It takes x times to complete.
29.5-3 * 4 = 2.5 times
17.5=2.5x
x=7
Seven more shipments are needed to complete.
2. The trapezoidal site covers an area of 90 square meters, with an upper bottom of 7 meters and a lower bottom of 1 1 meter. How high is it?
Its height is x meters.
x(7+ 1 1)=90*2
18x= 180
x= 10
Its height is 10 meter.
A workshop plans to produce 5480 parts in April. It has been in production for 9 days, and 908 more are about to complete the production plan. How many pieces will be produced on average every day in these 9 days?
During these 9 days, X was produced every day on average.
9x+908=5408
9x=4500
x=500
During these nine days, an average of 500 were produced every day.
4. Two cars, Party A and Party B, are driving in opposite directions from two places 272km apart. Three hours later, the distance between the two cars is still 17km. A travels 45 kilometers per hour, and B travels how many kilometers per hour?
B travels x kilometers per hour.
3(45+x)+ 17=272
3(45+x)=255
45+x=85
x=40
B is driving at a speed of 40 kilometers per hour.
5. There are two classes in grade six in a school, and the average score of mathematics last semester is 85. There are 40 students in six classes (1) with an average score of 87. 1. There are 42 students in Class Six (2). What is the average score?
The average score is X.
40*87. 1+42x=85*82
3484+42x=6970
42x=3486
x=83
The average score is 83 points.
6. The school bought 10 boxes of chalk. 250 boxes were used, and there are 550 boxes left. How many boxes per box?
Average x boxes per box
10x=250+550
10x=800
x=80
80 boxes per box on average.
There are 200 students in the fourth grade. During extracurricular activities, 80 girls went to jump rope. The boys are divided into five groups to play football. How many people are in each group?
There are x people in each group on average.
5x+80=200
5x= 160
x=32
There are 32 people in each group on average.
8. The canteen brought 150 kg of rice, which was 30 kg less than the flour. How many kilograms of flour does the canteen send?
The canteen brought x kilograms of flour.
3x-30= 150
3x= 180
x=60
The canteen brought 60 kilograms of flour.
9. There are 52 peach trees and 6 rows of pear trees in the orchard. There are 20 more pear trees than peach trees. How many pear trees are there in each row on average?
There are x pear trees per row on average.
6x-52=20
6x=72
x= 12
There are 12 pear trees in each row on average.
10, the area of a triangle is 840 square meters, the base is 140 meters, and the height is how many meters?
The height is x meters.
140x=840*2
140x= 1680
x= 12
The height is12m.
1 1, Li Shifu bought 72 meters of cloth to make 20 clothes for adults and 16 clothes for children. Adult dresses are 2.4 meters each, and how many meters are children's dresses?
Each piece of children's clothing is made of x meters.
16x+20*2.4=72
16x=72-48
16x=24
x= 1.5
Each piece of children's clothing1.5m.
12, three years ago, my mother was six times older than my daughter. This year, my mother is 33 years old. How old is my daughter?
My daughter is x years old this year.
30=6(x-3)
6x- 18=30
6x=48
x=8
My daughter is 8 years old this year.
13. How long will it take for a car with a speed of 50 kilometers per hour to catch up with a car with a speed of 40 kilometers per hour that left two hours ago?
It takes x time
50x=40x+80
10x=80
x=8
It takes eight hours.
14. Xiaodong bought 3 Jin of apples and 2 Jin of pears at the fruit shop and paid 15 yuan. 1kg apples are more expensive than 1kg pears in 0.5 yuan. How much are apples and pears per kilogram?
Apple x
3x+2(x-0.5)= 15
5x= 16
x=3.2
Apple: 3.2
Pear: 2.7
15, A and B start from A and B at the same time, respectively, in opposite directions. A travels at a speed of 50 kilometers per hour, and B travels at a speed of 40 kilometers per hour. A reaches the midpoint 1 hour earlier than B. How many hours does it take for A to reach the midpoint?
X hours to reach the midpoint.
50x=40(x+ 1)
10x=40
x=4
A reaches the midpoint in 4 hours.
16, Party A and Party B set out from A and B at the same time, face to face, and meet two hours later. If A starts from place A and B goes in the same direction at the same time, then A will catch up with B after 4 hours. Given that the speed of A is 15km/, find the speed of B. ..
Speed x of b
2(x+ 15)+4x=60
2x+30+4x=60
6x=30
x=5
B's speed 5
17. Two ropes with the same length, the first one was cut15m, and the second one was 3m more than the first one. How long are these two ropes?
