In the first year of junior high school, three application problems for solving equations are helped

1. To build a highway, it takes 80 days for engineering team A to be contracted separately, and it takes 120 days for engineering team B to be contracted separately.

It is now contracted by two engineering teams and can be completed in a few days.

Set up two engineering teams to cooperate in contracting, which can be completed in x days. According to the title:

1/80+1/120）x=1

Solution: x=240 5=48 (days).

If the two teams have worked together for 30 days, and B has another task, and B completes the rest of the work, it will take a few days to repair the road.

The two engineering teams of A and B cooperated for 30 days, and the rest of the work was completed by the B team in x days

1/80+1/120）×30+（1/120）x=1

Remove the parentheses, simplify and move the items to:

1/120）x=1-5/8

Solution: x=3 120 8=45 (days).

It takes a total of 30 + 45 = 75 days to repair this road.

For a project, it takes 9 days for A to complete alone, 12 days for B to complete alone, and 15 days for C to complete alone. After C had been working for 3 days, A left for some reason, and B took over A's work, asking how many days it would take to complete five-sixths of the project.

It will take x days to complete the project 5 6, according to the title:

1/9+1/15）×3+（1/12+1/15）x=5/6

Remove the brackets and simplify it:

8/15 +（3/20）x=5/6

3/20）x=3/10

x = (3 10) 20 3) = 2 (days).

For a project, it takes 20 days for A to complete alone, and 25 days for B to complete alone, so A will do it for 2 days first, and then how many days will it take for A and B to complete the remaining part of the cooperation.

The remaining part of the cooperation between A and B will take x days to complete, according to the title:

1/20）×2+（1/20+1/25）x=1

Simplify, move items to:

9/100）x=1-1/10

9/100）x=9/10

x = 10 (days).

1. (1) (1 80 + 1 120) x = 1, the solution is x=482) (1 80 + 1 120) * 30 + 1 120x = 1, the solution is x = 452, (1 9 + 1 15) * 3 + (1 12 + 1 15) x = 5 6, and the solution is x = 2

20*2+(1 20+1 25)x=1, the solution is x=10

One. (1) Solution: Let the total amount of work be x.

x/(x/80+x/120)

x/x/48

2) Solution: Set x days to complete.

1-30 (1 120 + 1 80) = (x-30) 1 120x 75 two. Solution: It will take X days to complete.

5 6-3 (1 9 1 15) x (1 12 + 1 15) x 2 three. Solution: It will take X days to complete.

1-1/20×2=x（1/20+1/25)x＝10

1. Set up x times.

18+4x=2×（1+3x）

18+4x=6x+2

2x=16x=8

After going 8 times, there may be a situation where there is 1 white left and 18 sunspots left.

2. Solution: There are x kilograms of large watermelons.

7x/20-x/3=250-290×5/6x/60=250-290×5/6

x=250×60-290×0

x = 500 kg.

The first question is set to white x, black is 2x, a total of several y times, then.

2x-4y=18

x-3y=1

Finding y=8 (times) means that the answer is obtained after taking eight times.

In the same way, the second question, the big x catty, the small y catty.

x=500 (catty).

Solution: Suppose that the number of whites is x and the number of blacks is 2x, and after going to y times, there may be 1 white left and 18 blacks left.

x-3y=1①

3x-4y=18②

3, get: 3x-4y-3x+9y=18-1 3

5y=15y=3

Therefore, after going 3 times, there may be a situation where there is 1 white left and 18 sunspots left.

1 set: white: x black: 2x take n times.

2x-4n=18

x-3n=1

Result: n=8,x=25,2 Method 1: 290-250=4040

Set large watermelon: xkg small watermelon: ykg

x+y=800

Method 2: Set large watermelon: xkg small watermelon: ykg

Answer for yourself

1. This situation will occur after setting n times.

1+3n）*2=18+4n

n = 8 2, with n kg of large watermelon.

