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?