Fifth grade Olympiad chicken and rabbit in the same cage hypothetical method application problem, wi

Removed 5 full pairs and only 1 pair.

There are still 144 questions and 39 people left, because the number of questions 2 and 3 is the same, assuming that these students have done the questions correctly, it will not affect the number of questions and the number of people, and then do the same as the classic question of chickens and rabbits in the same cage.

Suppose 39 people have done 4 questions correctly, and there are a total of 39 4=156 with 12 more, which means that there are fewer students in the question.

Get 12 people.

So there were 31 people who got 4 questions right, and 4 people who got 2 and 3 questions right.

Don't have a title?It can be solved with binary equations, and of course there are also solutions for Olympiad numbers.

Solution 1: (Number of rabbit feet, total number of feet, total number of feet) (number of rabbit feet, number of chickens) number of chickens, total number of chickens, number of chickens = number of rabbits.

Solution 2: ( Total number of feet Number of Chicken Feet Total Number of Feet) (Number of Rabbit Feet Number of Chicken Feet) Number of Rabbits. Total number of rabbits = number of chickens.

Solution 3: Total number of feet 2 - total number of heads = number of rabbits.

Total number of rabbits = number of chickens.

Excluding those who did 1 and 5 correct, there were 52-7-6 = 39 people, and 39 people did a total of 181-7-6 * 5 = 144 questions correctly. Suppose 39 people do 4 questions correctly, a total of 39*4=156 questions are done correctly, but in fact, only 144 questions are done correctly, and 156-144=12 questions are more. Swap 1 person who does 2 questions correctly for 1 person who gets 4 questions right can reduce 2 questions;Swapping 1 person who does 3 questions correctly for 1 person who gets 4 questions right can reduce 1 question.

And because the number of people who do 2 or 3 correctly is the same, then the number of people who do 2 or 3 correctly = 12 (1+2) = 4 people, so the number of people who do 4 correctly = 39-4 * 2 = 31 people.

It is possible to set up x people in 4 lanes and y people in 2 to 3 lanes.

then x+2y=52-13

4x+5y=181-（7×1+5×6）

Get y=4Bring in x = 31

You should be able to understand that the key is to set the unknown, and you will definitely find the relationship according to the conditions.

Let's assume that the number of people who do 2 questions correctly is x

The number of people who get 4 courses right is y

Well according to the topic.

7+2x+3x+4y+5*6=181

7+x+x+y+6=52

7+5x+4y+30=181

2x+y+13=52

5x+4y=144

2x+y=39

y=39-2x

Substituting the equation 15x+4(39-2x)=144

5x+156-8x=144

x = 4 launch y = 31

Then the number of people in the most pair of 4 lanes is 31.

Let's say there are 0 rabbits and 15 chickens.

Chickens and rabbits have a total of legs: 15 2 = 30.

Less: 132-30=102.

For each additional 1 chicken, 1 rabbit, foot increase: 2 + 4 = 6 rabbits have: 102 6 = 17 rabbits.

There are 15 + 17 = 32 chickens.

The hypothetical method is the arithmetic method.

Suppose 15 more rabbits are added, and the number of chickens and rabbits is the same, with a total of 132 + 15 4 = 192 (bar) legs.

At this point, 1 chicken and 1 rabbit are grouped together.

The number of legs in each group is 2 and the number of legs is 6

Total: 192 6 = 32 groups.

So there are 32 chickens and 32-15=17 rabbits

Let's say there are x chickens, then rabbits have x-15.

2x+4(x-15)=132

The solution is x=32

A: There are 32 chickens and 17 rabbits.

In group 1, ants had 6 legs and spiders had legs24 for a total of 30 minus 5 spiders' legs.

400-40) 30=12pcs.

There are 12 ants.

Spiders have: 12 3 + 5 = 41 individuals.

Is it a list method? As follows:

Spider counts: 8, 11, 14, 17, +3) 41 each time

Ants only count 1 2 3 4 +1) 12 each time

Total number of legs: 70, 100, 130, 160, +30) 400 each time

A: There are 41 spiders and 12 ants.

Set: Ants x only.

6x+8（3x+5）=400

30x=360

x=12, then 3x+5=41

A: There are 12 ants and 41 spiders.

Set x ants and 3x+5 spiders.

6x+8（3x+5）=400

x=123x+5=41.

What's the list answer?

Set x ants, so it's 3x+5 spiders.

6x+8（3x+5）=400

The solution is x=12

So there are 12 ants and 41 spiders.

Solution: If there are x ants, then there are (3x+5) spiders.

3x+5)8=6x=400

x=12 12*3+5=41 (only) Answer: There are 41 spiders and 12 ants.

If it is a solution question, there are two ways to solve it.

Solution 1 (No.)

Solve the equation): rabbit = (116-40*2) (4-2) = (116-80) 2 = 36 2 = 18 (chickens) = 40-18 = 22 (chickens).

Solution 2 (Solving Equations):

Let the chicken x, the rabbit y, then:

x+y=40

2x+4y=116 solves the equation to get x=22, y=18

There are 22 chickens and 18 rabbits.

Fill-in-the-blank quick answer tips:

1.If you blow a whistle and all animals raise one leg, there are 76 legs2One more whistle blows, and all the animals raise one more leg, then there are still 36 legs, and at this time all the chickens fall to the ground, and the rest are rabbits, and each rabbit has 2 legs, then the rabbits have 36 2 = 18.

There are 40-18 = 22 chickens.

Let's say it's all chickens.

Total number of feet - (number of chicken feet * total number of heads) (more per rabbit and number of feet per chicken) = number of rabbit heads total number of heads - number of rabbit heads = number of chicken heads.

Or let's say it's all rabbits.

Number of rabbit feet * total number of heads) - total number of feet (more per rabbit and number of feet per chicken) = number of heads of chickens Total number of heads - number of chicken heads = number of rabbit heads.

I'm a 6th grader, it's knowledge from books, can't be wrong)

There are x boys and 100-x girls.

60*x+（100-x）*70=6300

x=70 40 more than girls.