Solve n = 500

A and B are 8 kilometers apart, both of them set off at the same time, if they go in the same direction, A catches up with B; If they are walking in the opposite direction, meet in 1 hour, and find out what the speed of the two people is.

A train crosses two bridges at a speed of 840m per minute, the time to cross the second bridge is 4 seconds longer than the first bridge, and the second bridge is 100m shorter than 2 times, find the length of the two bridges.

Set x cubic meters as a tabletop. 5-x cubic meters to make table legs.

x*50*4=(5-x)*300

200x=(5-x)*300

2x=3(5-x)

2x+3x=15x=3

3 cubic meters for the tabletop, 2 cubic meters of wood for the legs, just 150 square tables.

Pedal boats are relatively cheap.

Pedal boats as much as possible.

And it has to be full. If there are x people sitting on a pedal boat, then the hand rowing boat is Y people.

5x+2y=52

y=(52-5x)/2

y min=4x max=8

Minimum rent = 8 * 160 + 4 * 105 = 1700 this.

x cubic meters for the tabletop, 5-x cubic meters of wood for the legs.

4*50x=300*(5-x)

200x=1500-300x

x=3 is exactly 3 square tables.

1705 yuan.

1.Solution: Set x cubic meters as the desktop, and Y cubic meters as the table legs

x+y=5x(1 50)=4y(1 300)The solution gives x= y=

2.Solution: The average cost of renting a pedal boat is 160 5 = 32 yuan per person, and the average cost per person is 105 3 = 35 yuan, so renting a pedal boat is relatively cheaper, and you should rent a pedal boat as much as possible, so renting a pedal boat is 52 5 = 10....

2. The remaining two people will rent 1 hand rowing boat, so the minimum rent is:

1) Set x cubic meters as the surface, 5-x cubic meters as the legs, and establish the equation.

50x：300（5-x）=1：4

200x=1500-300x

500x=1500

x=3 So 3m of wood for noodles and 2m of wood for legs.

Pedal boats are relatively cheap.

Pedal boats as much as possible.

And it has to be full. If there are x people sitting on a pedal boat, then the hand rowing boat is Y people.

5x+2y=52

y=(52-5x)/2

y min=4x max=8

Minimum rent = 8 * 160 + 4 * 105 = 1700

The mountain city of Huanshan is one of the eight scenic spots in Zichuan County. But it often doesn't appear once for several years. One day, Sun Gongzi Yu Nian was drinking upstairs with his friends in the same industry, and suddenly saw a lonely pagoda standing up on the mountain, high into the sky, everyone look at me, I look at you, and surprised and puzzled, thinking that there is no temple nearby.

After a while, I saw dozens of palaces, the tiles were turquoise, and the eaves were high up, so I knew that there was a "mountain market". Not long after, high and low walls appeared, six or seven miles long, and they looked like a city. Among them, there are those like pavilions, some like halls, and some like neighborhoods, all of which are clearly presented in front of you, and the number can be counted in billions.

Suddenly, a strong wind blew, and the whole city became obscured. After a while, the wind stopped, the sky cleared, and all the previous sights were gone, except for one tall building, towering as if it were connected to the sky, with five rooms on each floor, and the windows were open, and there were five bright places, and there was the sky outside. Counting with your finger layer by layer, it is no longer possible to count the number of layers.

The higher the room, the smaller the highlights; Counting to the eighth layer, the bright spot is only as small as a star; Further up, it is dimly indistinguishable, and its layers cannot be counted. People on the lower floors came and went in a hurry, some leaning (railings) and some standing, with different postures. After a while, the building gradually lowered and the roof could be seen; Gradually, it became the same as an ordinary building; Gradually, it became a high bungalow again; Suddenly, it shrank to the size of a fist, then to the size of a bean, and finally disappeared completely.

I also heard that there were people who got up early and rushed to see houses, markets, and shops on the hills, which were no different from the conditions of the earthly world, so people called it a "ghost market."

1.Nanchang, Wuhan.

