Junior high school mathematics questions in the first year, junior high school mathematics in the se

The solids between each two hollows are seen as a group, and the solids are formed into a series of equal differences, i.e.: 1, 2, 3... It is easy to see that if there is a set of solid elements with a space element, and if there are n hollow elements, then n(n+1) 2+n<=2005 and n is the largest integer satisfying the inequality, n=61

Using Gaussian formula: n(1 n) 2 2005, n 62, 62 1 61

There are 2005 hollow circles in the 61st circle.

、..n+1）

That is, to find the above number of equal difference columns.

2005 + 1 = 2006 (not always better) 2006 = 1 + 2 + 3 + 4 + 5 + ...62 + 53 (estimate required) 62-1 = 61 (for the sake of simplicity, one item was added in front, and now it will be subtracted).

There are n hollow circles.

1+1+2+1+。。n+1≤2005

i.e. n(n+1) 2+n 2005

n is the maximum value that satisfies the condition.

n（n+3)≤4010

There are 60x60=3600, 65x65=4225 with one try.

n=61

Looking at the solid circles, use the formula s=n*(n+1) 2, n represents the number of solid circles between adjacent open circles, and s represents the sum of all the previous solid circles. For example, at this time, n=5, s is equal to 15, the total circle is s+n, calculate it yourself, I wish you success!

If you don't take into account the time of collecting medicine, it is a walking time from 8 a.m. to 6 p.m., a total of 10 hours.

Set up slope road x km, flat road y km.

x/3+y/4+x/6+y/4=10

That is: x+y=20

Answer: The old man walked a total of 40 kilometers back and forth.

Solution: There are x kilometers of slope roads and y kilometers of flat roads.

x/3+y/4+x/6+y/4=10

Combining similar terms yields: x 2 + y 2 = 10

x+y=20

20 2 = 40 (km).

Answer: The old man walked a total of 40 kilometers back and forth.

Solution: Departure at 8 a.m. and return home at 6 p.m., time = (6 12 8) hours = 10 hours.

The length of the flat road is x km, the length of the hill road is y km, and the time consumed on the flat road at the time of departure = x km 4 km hours = (x 4) hours on the uphill slope = y 3 km hours = (y 3) hours on the downhill = y 6 km hours = (y 6) hours on the flat road = x km 4 km hours = (x 4) hours by the title, (x 4 y 3 y 6 x 4) hours = 10 hours, x 2 y 2 = 10, 1 2 (x y) = 10

x y = 20 (20 km).

The distance traveled by this old man collecting medicine = x y y x = (20 20) kilometers = 40 kilometers.

A: The old man walked a total of 40 kilometers.

1. Solution: Let B have x people and A have 2x people.

According to the title.

One-third x-2x-two-thirds x = 15

The number of people who get x = 9 A is.

2x=9×2=18。

2. Solution: Let the ten digits be x and the single digit be y

According to the proposal.

10x+y=4（x+y）①

10x+y+27=10y+x②

2x=y is obtained from

Substituting 2x=y into .

10x+2x+27=20x+x

Solve x=3 and substitute x=3 into 2x=y.

y=6 The original number is 36.

The number of people in groups A and B is 9 18, respectively

The original number is 36

1.Let the number of B be x and the number of A be 2x

2x+x/3)-(x-x/3)=15

x=92.Let the ten digits be ab

10a+b=4(a+b)

10a+b+27=10b+a

Get a=3, b=6

Original number 36

In the first question, if A is 2x and B is x, then 2x+x 3=2x 3+15, and x=9, then the number of A is 18 and B is 9;

In the second question, let the ten digits of the ten digits be n and the single digit be m, then.

n+m）4=10n+m ；10n+m+27=10m+n, solve the equation, and obtain, n=3 m=6

So the original number is 36

Solution:1If the number of people in Group A is x (people), then the number of people in Group B is x 2 (people), which is derived from the title:

x+(x/2)*(1/3)-(x/2)(1-1/3)=15.

x+x/6-x/3=15.

7x/6-2x/6=15.

5x=15*6.

x=18 (person) - number of people in group A;

x 2=18 2=9 (person) - the number of people in group B.

2.Let the number on the tenth digit of the original number be x and the number on the single digit be y, then the original number is: 10x+y

Set the equation according to the problem:

10x+y=4(x+y) -1)

10x+y+27=10y+x --2)6x-3y=0 --3)

9x-9y=-27 --4).

9x=27.

x=3.Substitute x=3 into (3):

3y=18.

y=6.The original number is 10*3+6=36

Sheet.

Three, Li Si and the two of them are at the east end of the Baligou Bridge, there is a beautiful woman at the west end of the bridge, the three of them set off at the same time, Zhang San and Li Si go in the same direction, the beauty rushes to the sky, Zhang San walks 100 meters per minute, Li Si walks 110 meters per minute, the beauty walks 125 meters per minute, if the beauty meets Li Si 10 minutes after meeting Zhang San, ask how long is the Baligou Bridge at the head of the village?

After setting m time, the beauty and Li Si meet, and after n time, the beauty and Zhang San meet, and the bridge length is L, then 125m+110N=L

125m+100n=l

n-m=10

It is not difficult to find that m=225min, n=235min, l=52857m! You can find some similar questions to do!!

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