Uncle Wang bought a total of 14kg of 120 yuan 1kg black tea and 160 yuan 1kg green tea, sharing 2080 yuan: how many kg did he buy each of the two kinds of tea?

Uncle Wang bought a total of 14kg of 120 yuan 1kg black tea and 160 yuan 1kg green tea, sharing 2080 yuan: how many kg did he buy each of the two kinds of tea?

(160 × 14-2080) △ 160-120, = 160 △ 40, = 4 (kg), then green tea bought 14-4 = 10 (kg), answer: black tea bought 4 kg, green tea bought 10 kg

How to find the equivalent relationship in solving practical problems with equations in grade five of primary school

Unit 4 of this textbook (people's Education Society edition, grade 5) is simple equation. Students feel very difficult when they first learn equation, especially when they are writing equations to solve practical problems. I analyzed the reasons why these students can't write equations to solve practical problems, and found that the main reason is that they didn't master the method of finding the equivalent relationship, so they feel very difficult to write equations, In my opinion, the key to solving practical problems with equations is to find out the equal relationship between quantities. In my teaching, I used the method of "finding out the equal relationship between quantities in practical problems first, and then listing equations" to break through the difficulty of listing equations to solve practical problems. Only when the equal relationship between quantities is found out correctly, the listing equations can be regarded as the basis. I summarize the methods of finding the equal relationship into the following aspects
1、 Find the equivalent relationship from the result of the change of things
For example: (Textbook page 66, question 2) a total of 1428 tennis balls, each 5 loaded a tube, after loading, there are still 3 left, how many tennis balls in total? Guide students to analyze: with a total of minus loaded, is the rest. So the equivalent relationship is: a total of minus loaded equals the rest. Clear thinking, more methods. Most students can list three equations
Total - loaded = the rest
（1） 1428－5X=3
Finished + remaining = total
（2） 5X＋3=1428
All in all - the rest = finished
（3）1428－3=5X
Another example: there are 38 passengers on a bus, 12 people get off at the railway station, and some people come up. At this time, there are 54 passengers on the bus. How many people get on at the railway station?
Original number of people - number of people getting off + number of people getting on = number of people on hand
By analyzing the causes and results of the changes, we can get the same relationship
So we can set up the unknown number and set up the equation
38－12＋X=54
2、 Find equivalence in key sentences
For example: (example 1 on page 45) a football has 20 pieces of white leather, 4 pieces less than 2 times of black leather. How many pieces of black leather are there? Guide the students to analyze and learn to find the key sentence in the question: "seize the multiple to find the amount of two comparisons." the key sentence in the question is "white leather is 4 pieces less than 2 times of black leather." that is, the number of white leather is 20 pieces less than 2 times of black leather, The equivalent relation is found: black skin × 2 + 4 = 20
Xiao Ming is 24 years younger than his mother this year. His mother's age is just three times that of Xiao Ming. How old are Xiao Ming and his mother?
In this question, Xiao Ming is 24 years younger than his mother, which is based on his mother's age; mother's age is three times that of Xiao Ming, which is based on Xiao Ming's age. Students have doubts here; whose age is the standard, Whose age is unknown? I asked the students to use the method of "changing the standard" to determine who is more suitable for the standard quantity: Xiao Ming is 24 years younger than his mother. It can be said that his mother is 24 years older than Xiao Ming, and the difference remains unchanged
But it can't be said that Xiao Ming's age is three times of his mother's. it can only be said that Xiao Ming's age is one third of his mother's, and the multiple has changed. So it's more appropriate to use the "multiple ratio relationship" to find the standard quantity
Mother's age Xiaoming's age = 24
3X－X=24
3、 Find the equivalent relationship from the common quantitative relationship
Total price of chair + total price of table = total cost
For example: (question 5 on page 76) the school bought back 4 chairs and 2 tables. The price of chairs is 22 yuan and the total cost is 198 yuan. How much is the unit price of tables? "Unit price × quantity = total price" is the equivalent relationship of this question
Let the unit price of table be x yuan. The equation is 22 × 4 + 2x = 198
Another example is: one car travels 68 kilometers per hour, and the other car travels 98 kilometers per hour, How many hours do two trains meet? The quantitative relationship of the encounter problem in the question is the equivalent relationship: speed and X encounter time = the distance between two stations. (test paper topic) students have a further understanding of the equation solving application problems according to the quantitative relationship of the travel problem
4、 Find the equivalent relation from the formula
For example: (question 4 on page 75) the length of a picture is twice the width. The frame of the picture shares a 1.8-meter wooden strip. How much is the area of the picture? According to the formula of the circumference of a rectangle: (length + width) × 2 = perimeter, the equation is: let the width be x meters, (2x + x) × 2 = 1.8 to get the width, and then use the length and width to get the area
Another example is: use 80 cm long iron wire to form a rectangle. If you want to make it 16 cm wide, how many cm long should it be? According to the formula of the circumference of the rectangle, list the equivalent relationship: (length + width) x 2 = the circumference of the rectangle. Let the length be cm, the equation is: (x + 16) × 2 = 80
Such exercises make students interested in solving practical problems with equations
5、 Find the equivalent relationship from the hidden conditions
For example: (question 6 on page 72) the number of chicken and rabbit is the same. There are 48 legs in two kinds of animals. How many are each of them? There is only one number in this question: the number of legs of chicken and rabbit is 48, but it hides two important conditions: chicken and two legs, and rabbit has four legs
The relationship between the number of legs and the number of legs is very simple
Suppose there are x chickens and X rabbits respectively, and the equation is: 2x + 4x = 48
Another example is: the sum of two adjacent odd numbers is 176, what are the two numbers? According to the characteristics of odd numbers, the difference between two adjacent odd numbers is 2
First odd + first odd + 2 = 176
Let the first odd number be x, and the equation is: x + X + 2 = 176
After a period of practice, students are interested in using equations to solve practical problems, have methods, and taste the happiness of success