It turns out that these two ropes are each x meters long.
3(x- 15)+3=x
3x-45+3=x
2x=42
x=2 1
It turns out that the two ropes are each 2 1 m long.
18. A school bought 7 basketballs and 10 soccer balls and paid 248 yuan. As we all know, the price of each basketball is equivalent to the price of three footballs. How much is basketball and football each?
Every basketball x
7x+ 10x/3=248
2 1x+ 10x=744
3 1x=744
x=24
Each basketball: 24
Each football: 8
18 A light in Xiaoming's house is broken. Now I want to choose two kinds of lamps, one is an energy-saving lamp with 1 1 watt (i.e. 0.01/kw), and the price is 60 yuan; The other is a 60-watt (0.06 kW) white lamp, 3 yuan. These two lamps have the same lighting effect and the same service life. Energy-saving lamps are expensive, but they save electricity; Although white light is cheap, it consumes a lot of electricity. If the electricity bill is 1 yuan/(kwh), that is, 1 kwh and 1 yuan, try to give Xiaoming some suggestions according to what he has learned in the third chapter of the textbook. What can be used to choose which kind of lamp is reasonable?
References:
(1) 1 kw = 1000 watt
(2) Total electricity charge (RMB) = electricity charge per kWh (RMB/kWh) × bulb power (kW )× service time (hours)
(3) 1 kwh = 1 kilowatt continuous use 1 hour
Suppose the current electricity price is 1 kwh, and 3.5 yuan is needed.
If the power of each light bulb is 2 1 watt, the electricity consumption per hour is 0.02 1 kwh.
Electricity charge per hour = 3.5 yuan X 0.02 1 =0.0735 yuan.
Daily electricity charge = 0.0735x24 hours = 1.764 yuan.
Monthly electricity charge =1.764x30 days = 52.92 yuan.
This is a simple problem to solve the equilibrium point of a linear equation with one variable. The goal is to find each equilibrium point from several decisions and find a better decision from different equilibrium points.
Answer process:
Assuming that the usage time is one hour,
1 * 0.0 1 1 * A+60 = 1 * 0.06 * A+3
This equation means that energy-saving lamps and white lamps take an hour, and the two lamps consume the same amount of money. Solve equations.
A= 1 163.265 hours
That is to say, when the light bulb can be used for 1 163.265 hours, that is, 48.47 days, the money spent by two light bulbs is the same.
Then, if the life of the light bulb is less than 48.47 days, then the white lamp is more economical, and the life is more than 48.47 days, and the energy-saving lamp is more economical.
19 in order to save energy, a company charges electricity according to the following regulations every month: the electricity consumption does not exceed 140 kwh, and it is charged at 0.43 yuan per kwh; If it exceeds 140 degrees, the excess will be charged at 0.57 yuan per degree. If the average electricity bill charged by Mexican consumers in April is 0.5 yuan per kWh, how much should consumers pay in April?
Let the total power consumption be x degrees: [(x-140) * 0.57+140 * 0.43]/x = 0.5.
0.57 times -79.8+60.2 = 0.5 times
0.07x= 19.6
x=280
Step by step: 140*0.43=60.2
(280- 140)*0.57=79.8
79.8+60.2= 140
19 the ratio of delivery staff to sales staff in the home appliance department of a shopping mall is 1: 8. Due to the obvious increase in the purchase of home appliances this summer, the manager of the home appliance department transferred 22 people from the sales staff to deliver the goods. Results The ratio of delivery staff to sales staff was 2: 5. How many delivery staff and sales staff are there in the home appliance department of this shopping mall?
Suppose there are x delivery people and 8X sales people.
(X+22)/(8X-22)=2/5
5*(X+22)=2*(8X-22)
5X+ 1 10 = 16X-44
1 1X= 154
X= 14
8X=8* 14= 1 12
The home appliance department of this shopping mall used to have 14 delivery staff and 1 12 sales staff.
We are now promoting a certain commodity and reducing the price by 10%. In order to keep the sales amount unchanged, how many percent will the sales volume increase over the original price?
Assumption: increase by x%
90%*( 1+x%)= 1
Solution: x = 1/9
Therefore, the sales volume increased by11.11%compared with the original price.
2 1 The sum of the original unit prices of the two commodities is 100 yuan. Due to market changes, a commodity has decreased by 10%. B After the price adjustment of the commodity is 5%, the sum of the unit prices of the two commodities has increased by 2%. What are the original unit prices of A and B respectively?
If the original unit price of commodity A is X yuan, then B is100-X.
( 1- 10%)X+( 1+5%)( 100-X)= 100( 1+2%)
The result x = one in X=20 yuan.
100-20=80 B
The number of people in workshop A is 30 less than 4/5 of that in workshop B. If you transfer 10 people from workshop B to workshop A, the number of people in workshop A is 3/4 of that in workshop B. Find the original number of people in each workshop.
There are x people in workshop B. According to the equality of the total number, the equation is listed as follows:
X+4/5X-30 = X- 10+3/4(X- 10)
X=250
So the number of people in Workshop A is 250*4/5-30= 170.
Description:
The left side of the equation is adjusted first, and the right side of the equation is adjusted later.
23 A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which move at a constant speed, so that we can know that they will start at 8 o'clock in the morning at the same time, and they are still 36 kilometers apart at 10 in the morning and 36 kilometers apart at 12 at noon. How can we find the distance between a and b? (Equation)
Let the distance between a and b be x.
x-(x/4)=x-72
x=288
Answer: The distance between A and B is 288.
The length of 24 cars and B cars is 180m. If two trains are driving relatively, it takes * * *12s from the moment when the front and rear meet; If driving in the same direction, it takes 60 seconds from the front of car A to the rear of car B, and the speed remains unchanged. Find the speed of a car and b car.
The sum of the speeds of the two vehicles is [180 * 2]/12 = 30m/s.
Let the speed of a be x, then the speed of b is 30-X.
180*2=60[X-(30-X)]
X= 18
That is, the speed of car A is 18m/s and the speed of car B is12m/s..
Two candles of the same length, the thick one can burn for 3 hours and the thin one can burn for 8/3 hours. When the power goes out, two candles are lit at the same time, and when the phone calls in, they are blown out at the same time. The thick one is twice as long as the thin one. Find the time of power failure.
Suppose the blackout time is X.
Let the total length be 1, then the coarse firing is 1/3 and the fine firing is 3/8.
1-X/3=2[ 1-3X/8]
X=2. Four
Is the power failure 2. Four hours.
26. The length of cars A and B is 180m. If two trains are driving relatively, it takes * * *12s from the moment the head and tail meet; If driving in the same direction, it takes 60 seconds from the front of car A to the rear of car B, and the speed remains unchanged. Find the speed of a car and b car.
27. Two candles with the same length, the thick one burns for 3 hours and the thin one burns for 8/3 hours. When the power goes out, two candles are lit at the same time, and when the phone calls in, they are blown out at the same time. Thick is twice as long as thin, and you can find the time of power failure.
Note: explain the reason! ! !
List the solutions of linear equations with one variable! ! !
The sum of the speeds of the two vehicles is [180 * 2]/12 = 30m/s.
Let the speed of a be x, then the speed of b is 30-X.
180*2=60[X-(30-X)]
X= 18
That is, the speed of car A is 18m/s and the speed of car B is12m/s..
Supplementary answer:
Suppose the blackout time is X.
Let the total length be 1, then the coarse firing is 1/3 and the fine firing is 3/8.
1-X/3=2[ 1-3X/8]
X=2. Four
Is the power failure 2. Four hours.
It is known that a garment factory now has 70M, B fabric A and 52M fabric B, and it is planned to produce 80 sets of M, N, 0.6M, B material A and 0.9M material B to make a set of M garments, and 1. 1m material B to make a set of N garments.
1) suppose that x pieces of m clothes are produced, and write the inequality group about x.
2) What are the production schemes that meet the requirements?
3) If making a set of M clothes can benefit 45 yuan and N clothes can benefit 50 yuan, Q: Which shooting scheme can benefit the factory the most? What is the profit?
1). solution: suppose that x pieces of m pieces of clothing are produced.
0.6x+ 1. 1(80-x)≤70 ①
0.9x+0.4(80-x)≤52 ②
The solution is ①x≥36.
②x≤40 means 36≤x≤40.
2) Scheme 1: 36 sets of M clothes and 44 sets of N clothes.
Scheme 2: 37 sets of M clothes and 43 sets of N clothes.
Scheme 3: 38 sets of M clothes and 42 sets of N clothes.
Scheme 4: 39 sets of m clothes and 4 1 set of n clothes.
Option 5: 40 sets of M clothes and 40 sets of N clothes.
3). Scheme 1: 45×36+50×44=3820 yuan.
Scheme 2: 45×37+50×43=38 15 (yuan)
Scheme 3: 45×38+50×42=38 10 (yuan)
Scheme 4: 45×39+50×4 1=3805 yuan.
