Four math problems all solved with a one dimensional equation .

1: If there are x people in class A, the number of people in class B is (100-x). Establish the equation according to the second condition:

There are 42 people in 1 3 of the number of people in class A and 1 2 of the number of people in class B: x*1 3+(100-x)*1 2=42 and x=48 100-x=52

2: Let the train speed be x, then the train length is 6x: establish a relationship: 350 + 6x=20x to get x=25 car length 150

3: Let the speed of the plane be x, then (x+24)*(2+5 6)=(x-24)*3 solve x by itself, and the distance is the value of x to the front or back of the equation.

4: Same as three, but let the time be unknown x: let him take x minutes at a speed of 12 km/h.

Then according to 15 kilometers of hours, x-24 is used (20 minutes later, 4 minutes in advance, draw a number line chart to understand) minutes: 12x=15(x-24) solution x=120 minutes Here it should be noted that the unit is minutes, which should be the same as the units on both sides can be eliminated, if you don't understand, you can change it to hours: 12*x 60=15*(x-24) 60

The distance is 24 km.

1.If there are x people in class A, then there are (100-x) people in class B.

1/3x+1/2(100-x)=42

The solution is x=48So there are 48 people in Class A and 52 people in Class B.

2.Set the train length x meters.

x/6*20=350

The solution is x=105

So the train is 105 meters long.

3.The speed of the aircraft is set at x km h when there is no wind

17/6*(24+x)=3*(x-24)

The solution is x=840

So the distance is 3*(840-24)=2448 km.

1.The number of people in class A is x, and the number of people in class B is 100-x.

1/3x+1/2（100-x)=42

x=48 Class B Student: 100-48=52 (person) 2Set the speed of the train to be x and the train length to be 6x

350+6x=20x

x=25 train length: 25*6=150 (m).

3.Let the speed of the aircraft be x

x+24)*(2+5 6)=(x-24) 3x=168 Distance: 168*(2+5 6)=476 (km)4Set the time to x

12x=15（x-24）

x=120 Distance: 24 km.

1. Solution: If there are x people in class A, then there are (100-x) people in class B. From the inscription: 1 3x+1 2(100-x)=42

The solution is x=48

So there are 48 people in class A and 42 people in class B.

2.Solution: If the speed of the vehicle is xm s, the length of the vehicle is 6x.

From the title: 350 + 6x = 20x

Solution x=25

So the length of the car is 150 meters.

3.Solution: Let the speed of the aircraft be xkm h when there is no wind

From the meaning of the question, 17 6 (24 + x) = 3 (x-24) solution x = 840

Therefore, the distance between the two cities is (840-24)*3=2448km4Solution: Set the original scheduled time to x hours.

From the meaning of the question, 12x=15 (x-1 3-1 15) is solved x=2, so the distance between the two places is 12*2=24 kilometers.

Solution: A and B are xm apart

x ( solution: x=20

The time it takes for A to drive to place B is: 20 (

The time for A to leave place B is: 4-2=2h

So, ship A leaves place b: 2*(

This question is not clear!

According to the title, the speed of drowning is 5km.

I understand the meaning of the topic to mean that two boats A and B arrive at place B at the same time, and then A goes down the river, and B goes upstream, and when B drives out for 4 hours, ask A about the distance between ship A and place B.

s=vt=10*4=40m

It may also be that the distance between ship A and place B when B arrives at place C, but there is no mention of any condition in the distance of place C in the question stem, so it cannot be calculated.

Set the armoured ship to leave place b x kmBecause it was a trip down the river, A sailed a total of x (hours) from place B.

In addition, because the speed of the downstream is twice that of the countercurrent (10 5), the time taken to travel from A to B is 1 2 of the time taken by the countercurrent to go from B to A. Assuming that ship B returns to point A, it takes a total of 6 hours (4+10 5). So it took 2 hours to get from A to B, and 2 hours to get from B to C.

i.e. x (. Get x=20

This question can be seen as a chase problem similar to a circular runway: distance walked + distance traveled by car = total distance * 2

Solution: (1) Pick up 25 people to the destination first, and then the car returns (2) When the car returns, it meets the rest of the people, and then picks up 25 people to the destination again, and then returns again (3) The car returns for the second time to meet the rest of the people, and then picks up 25 people to the destination again, and then returns again.

4) The car meets the remaining 22 people on the third return and then takes them to their destination.

The total time is equal to the sum of the time of these four transfers, and you only need to find the time of each stage of the transfer once.

1. Rough processing x days, finishing 30-x days.

8x + solution gives x=5

2. The question does not explain how much wastewater is produced per month.

Set to treat x cubic meters of wastewater per month.

The first option costs 30,000+2x per month

The second option costs 14x per month

Subtract the two to see which is bigger.

Shejia bought x eggs.

Column: 12 30*x=14 30*x*2-96

Solution: x=180 (6 boxes).

Shejia bought x eggs.

Column: 12 30*x=14 30*x*2-96 solution: x=180 (6 boxes).

B is equivalent to buying 40 pieces for 24 yuan, with an average of one yuan, and the normal price is more than one yuan, which is not cost-effective.

Shejia bought x eggs.

Column: 12 30*x=14 30*x*2-96 solution: x=180 (6 boxes).

B spent 24 yuan to buy 40 eggs, an average of one egg yuan, the original price of one egg is more than one yuan, not cost-effective.

Actually, I don't understand why this problem needs to be a single equation.

Of course, the choice waited.

Question 2. Set the time for maintaining order to x.

3x+（12-x)x9=36

Well, I haven't done it in a long time.

Answer: (1) Teacher Wang should choose to take a detour to school 36 3 + 7 = 12 + 7 = 19 more than 15 minutes;

2) If the time in the order of Mr. Wang and others is 3 minutes.

3x+(36/3-6-x)*9=36x=3

（1）x=22/23

2)m=5/7 n=3/7

3) Let these three numbers be 2x, 3x, and 7x respectively

2x+3x+7x=144

x=12, so these three numbers are 24, 36, 84

4) What do you mean by "Team A remains the same".

According to other conditions, it can be solved:

Set Team A to win x games and draw Y games.

3x+y=22

x+y<=10

Since x and y must be integers, they can be solved to be x=7, y=1 or x=6, y=4

Solution: (1)1 5(2x-3)+3x-2 4=0, and the solution of x=11 34(2) 5n-2 power of 2a2b and the 2n-m power of 3a to the power of 1-m b are homogeneous terms.

2=1-m, 5n-2=2n-m, and m=-1 n=1 are solved

3) What does this number refer to? Is it to find these three numbers?

x=11/34

m=-1 n=1

Let the three numbers be 2x, 3x, 7x

Then 2x+3x+7x=144 gives x=12, so these three numbers are 2*12=24 3*12=36 7*12=84

The last question is to see if there is any missing information.

The basic solution of the application problem is to set what is x:

Let the profit margin at the beginning of the month be x, and set the purchase price at the beginning of the month as y (this y is to be eliminated, so it's okay), then the purchase price at the end of the month is: , and the sales price is y(1+x);

The profit margin at the end of the month is the sales price - the purchase price at the end of the month: y(1+x), excluding y1+, x=that is, 80%.