When a machine tool factory manufactures a certain kind of machine tool, it uses 1.5 tons of steel for each machine tool. In fact, it saves 0.25 tons for each machine tool. As a result, it manufactures 10 more machine tools than originally planned. How many machine tools did it originally plan to build?

The actual steel used for each set: 1.5-0.25 = 1.25 (tons), the actual total steel saved: 1.25 × 10 = 12.5 (tons), the original plan to build machine tools: 12.5 △ 0.25 = 50 (sets); answer: the original plan to build 50 machine tools

1. The school held the sports meeting, and planted a colored flag every 16 meters beside the 400 meter circular runway. Later, some colored flags were added, which shortened the distance between each two colored flags. One side of the starting point did not move. After the re insertion, it was found that five colored flags did not move. Q: what is the interval between the colored flags now?
2. Mark three times on a piece of wood with a red pen: the first time, the wood is divided into 12 equal parts, the second time, the wood is divided into 15 equal parts, and the third time, the wood is divided into 20 equal parts. How many pieces are sawed along these red marks?
3. A stationery shop sells pencils of 5 jiao each, and few people buy them. So the stationery shop sells them at a lower price. As a result, all the pencils in stock are sold out, and the total price is 31.93 yuan. How many pencils are in stock in this stationery shop? How much is each pencil?
4. Car a and car B are running backward on the road parallel to the railway, traveling 10 meters per second. A train comes to car a at a constant speed. It takes 9 seconds to drive next to car a, and then it takes 39 seconds to drive next to car B. find out the speed of this train
5. A goes from a to B, and B goes from B to A. after 14 minutes, the distance between them is 90 meters. It is known that the whole journey of a takes 24 minutes, and B travels 60 meters per minute. How many kilometers are there between a and B?
6. Party A and Party B walk from a and B at the same time. They can meet each other in 30 minutes. If Party A travels 12 meters more per minute and Party B travels 8 meters less per minute, they can meet each other in 29 minutes to find the distance between the two places
I can't do it. I can do four of them!

There are X students in one class and y students in three classes
（x+65）/y=2/1 （65+y）/x=3/1
By solving the above two equations, we get x = 39, y = 52
So there are 39 + 65 + 52 = 156

5 mathematical problem analysis, requires primary school formula steps:
1. The pasture is full of grass, and the grass grows at a constant speed every day. This pasture can feed 10 cows for 20 days, 15 cows for 10 days, and 25 cows for how many days?
2. There is a leak in a boat. Water enters the boat at a uniform speed. When the leak is found, some water has been put in. If there are 12 people scouring the water, they can finish it in three hours. If there are five people scouring the water, they can finish it in ten hours. Now it takes two hours. How many people do they need?
3. A piece of grass grows at the same speed every day. Now this piece of grass can feed 16 cows for 20 days, or 80 sheep for 12 days. If the grass consumption of one cow is equal to that of four sheep, how many days can 10 cows and 60 sheep eat together?
4. There are already some people queuing at a certain train ticket gate before the beginning of ticket checking. After the beginning of ticket checking, there are 10 people queuing for ticket checking every minute. One ticket gate can let 25 people check in every minute. If there is only one ticket gate, there will be no one queuing 8 minutes after the beginning of ticket checking. If there are two ticket gates, how many minutes after the beginning of ticket checking, there will be no one queuing?
5. There is a pasture where grass grows evenly every day. If 24 sheep eat grass for 6 days, they can eat it in 8 days. If 16 sheep eat grass, how many days?

1) 10 * 20 = 20015 * 10 = 150200-150 = 5050 / (20-10) = 5200-5 * 20 = 100100 / (25-5) = 5 (days) 2) 12 * 3 = 365 * 10 = 50 (50-36) / (10-3) = 236-2 * 3 = 3030 / 2 + 2 = 17 (people) 3) 16 * 20 = 32080 / 4 * 12 = 240 (320-240) / (20-12) = 10320-10 * 20 = 120120 / (10 + 60 / 4-10) = 8 (...)

Please list the formula
If the length of each side of a square test field is increased by 5 meters, the area will be increased by 875 square meters?

Let the length of a square be X
(x+5)^2-x^2=875
x^2+10x+25-x^2=875
10x=850
x=85
85 * 85 = 7225 square meters
So the original experimental field area is 7225 square meters

Solving practical problems with linear equation
With 100 yuan, I just bought 100 pens of three kinds, including 10 yuan for each gold pen, 3 yuan for each platinum pen and 0.5 yuan for each ballpoint pen. How many pens did I buy for each of the three pens?

Suppose x gold pens and Y platinum pens, then 100-x-y ballpoint pens
So 10x + 3Y + 0.5 (100-x-y) = 100
9.5x+2.5y+50=100
19x+5y=100
19x=100-5y=5(20-y)
So x can be divided by 5
Because y > = 0
So 5Y > = 0
19x+5y=100
So 19x

The cross section of a canal is trapezoidal, the area of known cross section is 0.78m2, the width of upper opening is 0.6m wider than the canal bottom, and the depth of canal is 0.4m less than the canal bottom

If the canal bottom is x m, then the upper entrance is (x + 0.6) m and the canal depth is (x-0.4). According to the meaning of the question, we get 12 (x-0.4) (x + X + 0.6) = 0.78, the solution is: x = 1 or x = - 1.6 (rounding off), the canal depth is 1-0.4 = 0.6 m, a: the canal depth is 0.6 M

Using the knowledge of grade nine to solve the application problems of quadratic equation with one variable
At the end of last year, the school library had 20000 books, which is expected to increase to 39200 by the end of next year

Let the average growth rate of these two years be X
2*(1+x)²=3.92
(x+1)²=1.96
x+1=1.4
x=40%
A: the average growth rate in the past two years is 40%

The application of one variable equation of degree one

There are several students who work voluntarily in the ceramic tile factory. If each of them moves 2 bricks, there are 6 bricks left. If each of them moves 4 bricks, they just finish moving. How many students are moving bricks? How many bricks are there?
There are X students
Because the number of bricks is always the same, 2x + 6 = 4x
-2X=-6
X=3
Number of bricks = 2x + 6 = 3 * 2 + 6 = 12
Problems deepen
When we go to the park for a spring outing in a certain grade, some people want to go boating. There are 6 people in each big boat and 5 people in each small boat. If we rent several small boats first, there are 4 people who can't go boating. If we rent the same number of big boats, there is only 4 people in one boat and there are two extra seats in the big boat. How many students are there in this grade?
Set began to rent x boats, a total of y students
5*x+4=y
6*(x-2)-2=y
The result is: x = 10. Y = 54

The calculation of equation of degree 1 with one variable

2 + B = 10, how much is B?

Mathematical univariate quadratic equation
Solve the following equation by factorization
What is the root of x2 + 4 = 4x; 9x2-16 = 0?

The first one: x = 2
x2-4x+4=0,(x-2)2=0,x=2
Second: x = plus or minus 4 / 3
(3x-4)(3x+4)=0
So I got the answer

Please list the formula If the length of each side of a square test field is increased by 5 meters, the area will be increased by 875 square meters?

Solving practical problems with linear equation With 100 yuan, I just bought 100 pens of three kinds, including 10 yuan for each gold pen, 3 yuan for each platinum pen and 0.5 yuan for each ballpoint pen. How many pens did I buy for each of the three pens?