Suppose all chickens and rabbits = (actual number of feet -2? Total number of chickens and rabbits) (4-2)

Suppose all rabbits and chickens =(4? Total number of chickens and rabbits-actual number of feet)? (4-2)

The second problem of chickens and rabbits in the same cage:

Suppose all chickens and rabbits =(2? Total number of chickens and rabbits-the difference between chicken and rabbit feet)? (4+2)

Suppose all rabbits and chickens =(4? The total number of chickens and rabbits+the difference between chickens and rabbits)? (4+2)

The ideas and methods of solving problems generally adopt the hypothesis method to solve such problems. It can be assumed that they are all chickens or rabbits. If we assume that they are all chickens, then change the rabbits into chickens; If we assume that they are all rabbits first, and then trade chickens for rabbits. This kind of problem is also called substitution problem. Suppose first and then replace, and the problem will be solved.

Example 1 angora rabbit and Lu Hua chicken, put the chicken and rabbit in a cage. There are thirty-five heads to count and ninety-four feet to count. Please count carefully how many rabbits and chickens there are.

Assuming all 35 rabbits, the number of chickens =(4? 35-94)? (4-2)=23 (only)

Number of rabbits =35-23= 12 (only)

It can also be assumed that all 35 chickens are chickens, so the number of rabbits =(94-2? 35)? (4-2)= 12 (only)

Number of chickens =35- 12=23 (only)

A: There are 23 chickens and 0/2 rabbits.

Example 2: 2 mu of spinach should be applied 1 kg, 5 mu of cabbage should be applied with 3 kg, and two kinds of vegetables *** 16 mu should be applied with 9 kg. How many acres of cabbage are there?

Solving this problem is actually a makeover? Chicken and rabbit in the same cage? Question? Fertilize spinach per mu (1? 2) kg？ With what? How many feet does a chicken have? Corresponding? Fertilization rate per mu of Chinese cabbage (3? 5) kg？ With what? Each rabbit has four feet? Corresponding? 16 mu? With what? The total number of chickens and rabbits? Corresponding? Nine kilograms? With what? What is the total number of feet of chickens and rabbits? Correspondence. Suppose 16 mu is all spinach, with

Chinese cabbage per mu =(9- 1? 2? 16)? (3? 5- 1? 2)= 10 (management unit)

Answer: Chinese cabbage field 10 mu.

Example 3 Teacher Li bought 45 exercise books and diaries for the school with 69 yuan. 3.20 yuan for each exercise book and 0.70 yuan for each diary. How many exercise books and diaries did you buy?

The solution to this problem can be changed to? Chicken and rabbit in the same cage? The question assumes that 45 books are diaries, and there are

Number of exercise books =(69-0.70? 45)? (3.20-0.70)= 15 (Ben)

Number of diaries =45- 15=30 (copies)

Answer: 15 exercise book, 30 diaries.

Example 4 (the second question of chickens and rabbits in the same cage) There are 100 chickens and rabbits, and chickens have 80 more feet than rabbits. How many chickens and rabbits are there?

Suppose 100 chickens are all chickens, and there are

Number of rabbits =(2? 100-80)? (4+2)=20 (only)

Number of chickens = 100-20=80 (only)

There are 80 chickens and 20 rabbits.

Example 5: There are 100 steamed buns for 100 monks, one big monk eats three steamed buns, and three little monks eat 1 steamed buns. How many monks are there?

Assuming that all monks are big monks, then * * * eats steamed stuffed buns (3? 100), eating more than the actual (3? 100- 100), this is because the little monk is also a big monk, so we take it? Small? Change? Big? Replacing a young monk with a big monk can reduce steamed buns (3- 1/3). Therefore, * * * has a little monk (3? 100- 100)? (3- 1/3)=75 (person)

* * * There is a big monk 100-75=25 (person)

A: * * * There are 25 big monks and 75 young monks.

More articles about junior high school math test questions: