Math problems in grade one. . . Reward 100 points

Party A and Party B set out at the same place at the same time. The speed of A is 7, and the speed of B is 3. Otsuichi has been going east. Party A goes directly to the south. After walking 10, A walked obliquely to the northeast for a while, then met B and asked how far they had gone when they met.

10 step

(10 step) square +(3T) square =[7(T- 10/7)] square.

Solve T==3.5 or 0, and discard 0.

So A took 7*3.5=24.5 steps.

B took 3*3.5= 10.5 steps.

10 square+10.5 square = 14.5 square.

3 bundles of excellent grain, 2 bundles of medium grain, 1 bundle of poor grain, * * * is 39 buckets;

2 bundles of excellent grain, 3 bundles of medium grain, 1 bundle of poor grain, * * * is 34 buckets;

Upper valley 1 bundle, 2 bundles in middle valley, 3 bundles in lower valley, and * * * is 26 buckets;

Please list the equations and find out how many buckets there are in the upper, middle and lower third-class valleys.

The upper, middle and lower valleys are X, Y, Z, Y and Z barrels.

3x+2y+z=39

2x+3y+z=34

x+2y+3z=26

x=9.25 y=4.25 z=2.75

Today Tian Guang is fifteen steps away from sixteen. Find field geometry?

Answer: one acre.

Twelve steps from Tian Guang and fourteen steps from Tian Guang. Find field geometry?

Answer: 168 step.

Tian Fang said: multiply the steps extensively to get the product steps.

Divided by 240 steps, that is, the number of acres. One hundred acres equals one hectare.

Today, Tian Guang is one mile away. Find field geometry?

A: Three hectares and seventy-five acres.

And Tian Guang Erli, from Li San. Find field geometry?

Answer: 22 hectares and 50 acres.

A square pond, the depth is equal to the width of the pond, and a reed grows in the middle of the pond, which is 1 m above the water level. Just take the reed to the shore, flush with the water surface, and find out the depth and the length of the reed (the number of reeds can be kept as a result).

When the water depth is x meters, the length of reed is x+ 1 meter.

x^2+(0.5x)^2=(x+ 1)^2

(x-4)^2=20

X-4=2* radical number 5, x-4=-22* radical number 5 (omitted)

X=4+2* radical number 5

Find the water depth (4+2* root number 5) meters and the reed length (5+2* root number 5).

Log buried in the wall: Today, a log was buried in the wall. I don't know its size. I saw them with a saw an inch deep and a foot long. What is the diameter geometry?

Draw a picture first and you can see it at a glance. 1 foot = 10 inch. That is, if the radius of a circle is r, when it enters 1 inch from a point to the center, that is, the chord length of a chord (r- 1) inches from the center is 10. Then we can use Pythagorean theorem. (r- 1) inches and 5 inches are two right angles, and the radius r is the hypotenuse. That is, (R- 1) 2+5 2 = R 2, we can get r= 13, so the diameter is 26 and the radius is 65438+.

A person drives a car to transport rice from A to B. The car carrying rice travels 25 kilometers a day, the empty car without rice travels 35 kilometers a day, and it goes back and forth three times on the 5th. How many kilometers are there between these two places?

The speed ratio of rice loading and non-loading is 25: 35 = 5: 7, and the time ratio is 7: 5. The traveling time of the rice truck is 5×(7/5+7)=35/ 12 (days), and the traveling distance of the rice truck is 25× (35/65438+).

1. Han Xin points soldiers.

Legend has it that Han Xin, a general of the Han Dynasty, used a special method to count the number of soldiers. His method is: let the soldiers line up in three rows (three people in each row), then five rows (five people in each row) and finally seven rows (seven people in each row). As long as he knows the approximate number of soldiers in this group, he can calculate the exact number of soldiers in this group according to the number of soldiers in the last line of these three parades. If Han Xin saw three processions at that time, and the number of soldiers in the last line was 2, 2 and 4 respectively, knowing that the number of soldiers in this team was about 300 to 400, can you quickly calculate the number of soldiers in this team?

2. monks eat steamed bread

Big monks eat four each, and young monks eat 1 four. Monk monk 100, * * * ate 100 steamed bread. How many monks are there? How many steamed buns do you eat?

wash the bowl up

There is a woman washing dishes by the river. Passers-by asked her why she washed so many dishes. She replied: There are many guests at home. They share a rice bowl for every two people, a soup bowl for every three people and a vegetable bowl for every four people, and * * * uses 65 bowls. Can you infer how many guests have been to her house from the situation of her household bowls?

4. suan Anjing in "One hundred dollars for a hundred chickens":

Every cock is worth 5 yuan, every hen is worth 3 yuan, and every three chicks are worth 1 yuan. Now 100 yuan is used to buy 100 chickens. /kloc-How many chickens are there in 0/00 chickens?

5. < < Problems in Chapter Nine Arithmetic Chapter Nine Arithmetic is one of the oldest mathematical works in China. This book is divided into nine chapters and has 246 themes. One of them is like this: a person uses a car to transport rice from place A to place B. The car carrying rice walks 25 kilometers a day, the empty car without rice walks 35 kilometers a day, and goes back and forth three times on the 5 th. How many kilometers are there between these two places?

6. The problem in Arithmetic Unity is one of China's ancient mathematical works. There is a topic in the book: A took a fat sheep and asked the shepherd, "There are about 100 sheep you drove." The shepherd replied, "If you double this flock of sheep, add half of the original flock of sheep, and add 1/4 of the original flock of sheep, even the fat sheep you are leading will only make up a hundred." Please count how many sheep this shepherd has driven.

7. The problem of "chickens and rabbits in the same cage" in Sun Tzu's calculation: Today there are pheasants and rabbits in the same cage, with 35 heads above and 94 feet below. What are the geometric shapes of pheasants and rabbits?

8. Measure the depth of the well with a rope, fold the rope three times and leave 4 meters outside the well; Fold the rope four times and measure it, leaving 1 m outside the well. What is the depth of the well and the length of the rope?

9. In the book Comparison of Algorithms in Nine Chapters in the Ming Dynasty, a math problem appeared in the form of poetry. The whole problem is: looking at the towering seven-story building from a distance, the red light is doubled, and the * * * light is 38 1. How many lights are there at the top?

10, there is a folk saying: 36 bricks, 36 people moving, four men moving, three women moving, two children carrying a brick. How many men, women and children are there?

1 1, the original title in "Nine Chapters of Arithmetic": "Today, Pusheng is one day, three feet long; Wan was born one day and grew a foot. Pu's birthday is half, and Wan's birthday is two. The longer the geometry is, the longer it is? "

None of the above questions is too difficult. Can you solve them?

Attached reference answer:

1,(2×70+2×2 1+4× 15)÷ 105=2……32 105×3+32=347

A: It is 347 people.

2. Little monk: (100× 4-100) ÷ (4-1/4) = 80.

Big monk: 100-80=20

3, solution: there are x people. 1/2x+ 1/3x+ 1/4x = 65 x = 60

4. Solution: Suppose there are X cocks, Y hens and (100-x-y) chickens.

5x+3y+1/3 (100-x-y) =100x = 4 or 8 or 12 y= 18 or1.

Chicken: 78 or 8 1 or 84

5. Solution: Let Party A and Party B have X kilometers. 1/25×3x+ 1/35×3x = 5x = 875/36。

6. Solution: Let * * have x sheep. X+x+x÷2+x÷4= 100 x=36。