1. Xiao Wei and Xiaoming exchanged activities during the summer vacation. Xiao Wei said, "I attended the summer camp for science and technology and went out for a week. The sum of the dates of these seven days is 84. Do you know what date I left? " Xiao Ming said: "I stayed at my uncle's house for seven days during the holiday, and the date and number of months were also 84." Guess what date I went home? "

Solve Xiao Wei and Xiao Ming's problems with column equations ~

2. Cut two pieces with the same weight from two alloys with different copper contents, with the weight of 12kg and 8kg respectively, and melt each piece together with the remaining alloy. After smelting, the percentage of copper in the two pieces is the same. What is the weight of the cut alloy?

3. There is a reservoir, which has a certain water flow per unit time and is also discharging water. According to the current flow rate, the water in the reservoir can be used for 40 days. Due to the recent rainfall in the reservoir area, the amount of water flowing into the reservoir has increased by 20%. If the discharged water volume is also increased by 10%, it can still be used for 40 days. Q: If the water is discharged according to the original discharge, how many days can it be used?

4. There are three classes, A, B and C. Class A has four more girls than Class B, and Class B has/kloc-0 more girls than Class C. If the first students of Class A are transferred to Class B, the first students of Class B are transferred to Class C at the same time, and the first students of Class C are transferred to Class A at the same time, the number of girls in the three classes is exactly equal. It is known that there are two girls in the first group of Class C. How many girls are there in the first group of Class A and Class B?

5. Uniformly arrange 1987 natural numbers 1, 2, 3, 4, ..., 1986, 1987 in a big circle, and count from 1 every 1. Cross out 5 and 6 every 4, so that two numbers are crossed out every other number, and the circle is crossed down. Q: How many numbers are left in the end?

6. Let 2002x3=2003y3=2004z3, x>0, y>0, z>0, and

3√2002 x2+2003 y2+2004 z2 = 3√2002 = 3√2003 = 3√

Found1/x+1/y+1/z.

7. There are two shepherds, each with X sheep. A said, B, if you give me a sheep, I will have twice as many sheep as you. B said, or if you give me one of your sheep, we will have the same number. How many sheep are there in A and B?

1 & gt； Question 1: Suppose the departure date is X.

X+X+ 1+X+2+X+3+X+4+X+5+X+6 = 84

X=9

Xiao Wei left on the 9th.

The second question: Because it is a summer vacation activity, it can only be held in July and August.

Set the date back to x.

rank

7+X+X- 1+X-2+X-3+X-4+X-5+X-6 = 84

or

8+X+X- 1+X-2+X-3+X-4+X-5+X-6 = 84

The first formula solves X= 14.

The result of the second formula is not an integer.

So I can only get home in July 14.

2> Let the copper content of the two blocks be M and N respectively, and the cutting quality be X..

Then [(12-x) m+xn]/12 = [(8-x) n+XM]/8 can directly solve x=4.8.

3> Let the total water volume of the reservoir be X, and the daily water inflow and water outflow are M and N respectively.

Then x/(n-m) = 40 = x/[n (1+10%)-m (1+20%)] needs x/[n-m( 1+20%)].

You can simplify n=2m x=40m and bring it into the second formula to get x=50 days.

There are m and n girls in the first group of Class 4>A and Class B respectively. If there are x girls in class C, there are x+ 1 in class B and x+5 girls in class A, with an average of x+2 (calculated by change). Class c:-2+n = (x+2)-X.

Class a: +2-m=(x+2)-(x+5) can get m=5 n=4.

5> Only 3k+ 1 remains in the first cycle. In the second cycle, you can change all the numbers into 3k+ 1, and then analyze k. Only 3p+2 is left in the second cycle, then P is analyzed, and so on, and the last number is 1987.