There are three ways to avoid the problem of chickens in the same cage and chickens to avoid the sam

1 point will be deducted for not doing or doing it wrong, and 3 points will be awarded for being right.

Therefore, if you don't do or do 1 question incorrectly, you will lose 4 points from the full score.

The maximum score of 50 questions is 50 3=150

A total of 150-82=68 points less.

Therefore, the number of questions that can be judged to have not been done or done incorrectly is 68 4=17

If all the answers are correct, 50*3=150 points will be awarded.

The difference from the actual is 150-82=68 points.

For each mistake, not only do you not get 3 points for answering correctly, but you also lose 1 point, and you actually lose 4 points.

4 points were lost for one question and 68 points were lost for 17 questions.

Didn't answer or did 17 questions incorrectly.

3x-1(50-x)=82

x=33, so 50-x=17

Hypothetical method. Suppose it is all chickens, multiply the number of heads by 2, and then subtract this number from the total number of legs, which is the number of legs that the rabbit has more than the chicken, because each rabbit has 2 more legs than each chicken, so divide the difference by 2 to calculate the number of rabbits, and then subtract the number of rabbits from the total number of heads to calculate the number of chickens.

Equation method. Its essence is to use two equality relations.

The number of chickens + the number of rabbits = the total number of heads; The number of chickens 2 + the number of rabbits 4 = the total number of legs.

Unary Linear Equations.

If there are x chickens, then there are rabbits (total number of heads - x). According to the title, yes.

2x + 4 (total number of heads - x) = total number of legs.

Just solve the equation.

Unary quadratic equations.

There are x chickens and there are y rabbits. According to the title, yes.

x+y = total number of heads.

2x+4y=total number of legs.

Just solve the equation.

I hope it helps, and I wish you progress in your grades.

Solution: Set x questions correctly and answer (50-x) questions incorrectly.

According to the title, 3x-(50-x)=82

Remove the brackets to get 3x-50+x=82

Move the item to get 3x+x=82+50

Combine similar terms to get 4x=132

The coefficient is 1 to give x=33

50-x=17

Answer: 33 questions were answered correctly and 17 questions were answered incorrectly.

Untie; Set x questions correctly, no answers, or wrong (50-x) questions.

3x-（50-x)*1=82

3x-50+x=82

4x=132

x=3350-x=50-33=17

Another way; Untie; Let's do X questions correctly, but I don't answer the questions or I do Y questions incorrectly.

x+y=50 3x-y=82

Use x+y=50 plus 3x-y=82.

4x=132

x=33: Substitute x=33 into x+y=50.

33+y=50

y=17A; Didn't answer or did 17 questions incorrectly.

The four-step method solves the problem of chickens and rabbits in the same cage.

Comparison: The cost of buying B is 46 yuan more than the cost of buying A.

Hypothesis: Suppose all of them buy B, so B is 98 more than A 12 = 1176 yuan to replace: for every 1 kg of B is replaced by A, B will reduce the amount of more than A by 128 + 98 = 226 yuan.

So in total, (1176-46) 226 = 5 kg is replaced.

So A has 5 kilograms and B has 7 kilograms.

Check: 98 7 - 128 5 = 46 yuan.

If you buy x kg of tea A and y kg of B tea leaves, you can know from the title:

x+y=12

128x+46=98y

Just find the answer.

Three ways to cage chickens and rabbits.

The solutions of chickens and rabbits in the same cage include hypothetical method, formula method, equation method, etc.

Equation 1: (Number of Rabbit's Feet, Total Feet, Total Feet) (Rabbit's Feet, Chicken's Feet) = Number of Chickens.

Equation 2: (Total number of feet, number of chicken's feet, total number) (number of rabbit's feet, number of chicken's feet) = number of rabbits.

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

Chickens and rabbits in the same cage is one of the famous interesting topics in ancient China, recorded in the "Sun Tzu Sutra". The problem of chickens and rabbits in the same cage is a common question type in the Mathematics Olympiad in primary schools. Many elementary school arithmetic problems can be transformed into this type of problem, or they can be solved in the typical way of solving it"Hypothetical method. "to solve.

Therefore, it is necessary to learn its solutions and ideas. About 1,500 years ago, this interesting question was recorded in the "Sun Tzu's Sutra". The book tremor is described in this way:

Now there are pheasant rabbits in the same cage, there are thirty-five heads, and there are ninety-four feet below. The meaning of these four sentences is: There are several chickens and rabbits in the same cage, counting from above, with 35 heads, and counting from below, with 94 legs.

Q: How many chickens and rabbits are in the cage? There's a simplest algorithm for this. (Total number of feet - total number of heads Number of chicken's feet) (Number of rabbit feet - Number of chicken's feet) = Number of rabbits (94 35 2) 2 = 12 (number of rabbits) Total number of heads (35) Number of rabbits (12) = Number of chickens (23) Explanation:

Let the rabbit and the chicken lift two feet at the same time, so that the number of feet in the cage is reduced by 2, because the chicken only has 2 feet, so there are only two feet left in the cage of the rabbit, and then 2 is the number of rabbits.

Chickens and rabbits in the cage is very simple, that is, first all animals as a kind, its feet will be poor, there is a difference to find one of them, the problem will be solved: such as acres of round chickens and rabbits, a total of 40 heads, a total of 100 feet, how many chickens and rabbits are there?

Assuming that all of them are chickens, then 40 2 = 80 feet, but in fact there are 110-80 = 30 feet, which means that each rabbit is 4-2 = 2 feet less, and Bisen is 30 (4-2)=15, finding that there are 15 rabbits.

Then there are chickens: 40-15 = 25.

It can also be assumed that they are all rabbits, then 40 4 = 160 feet, then 160-110 = 50 feet more, which is 4-2 = 2 feet more per chicken, and it collapses quickly.

50 2 = 25, find the number of chickens.

Then 40-25=15, find the number of rabbits.

One 1: The quantity is the same. 9.Giraffe 2: Ostrich.

II 1:2: 3:

Three methods one: set up chickens x and rabbits y.

2x+4y=110

2y+4x=100

Solve the equation to get x=15 y=20

Method 2: 110-100 = 10 10 2 = 5

So 15 chickens and 20 rabbits.

Two. (1) There are 48 legs and 18 heads of chickens and rabbits in the same cage, 6 chickens and 12 rabbits.

2), chickens and rabbits in the same cage, rabbits are 12 less than chickens, a total of 132 feet, chickens have (30), rabbits have (18).

3) Chickens and rabbits in the same cage, a total of 100, 20 more chickens than rabbits, 55 chickens, 45 rabbits.

4. Chickens and rabbits have a total of 110 feet, if the number of chickens and rabbits are interchanged, there are 100 feet, how many chickens and rabbits are there? There are (15) chickens and (20) rabbits.

One of the types of civil service exam questions, if you study it carefully, you may be able to get admitted to the civil service.