Hypothesis is a common method to solve problems. "Hypothesis method" is to make some assumptions according to the known conditions or conclusions in the topic, then calculate according to the known conditions, and make appropriate adjustments according to the contradiction in quantity, so as to find the correct answer.

To solve practical problems by using the idea of hypothesis method, we must first assume that two unknown quantities are the same quantity according to the meaning of the problem, or that the two unknown quantities needed are equal; Secondly, according to the assumptions made, pay attention to what changes have taken place in the quantitative relationship and make appropriate adjustments.

Example 1: Today, chickens and rabbits live in a cage. There are 35 rabbit heads with chicken heads and 94 rabbit feet with chicken feet. How many chickens and rabbits are there?

Analysis and solution: the problem of chickens and rabbits in the same cage is often solved by hypothetical method, that is, it is assumed that the total number of feet of all chickens or rabbits is bound to contradict the conditions, and the correct answer can be found by appropriate adjustment according to the contradiction in quantity.

Assuming that they are all chickens, the corresponding total number of feet should be 2×35=70, which is 94-70 = 24 less than the actual number. The reason for the decrease is that the rabbit should be treated as a chicken, and it should be reduced by 4-2 = 2 feet. So there are 24÷2= 12 rabbits and 35- 12 = 23 chickens.

Exercise 1

1, 30 chickens and rabbits, 70 feet. How many chickens and rabbits are there?

There are 20 chickens and rabbits and 50 feet. How many chickens and rabbits are there?

3. Chicken and rabbit 100, chicken feet are 80 more than rabbit feet. How many chickens and rabbits are there?

Exodus 2: 27 RMB * * * face value 2 yuan 5 yuan, both of which are 99 yuan. How much RMB are there in 2 yuan and 5 yuan?

Analysis and answer: This question is similar to the problem of "chickens and rabbits in the same cage". Assuming that all RMB is denominated in 2 yuan, then 27 RMB is 2×27=54 yuan, which is 99-54 = 45 yuan compared with the actual situation. The reason for the decrease is that each RMB with face value of 2 yuan is regarded as RMB with face value of 5 yuan, that is, 5-2 = 3 yuan. So there are 45 RMB with face value of 5 yuan = 15 RMB with face value of 2 yuan.

Exercise 2

1, Sun Jiayou has 40 quarters * * *, and one * * is 1 Yuan 70. How many coins are there in each of these two kinds?

250 students went boating, and took a 1 1 boat, including 6 people in the big boat and 4 people in the small boat. How many big boats and small boats are there?

3. Xiaoming took part in the quiz competition, with 20 questions. It is stipulated that 5 points will be deducted for guessing correctly, and 3 points will be deducted for guessing wrongly (if you don't guess correctly, you will be wrong). Xiaoming got 60 points in the exam. How many times did he guess right?

Ex. 3: A batch of cement is transported by handcart, using 45 vehicles. By cart, as long as 36 cars. Each big car is loaded with 4 tons more than the small one. How many tons is this batch of cement?

Analysis and solution: It is the key to solve the problem to find out how many tons are loaded in each cart. If 36 trolleys are used to transport cement, there are 4×36= 144 tons left, and 45-36 = 9 trolleys are needed to transport cement, so the loading capacity of each trolley is 144÷9= 16 tons, so this batch of cement has 16 tons.

Exercise 3

1, a batch of goods should be loaded with 16 trucks and 48 trucks. It is known that large trucks carry 4 tons more than small trucks. How many tons is this shipment?

2. There is a pile of yellow sand, which needs to be transported 50 times by car and 80 times by car. Each big car carries 3 tons more than the small one. How many tons is this pile of yellow sand?

3. A batch of steel is loaded with 35 cars and only 30 cars. Each car is 3 tons less than the big one. How many tons is this batch of steel?

Example 4: A glass factory wants to transport 65,438+0,000 pieces of glass for the shopping center. Both parties agree that the freight for each glass is 1 yuan. If you break a glass, you will not only lose the freight, but also pay 3 yuan. In this way, when it is delivered to the destination and settled, the glass factory will have to pay the freight to 920 yuan. How many glasses did Qiu break?

Analysis and solution: Assuming that 1 0,000 glasses all arrived in good condition, the freight should be 1× 1 0,000 yuan, which is actually 1 0,000-920 yuan, which means that the glasses were broken during transportation. Every broken one will not only lose the freight, but also compensate 3 yuan, so the loss of the glass factory 1+3 = 4 yuan. And it has been found that * * * has less income in 80 yuan, so the number of broken glass is 80÷4=20.

Exercise 4

1, handling 1000 glass bottles, it is stipulated that one glass bottle can be safely transported, and the handling fee is 30 cents. But if you break one, you will not only lose the handling fee but also lose fifty cents. If * * * is shipped to 260 yuan, how many pieces are broken during handling?

2. There are ***20 questions in a math contest, and the scoring standard is 5 points for each correct question and 1 point for each wrong question. Liu Liang took part in the competition and scored 64 points. How many questions did Liu Liang answer correctly?

3. A chemistry contest held by a school had 15 questions. It is stipulated that each correct question will get 10, and each wrong question will get 4 points. Xiaohua got 66 points in this competition. How many questions did he answer correctly?

Example 5: In a table tennis match, 200 tickets were sold from 30 yuan, 40 yuan and 50 yuan, and the income was 7,800 yuan. Among them, 40 yuan and 50 yuan have the same number of votes. How many tickets were sold for each type?

Analysis and answer: Because "the votes in 40 yuan and 50 yuan are equal", the votes in 40 yuan and 50 yuan can be regarded as those in 45 yuan. Assuming that these 200 tickets are in 45 yuan, the income should be 45×200=9000 yuan, which is 9000-7800 = 1200 yuan more than the actual income. This is because the tickets in 30 yuan are counted as 45 yuan. So 30 yuan has 1200 ÷ (45-30) = 80 tickets, and 40 yuan and 50 yuan each have (200-80) ÷ 2 = 60 tickets.

Exercise 5

1, a game sold 400 tickets from 40 yuan, 30 yuan and 50 yuan, and earned 15600 yuan. Among them, 40 yuan and 50 yuan have the same number of votes. How many tickets were sold for each type?

There are 20 questions on the math test paper. Answer a question correctly and get 7 points; If you do something wrong, deduct 4 points; If you don't do it, you will get 0 points. Red test 100. She didn't do many questions.

There are three kinds of exercise books: A, B and C, and the prices are 7 points, 3 points and 2 points respectively. I bought 47 copies of three kinds of exercise books and paid 2 1 yuan for 2 cents. The number of copies of type B exercise books is twice that of type C exercise books. How many copies did you buy for each of the three types of exercise books?