There is a basket of eggs divided equally among 7 people with 3 left, 8 people with 2 left, and 9 pe

In this question, let's first look at "3 left in the average score of 7 people, and 2 left in 8 people", we can see that if there is no remainder, if we want to find out the number of numbers where the product of 7 is less than the product of 8 and the product "1", we use the enumeration method to be more intuitive:

7 of 8.

From the above enumeration, we can find out 7 and 8; 63 and 64 two sets of numbers, and then through the calculation, 63 + 3 or 64 + 2 is the total number of hypothetical eggs, and then look at the condition to divide 9 people and leave 7, calculate (66-7) 9 is not eligible. Look again to find 7 and 8; 63 and 64 two sets of numbers, it is not difficult to find that there is a difference of 56 between them, so try further, 63 + 56 = 119;Then use 119 + 3 (3 left for 7 people according to the average score) = 122;Another hypothetical total number of eggs was found, and then tried again, (122-7) 9 still didn't work, and then down 122+56=178, (178-7) 9=19;（178-2）/8=22；（178-3）/7=25；If all three conditions are met, it means that the total number of eggs is 178, understand? In fact, I wrote so much and did it very quickly, if I can't write clearly, you continue to ask, I am willing to serve!

178, I've already handed it in, it's definitely right.

Find their greatest common factor.

This is the topic of flexibility. The minimum value is found.

Analysis: At first glance, I have no clue and I don't feel like I know where to start.

Because people divide eggs, it is easier to understand by considering the number of people first.

If there are 7 people and there are 7 eggs left, they can still continue to divide evenly.

By analogy, the number of people cannot be less than or equal to 7, but can only be greater than 7.

There were only 8 people, which met the requirements. Because the question is at least how many eggs there are.

Conclusion: 8 5 + 7 = 47 (pcs).

There are 7 left that are not enough to average the score, which means that there will be at least 8 people, if there are 8 people, then this pile of eggs is 8 5 + 7 = 47.

You can assume, that is, how many people there are, how many eggs, and then try it. First of all, there are 7 left to understand that the average score is not enough, and if the average score is not enough, there should be at least 8 people, knowing the minimum number of people, you can know how many eggs there are at least, 5x8 + 7 = 40 + 7 = 47, this pile of eggs has at least 47.

This number is a multiple of bai8 + 1 and is divisible by 9. Single digits are odd numbers.

zhi。This number +1 is possible.

The DAO is divisible by 5, and the single digit inside is odd, so the single digit can only be 9.

Let this number be (9-1)n+1

9-1)n+1=9n-(n-1), to (9-1)n+1 divisible by 9, n-1 divisible by 9.

Let n-1=9k

8n+1=8(n-1)+9=72k+9

72k+9=7p+5

p=(72k+4)/7=(70k+2k+4)/7=10k+2(k+2)/7

For p to be a positive integer, 2(k+2) 7 is divisible by 7, and 2 is coprime with 7, so only k+2 is divisible by 7.

k is a positive integer, and k is a minimum of 5

n=9k+1=9×5+1=46

8n+1=8×46+1=369

There were at least 369 eggs in the basket.

The number of eggs is a multiple of 7 and 9, that is, a multiple of 63, and the number of eggs is divided by 8 and the remainder of 1, so the congruence formula is obtained, 63n 1 (mod8), n = 7, 63n = 441, and there are 441 eggs in the basket.

is 369, excluding some distractors, and the remaining useful information is.

1) Multiples of 9.

2) Divided by 8 by 1

3) Divided by 7 by 5

4) Divide 4 by 5

Then, enumeration, the minimum number that satisfies the first two conditions is 9, and then increases 8 9 = 72 in turn, and when it is added to 5 times, the minimum number that satisfies (3) and (4) is found

7x9=63pcs.

63x7 = 441 pcs.

So there were 441 eggs in the basket.

The common multiple of 2345678910 is 810, 810n+1 can be divided by 11, try n=1,2,32,431 eggs can be obtained.

This type of question examines the least common multiple.

Everyone gives eggs or divides eggs, and it can't be counted to divide eggs, because the more people get eggs, there are more, but the equation can be listed for eggs, because the number of eggs is the same, set a total of x people, 10x-9=8x+7, calculate a total of 8 people!!

The number of eggs and the number of people is fixed, when there are 10 eggs per person, take 9 more;

When 8 per person, take 7 less, then:

9+7) (10-8) = 8 (person).

There are 8 people in his family.

The question is incorrect, it should be "9 eggs out of 10 eggs per person, 7 eggs more than 8 eggs per person".

This kind of problem lends itself to the hypothetical approach. For example, according to the sentence "10 eggs per person is 9 eggs", if there are 9 more eggs, it becomes "10 eggs per person is just right", and of course, "8 eggs per person will become 9 + 7 = 16 more". 10 eggs per person is just right, why give 10-8=2 less per person and leave 16?

Find the total number of people as (9+7) (10-8)=8.

There is a problem with the question, 10 per person is left, and 8 per person is not enough points, it is impossible.

Guess your question should be 10 per person with a difference of 9, 8 per person and 7 more. Let's do it according to the conjecture of the question number.

This question is a profit and loss problem:

Population = (9 + 7) (10-8) = 16 2 = 8 people.

Why is there a lack of everyone's points, you got the question wrong, welcome to ask.

It should be 10 eggs per person, 7 eggs less, 8 eggs per person, 9 more eggs, this question is not rigorous, if it is a student test paper, don't do it.

Your question, according to your calculations, the number of people is negative.