Wenzhou 6-x 4+x

Hangzhou x 4-x

Therefore, after multiplying and simplifying the corresponding fare, we get 7600+200x yuan, where 0<=x<=4

2. x=4

3.7400 is clearly impossible.

The amount to be used for the construction of the house is $A.

1350x75x2/3=(1350x75-a)x(1+50%)

a=56250 yuan.

Solution: Set up gunboats to share x hours from the barrage boats.

90-18x=22x

40x=90

x = A: Gunboats share hours from the ship to stop the boat.

Let the common number of x hours be, then the equation is: 22x+18x=90. The solution equation is x=.

The total workload can be regarded as 1, let B complete y every day, 1, A and B cooperate for 6 days to complete the workload 1 3, A and B complete the workload 1 18 per day;

So A completes 1 18-y a day;

B, C cooperates in 2 days to complete 1 4 of the remaining tasks, B, and completes 2 3x1 4x1 2=1 12 of the workload every day

So C completes 1 12-y per day;

So the equation is obtained:

5x（1/18-y+y+1/12-y）=1-1/3-(1-1/3) (1/4)

Solve the equation to get x=7 180

A completed 1 60 (6+5) = 11 60

B completed 7 180 (6 + 2 + 5) = 91 180 C completed 2 45 (2 + 5) = 14 45

2. Set the single digit x, and the ten digit is 15-x

Equation 10 (15-x) + x - (10x + 15-x) = 27 is obtained and x = 6

15-x=9

So this two-digit number is 96

1.Let B work alone in x days to complete, and B will complete 1 x of the workload per day

A and B cooperate to complete 1 3 of the workload in 6 days, that is, A and B cooperate to complete the workload of 1 18 in one day, then A's work efficiency is 1 18-1 x

Then B and C cooperate for 2 days to complete 1 4 of the remaining tasks, that is, 1 6 of the total workload, then B and C cooperate to complete 1 12 of the total workload in 1 day, then C's work efficiency is 1 12 - 1 x

A and B cooperate for 6 days to complete 1 3 of the workload, and then B and C cooperate for 2 days to complete the remaining 1 4 of the remaining tasks, and the total workload is still 1 - 1 3 - 1 - 1 3) x (1 4) = 1 2, and the three people cooperate for 5 days to complete, and the equation can be listed as follows:

1/18 - 1/x）+ 1/x +（1/12 - 1/x）】x 5 = 1/2

Solution x =180 7

Count the rest yourself.

The answer I calculated was that A had done 33,180 of the total work, B had done 91,180 of the total work, and C had done 56,180 of the total work

2. A two-digit number, the sum of the single digit and the ten-digit number is 15, if the two-digit number obtained by the single-digit number and the ten-digit number is 27 smaller than the original two-digit number, find the original two-digit number.

Let the single digit be x and the tens digit be 15-x, which is 10 (15-x) + x = 150 - 9x

After the two-digit reversal, the new number is 10x + 15-x) = 15 + 9x

By the title, the column equation is.

150 - 9x）-（15 + 9x）= 27

The solution is x=6 and the tens are 9

The two-digit number is 96

15=6+9=7+8

87-78=9 false.

96-69=27 pairs.

A: The original tree was 96.

1. First of all, the amount of work completed by the last three people is 1-1 3-2 3*1 4=1 2.

The amount of work done by A = 1 3 * 1 2 + 1 2 * 1 3 = 1 3.

The amount of work done by B = 1 3 * 1 2 + 2 3 * 1 4 * 1 2 + 1 2 * 1 3 = 1 4.

C: The amount of work done = 2 3 * 1 4 * 1 2 + 1 2 * 1 3 = 5 12.

2. Let the unit digit of the original number be x, then the ten-digit number is 15-x, then the original number = 10 (15-x) + x, the number after the reversal = 10x + (15-x), according to the problem can get 10 (15-x) + x - [10x + (15-x)] = 27, solve this equation to get x = 6, then the original two digits are 96.