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Mathematics of tug-of-war competition
The sum of 1. two numbers is 60, and their greatest common factor is 12. What are these two numbers?

Suppose one number is 12x and the other number is 12y, then

12x + 12y = 60

Positive integer solutions satisfying the equation are x=2, y=3 or x=3, y=2.

So these two numbers are 24 and 36.

Students take part in tug-of-war competition. They are divided into groups of 6, 8 or 10, and there are 3 people left. What is the minimum number of students taking part in the tug-of-war?

According to the meaning of the question, there are 6 people in each group, 8 people in each group or 10 people in each group, and there are 3 people left. If the number of groups is x, y, z, y and z, then

6x + 3 = 8y + 3 = 10z + 3

That is 3x = 4y = 5z.

X, y and z are all positive integers, and the number of students required to participate in tug-of-war is the least, so x=20, Y = 15 and Z = 12.

Therefore, the minimum number of people participating in tug-of-war is 6*20+3= 123.

From the meaning of the question, if every 7 pieces are divided into a pile, there will be 3 more pieces. Let the number of piles at this time be x (excluding the extra 3 blocks), then

80 & lt= 7x+3 & lt; = 100 (note:

So 1 1

When x= 1 1, there are 80 pieces in this pile * *, so if you divide a pile every 1 1, it will be 8 pieces short, which is irrelevant and will be discarded;

When x= 12, there are 87 pieces in this pile * * *, so if a pile is divided every 1 1, the difference is 1, which is in line with the meaning of the question;

When x= 13, there are 94 pieces in this pile * * *, so if a pile is divided every 1 1, it is short of 5 pieces, which is irrelevant and discarded;

All in all, there are 87 pieces in this pile.

There is a pile of chess pieces between 3.80 and 100. If every 7 pieces are divided into a pile, there will be 3 more pieces. If every 1 1 block is divided into a heap, there will be a difference of 1 block. How many pieces are there in this pile?