In the second category, the equation in the form of AX BX = C is used to solve the problems of "sum times" and "difference times" in real life. The key to solve this kind of problem is to find the equal relationship between the quantities in the problem and list the equations. When solving the equation, we can simplify it according to the law of multiplication and distribution, and then solve it with the prime number of the equation and substitute it into the problem for testing.
Difficult point analysis
How to find the equation of equal relation sequence
The key to solving practical problems with column equations is to correctly understand the meaning of the problem and find out the equal relationship between the quantities in the problem. How to find equivalence relation?
According to the common basic quantitative relations, the equations are listed.
For example, Party A and Party B process 300 pieces per hour * 25 pieces, and Party B processes 35 pieces per hour. How many hours can two people work together to finish?
Solution: Let two people work together for x hours.
According to the basic quantitative relationship of engineering problems:
Work efficiency × working hours = total workload.
The solution of the column equation: (25+35)×x=300
Grasp the key sentences in the topic and find the equation of equal relation series.
For example, a chemical fertilizer plant produces 2800 tons of chemical fertilizer this year, which is less than last year 100 tons. How many tons of chemical fertilizer were produced last year?
By analyzing the key sentence "This year's output is twice as low as last year100t", we can know that twice last year's output-100t = this year's output.
Solution: Suppose that X tons of chemical fertilizer were produced last year.
For the equation: 2x- 100=2800.
Solving the equation of equal relation sequence with line segment diagram.
For example, Nansha village has 1.20 hectares of vegetable planting land, of which the planting area of Chinese cabbage is three times that of vegetables. How many hectares are there to grow green vegetables and Chinese cabbage?
Solution: Suppose that the area for planting green vegetables is x hectares and the area for planting Chinese cabbage is 3x hectares.
Draw a line chart:
X hectares
Planting area of green vegetables
3 hectares ***300 hectares
Planting area of Chinese cabbage
It is not difficult to find the equivalence relationship from the figure: the area planted with green vegetables+the area planted with Chinese cabbage = the total area.
Equation: x+3x=300
List equations according to related formulas or concepts.
For example, put a 18m fence around a rectangular vegetable field. It is known that the vegetable field is 5 meters long and how many meters wide?
Solution: Let the width be x decimeters. According to the formula "perimeter of rectangle = (length+width) ×2", the equation is: (5+x)×2= 18.