yuan, it can sell 8 units per day on average. When the sales price is reduced by 50 yuan, it can sell 4 more units per day on average. If the shopping mall wants to make the sales profit of this product reach 5000 yuan per day on average, how much should the price of each product be
Set a price reduction of X Yuan
[2900-2500-X][8+X/50*4]=5000
X^2-300X+22500=0
[X-150]^2=0
X=150
The price of this product should be 2900-150 = 2750 yuan

How to solve practical problems with quadratic equation of one variable

First of all, we should choose the unknown set element (that is, we should choose an unknown quantity as x). When we choose the unknown, we should consider making the equation as simple and easy to solve as possible. Then we need to find the quantitative relationship, that is, we should use X and known quantity to express the unknown quantity in the question as much as possible (it is suggested to analyze it in a list on the draft paper), It is to find out the quantity that can be expressed in two forms (that is, the quantity that can be expressed in two formulas, the total distance in the general distance problem and the total workload in the work efficiency problem) and then connect the two formulas to form the equation with an equal sign. Finally, solve the equation and answer it (pay attention to the mistakes in the process of solving the equation, and the points will be deducted for solving the wrong equation)

Practical problems of quadratic equation of one variable
In order to protect the ecological balance and green the environment, the state strongly encourages "returning farmland to forest and grass". The compensation policy is shown in table (1). A farmer contracted a hillside to plant trees and grass, and the state's compensation is shown in table (2)?
And the second table of the farmers received from the township government that year planting trees and grass Mu compensation notice to complete
Table 1
Plant trees and grass
Supplementary grain 150kg 100kg
200 yuan, 150 yuan
Table 2
Planting trees and grass to supplement food and money
30 mu 4000 kg 5500 yuan
Table 2 should be like this, there is no 5500 yuan
Table 2
Planting trees and grass to supplement food and money
30 mu, 4000 kg

If a mu of trees is planted, 30-a mu of grass is planted
According to the meaning of the title
150a+100（30-a）=4000
50a=4000-3000
50a=1000
A = 20 mu
Planting grass 30-20 = 10 mu
The subsidy for planting trees is 200x20 = 4000 yuan
150 x 10 = 1500 yuan for planting grass
Table 2: 4000 + 1500 = 5500 yuan
This problem can also be solved by binary linear equations
There are x Mu trees and Y Mu grass
x+y=30
150x+100y=4000
The result is the same

Ninth grade practical problems and one variable quadratic equation, as long as the equation is good
The cost price of a commodity is 200 yuan per piece, and the selling price is 50% higher than the cost price. Due to the poor market, those who sell it twice in a row can still earn 43 yuan per piece. If the discount is the same for two times, how much discount do you give each time?

200*（1+50%）x^2=200+43