Ask for the application problems of the first semester of junior high school mathematics! Thank you!

1. The square of (1+x) = 1+44%.

Analysis: The average annual growth rate of green space area is x

After two years) (the area of green space increased by 44%), it is necessary to grasp the keywords of the topic.

So: annual growth rate: (1+x) two years: (1+x) (1+x) = (originally) 1 + (increase) 44%.

So wait until the above equation.

2. Set: the number of purchases last week x, the number of purchases this week x+2;

10 Analysis: (Each bottle is cheaper than Wednesday) (2 yuan more than last time) (2 more bottles of yogurt than last time) to grasp the keyword of the topic.

10+2 (money spent on Wednesday + extra money spent on Saturday).

10 x out of 10 is the unit price per bottle – that's cheaper than on Wednesday.

x+2 (number of bottles bought on Wednesday + number of bottles bought on Saturday).

So get the above equation.

The solution yields two values: x1=4, x2=-10 (rounded).

1) The quadratic equation for the same growth rate problem has a model a(1+x) =b

Solution: Suppose the average annual growth rate of green space area in these two years is x, according to the question, (1+x) = 1+44%, so 1+x= or 1+x= rounded), the solution is x=20%.

2) Suppose I bought x bottles on Wednesday, so each bottle ** is 10 x yuan, and on Saturday I spent a total of 12 yuan and bought (x+2) bottles, so ** is 12 (x+2) yuan, according to the title, 10, solve x=4

Pay attention to how to list algebraic formulas.

1+a)^2=

A = the second question A bottle for the first time and the unit price of B yuan for the second time.

a(b+a+2)b=12

I'll only do the second question.

In the second question, the price of the yogurt bought on Wednesday is x, and the number of bottles is y.

The number of yogurt bottles bought on Saturday was y+2The price is:

Column equation xy=10 (

Just solve it.

1. A correctly solves x=2 y=4 and brings in: 2a+4b=9 (1) B just copied the wrong c when solving the problem, so B's answer x=4 y=-1 should also satisfy ax+by=9, and substitute it: 4a-b=9(2).

From (1) 2-(2), b=1, a=

Then substitute x=2 y=4 into 3x-cy=-2 to get: 6-4c=-2 so c=2

2. Set the sum of the speeds to v1 when traveling in opposite directions

168+184) v1=4 v1=88, let the speed difference be x when traveling in the same direction

168+184) v2=16 v2=22Let one express train speed be x1 and the other fast train speed x2x1+x2=88(1).

x1-x2=22（2）

1)-(2), got.

x1=55 x2=33

3. Set X yuan for each piece of A, Y yuan for each piece of B, and Z yuan for each piece of C.

3x+7y+z=

4x+10y+z=

1) 3-(2) 2, got.

x+y+z=

Therefore, it costs a total of yuan to buy A, B, and C.

4. If the solution is the opposite of each other, then y=-x is substituted into the equation.

3x-5y=2m

2x+7y=m-18

3x+5x=2m

2x-7x=m-18

8x=2m

5x=m-18

The solution is m=8

3x-5y=16

2x+7y=-10

The solution yields x=2 and y=-2

1.Substituting two sets of solutions into the first equation gives 2a+4b=9,4a-b=9, solving the system of equations gives a=,b=1, and substituting the first set of solutions into the second equation gives 6-4c=-2, then c=1

2.(v1+v2)*4=168+184 and (v1-v2)*16=168+184, the values of v1 and v2 can be obtained by solving the equation.

3.Let the unit prices of A, B and C be x, y, and z, respectively, and the columnable equations are 3x+7y+z=, 4x+10y+z=

Get x+3y=

2 gets 2x+6y=

Get x+y+z=

4.If the solution is the opposite of each other, x=-y is substituted into the system of equations to get -6y=2m and 5y=m-18, and the new system of equations is solved to get m=27 4

It's a bit stingy to give only five points.

1.Substituting two sets of solutions into the first equation gives 2a+4b=9,4a-b=9, solving the system of equations gives a=9 4,b=0, and substituting the first set of solutions into the second equation gives 12+c=-2, then c=-14

2.Walking in the opposite direction is the length of the two cars and, walking in the same direction, I don't quite understand what it means3Let the unit prices of A, B and C be x, y, and z, respectively, and the columnable equations are 3x+7y+z=, 4x+10y+z=

Get x+3y=

2 gets 2x+6y=

Get x+y+z=

4.If the solution is the opposite of each other, x=-y is substituted into the system of equations to get -6y=2m and 5y=m-18, and the new system of equations is solved to get m=27 4

1.A's answer is correct, so one of the two sets of equations is solved by x=2, y=4 and substituted into the equation to get (1)2a+4b=9

6-4c=-2 Solve c=2

I have mistaken c, so it is still true to substitute x=4, y=-1 into ax+by=9.

