Learning mathematics is inseparable from solving problems, which has always been recognized as the most distinctive activity in mathematics learning. The ability to solve problems depends largely on the mastery of problem-solving strategies, and the central content of problem-solving strategies is to learn problem-solving ideas, methods, rules and skills.

First, method guidance.

Given the sum and difference of two numbers, the application problem of finding the number of these two numbers is called the sum and difference problem. Commonly used quantitative relations:

(sum+difference) ÷ 2 = large number

(sum and difference) ÷ 2 = decimal

The key to solve the problem of sum and difference: first find out what the sum of two numbers is, then find out what the difference between the two numbers is, and then find out the large number by using the difference between the sum of two numbers equal to twice the large number, or by subtracting the difference between the two numbers from the sum of two numbers equal to twice the decimal number. If the sum or difference of the above two numbers is not directly given, it must be found according to the known conditions first.

Second, typical cases

Example 1: A grain store bought 24 tons of rice and flour, and it is known that rice is 6 tons more than flour. How many tons of rice and flour does this grain store buy?

Analysis: As shown in the figure, rice and flour are 24 tons, and rice is 6 tons more than flour. If you add 6 tons of flour, the total mass is (24+6) tons, which is exactly twice the mass of rice. You can calculate the quality of rice by division. Similarly, if you subtract 6 tons from the quality of rice, the total quality is (24-6) tons, which is exactly twice the quality of flour.

Scheme 1: rice: (24+6) ÷ 2 = 15 (ton)

Flour: 24- 15 = 9 (ton)

Solution 2: Flour: (24-6) ÷ 2 = 9 (ton)

Rice: 24-9 = 15 (ton)

A: This grain store bought 15 tons of rice and 9 tons of flour.

Example 2: There are three bags of fertilizers A, B and C, two bags of fertilizers A and B weigh 32kg, two bags of fertilizers B and C weigh 30kg and two bags of fertilizers A and C weigh 22kg. Ask how many kilograms each of the three bags of fertilizer weighs.

Analysis: There are two bags, A and B, and both B and C contain B bags, from which it can be seen that A bag is 32-30 = 2 (kg) more than C bag, so compared with the mass of C bag, the mass of A bag is a large number and that of C bag is a decimal. According to "large number = (sum+difference) ÷2" or "decimal = (sum)

Solution:

Quality of a bag of fertilizer:

32-30 = 2 (kg)

(22+2) ÷ 2 = 12 (kg)

The quality of c bag fertilizer:

(22-2) ÷ 2 = 10 (kg)

Quality of bag B fertilizer:

32- 12 = 20 (kg)

Or 30- 10 = 20 (kg)

Answer: The fertilizer in bag A weighs 12kg, the fertilizer in bag B weighs 20kg and the fertilizer in bag C weighs 10kg.

Example 3: Warehouse A and Warehouse B store 42 tons of rice. If 3 tons of rice is transferred from warehouse A to warehouse B, the rice in the two warehouses is exactly the same. How many tons of rice are there in these two warehouses?

Analysis: From the known "transferring 3 tons of rice from warehouse A to warehouse B, the rice in the two warehouses is the same", it can be known that warehouse A originally had 3 × 2 = 6 tons more rice than warehouse B, and it can also be known that there are 42 tons of rice in the two warehouses, which can be answered according to the sum and difference question.

Solution:

Originally a warehouse:

(42+3×2)+2

=48÷2

= 24 (ton)

Original warehouse b:

(42-3×2)÷2

=(42-6)÷2

= 18 (ton)

A: It turns out that warehouse A has 24 tons of rice and warehouse B has 18 tons of rice.

Example 4: Car A and Car B were originally loaded with 97 baskets of apples. We took 14 baskets from Car A and put them on Car B. As a result, Car A has 3 more baskets than Car B. How many baskets of apples were originally loaded in the two cars?

Analysis: According to "14 baskets were taken out of car A and put on car B, and as a result, car A had 3 more baskets than car B", it can be known that the number of baskets loaded by car A is a large number, while the number of baskets loaded by car B is a decimal number, and the difference between the number of baskets loaded by car A and that loaded by car B is (14× 2+3).

Solution:

Armor: (97+ 14× 2+3) ÷ 2 = 64 (basket)

Car B: 97-64 = 33 (basket)

A: Car A originally contained 64 baskets of apples, while car B originally contained 33 baskets of apples.

Third, actual combat drills.

Question 1: There are 50 kilograms of water in two barrels. If you pour 9 kilograms of water from the first bucket into the second bucket, the water in the two buckets is the same. How many kilograms of water is there in the first bucket?

Question 2: There are 98 students in Class A and Class B. After four students are transferred from Class A to Class B, the number of students in the two classes is equal. How many people are there in each class?

Question 3: The original paddy field in Xinzhuang is ***5.6 hectares. Last year, 0.54 hectares of dry land was transformed into rice fields. At this time, the dry land is 0. 18 hectares more than the paddy field. How many hectares of paddy and dry fields are there in Xinzhuang?

Question 4: There are * * * 230 children in kindergarten, of which the large class is 8 more than the middle class, and the middle class is more than the small class 12. How many children are there in the big, middle and small classes?

Question 5: The two brothers * * * have RMB 50 yuan. After the elder brother gave his younger brother 8 yuan money, he had more money from 2 yuan than his younger brother. How much money do brothers and sisters have?