So: (2) 4a-b = 9

Solve the system of equations (1) (2) and get a= b=1, so a= b=1 c=22If two cars are traveling in the opposite direction, it will take 4 seconds to leave from the meeting.

From this sentence, it can be seen that the sum of the speeds of the two cars is (168+184) 4=88m, and the speed of the fast train is x in 1 second

The slow speed is 88-x

x-(88-x)=(168+184) 16 solves x=55, the slow speed is 88-55=33, so the speed of the fast train is 55m per second, and the speed of the slow train is 33m per secondLet A and C be x,y,z yuan.

3x+7y+z=

4x+10y+z=

Solve x= z=2y

x+y+z==

4.The solutions of the system of equations 3x-5y=2m, 2x+7y=m-18 are opposite to each other, so x=-y

So 3x+5x=2m,2x-7x=m-18m=8x=2,y=-2

(1) The total number of 8th grade students in this school x <300

If you buy 60 more sticks, you can wholesale and reach 300 people, so the number of people to buy may be the minimum is 300-60 = 240, and the number of people is between 240 x <300.

2) The price for buying 6 sticks is the same as buying 5 sticks at the retail price, if you buy 60 sticks more, it is the retail price of 50 sticks, and 50 people are less.

It should be 240 + 60 = 300 people.

If you buy 60 sticks (there is a problem here), then you can pay according to the wholesale price, which also costs 120 yuan.

The number of 8th grade students is set to x.

1. If the number of 8th grade students is x, then x is greater than 240 and less than or equal to 300

2 120 x*5=120 (x+60)*6 The solution gives x equal to 300

...You tell me the topic first.

(1) The solution is x1=c, x2=m c

When x=c, left=c+mc, right=c+mc, left=right=right, so x=c is the solution of the equation.

When x=m c, left = m c + c, right = c + m c, left = right , so x = m c is the solution of the equation.

2) x-1+2 (x-1)=a-1+2 (a-1) from the above law x-1=a-1 or x-1=2 (a-1), so x=a or x=2 (a-1)+1=(a+1) (a-1).

x1=c, x2=m c

Just bring the solution into the equation.

2）x1=a，x2=[2/(a-)]1

(1) The solution is x1=c, x2=m c

2) x1=a ,x2=2 (a-1)+1 The solution is as follows: the original equation can be deformed to (x-1)+=(a-1)+We get x-1=a-1 or x-1=2 (a-1), i.e. x=a or x=2 (a-1)+1

Set up Xiao Zhang's house to the railway station x kilometers.

2/3*(x/40-x/80)=5/60

x/80=1/8

x=10 kilometers from Zhang's house to the railway station.

Taxi 80 km/h.

Set Xiao Zhang's house to the railway station is x kilometers.

then x 40-5 minutes = (2 3*x) 80

5 minutes for 1 20 hours.

So it counts as x=3km

1) Design: Spring outing separately rent 45-seater passenger car x volume.

According to the title: 45x=60(x-1)—30

15x=90

x=6 number of people on spring outing: 6x45=270

2) Set: Group of 45-seater car x volume, 60-seater car x +1 volume.

45x+60(x+1)=270

105x=210

x = 2 for 245 seats and 3 for 60 seats.

Rent: 2x250 + 3x300 = 1400

In the words of inequality:

Set up to rent 45 seats x cars, 60 seats x 1

45x＋60（x＋1）≥270

250x＋300（x＋1）＜1500

By x 2

By x 24 11

x takes 2 quantities for 245 seats and 3 quantities for 60 seats.

Rent: 2x250 + 3x300 = 1400

Hope to help you in time.

1) If x cars are used, then there are 45x=60(x 1) 30, and the solution is x=6. The number of participants is 270. (2) If you use a 60-seater Y car, there is 60Y 45 (Y 1) 270, and the minimum Y is 3, then the cost is 300 3 250 2 = 1400<1500, (in line with the title) So:

Rent 3 cars with 60 seats and 2 cars with 45 seats for a total fee of 1400.

1) (60 + 30) (60-45) = 6 vehicles 6 * 45 = 270 people.

2) Assuming 3 60-seater buses and 2 45-seater buses, check the calculation:

60*3+45*2=270 people correct.

Asking for money: 2 * 250 + 3 * 300 = 1400 yuan.

Question 1 Upstairs Solved Question 2: Set the distance x from somewhere along the way to the departure. Then there is: (90-x) 4=(90+x) 60 Solution: x= The distance is solved, the speed is known, and the time problem is solved.