Option 5: 45× 40+50× 40 = 3,800 yuan.
When Xiao Wang decorated his home, he went to the store to buy lamps. There are 100 watt incandescent lamps and 40 watt energy-saving lamps in the counter of the store. Their unit prices are two yuan and thirty-two yuan respectively. It is understood that the lighting effect and service life of these two lamps are the same. It is understood that the electricity price in Xiao Wang is 0.5 yuan per kilowatt hour. When the service life of these two lamps exceeds how long, can Xiao Wang choose energy-saving lamps? Power consumption (kWh) = power (kW) × time
Solution:
It is cost-effective for Xiao Wang to choose energy-saving lamps when the time is x hours:
0.5 * 100/ 1000 x+2 & gt； 0.5*40/ 1000x+32
0.5 * 0. 1x+2 & gt； 0.5*0.04x+32
0.05x+2 >0.02x+32
0.05 x-0.02 x & gt； 32-2
0.03x >30
x & gt 1000
Answer: When the service life of these two lamps exceeds 1000 hours, Xiao Wang only chooses energy-saving lamps.
1. There is a wire. For the first time, less than half of it was used 1 m, and for the second time, half of it was used, and the remaining thread exceeded 1 m. As a result, there are still 2.5 meters left in the wire. How long is this wire?
2. Pour a bucket full of water in a cylindrical bucket with an internal diameter of 200mm into rectangular iron boxes with internal length \ width \ height of 300mm.300mm.80mm respectively, and fill them up. How high is the water in the cylindrical barrel?
The train was blocked halfway, delayed for 6 minutes, and then the speed was increased from 40 kilometers to 50 kilometers per hour. How many kilometers can I make up for the delay?
4. A seventh-grade (1) class of a school organizes extracurricular activities, prepares to hold a badminton competition, and goes to the store to buy badminton rackets and shuttlecocks. 25 yuan for each racket, 2 yuan for each ball. Store A said "Badminton and racket are 10% off", while Store B said "Buy one racket and get two shuttlecocks. (1) The school is going to spend all the money from 90 yuan to buy two shuttlecocks. (2) If you have to buy two pairs of badminton rackets, how many pairs should you buy in two stores?
Three students, A, B and C, donated books to children in poor areas. It is understood that the proportion of books donated by these three students is 5:6:9. If the sum of the books donated by two students, A, B and C, is twice as much as that donated by B, which is greater than 12, how many books did they donate respectively?
Reference answer:
1. Solution: This line was originally x meters long.
x-[ 1/2( 1/2X- 1)+ 1]= 2.5
X=4
2. solution: the height is Xmm
100 100лX = 300 300 80
X = 720Л
3. Solution: Walk X kilometers.
X/50=[X-(40 6/60)]/40
X=4
4. Answer: After 10% discount, the racket is 22.5 yuan/ball, which is 1.8 yuan/ball.
Racket 22.5.2 = 45 yuan Ball: (90-45)÷ 1.8=25 (only)
B: 25.2 = 50 yuan (send two balls)
Need to buy balls: (90-50)÷2=20 (only)
A * * * ball: 20+2=22 (only)
A can buy 25, and B can only buy 22.
So a is more cost-effective.
5. solution: every copy is X.
A: 5xb: 6xc: 9X
5X+9X=6X 2+ 12
X=6
So: A: 5.6 = 30 (Ben)
B: 6.6 = 36 (Ben)
C: 9.6 = 54 (Ben)
1. The patrol car travels 200 kilometers every day, and each patrol car can be loaded with gasoline 14 days. At present, there are five patrol cars, starting from place A at the same time. In order to let the three of them patrol as much as possible (and then return together), after arriving at B, Party A and Party B only leave enough gasoline for themselves to return to the base, and the surplus gasoline is supplied to other cars. What is the longest driving distance of the other three cars?
A and b run for 4 days. Leave four days of oil for the return trip, and the remaining 12 days of oil for the other three cars, so that the other three cars can run for five days, so that they can run as far as possible.
200 km times 9 equals 1800 km.
2. The sum of the ages of Party A and Party B this year is 63. When Party A's age is half of Party B's present age, Party B is exactly Party A's present age. How old is A and B this year? One: Solution: Suppose A is X years old this year and B is Y years old this year.
x + y = 63
y-(x- 1/2 y)= x
Solve it and get it.
x = 27
y = 36
A: A is 27 years old and B is 36 years old.
Two: Solution: Suppose A is X years old this year and B is Y years old this year. M years later, A is half the age of B this year.
x + y = 63
x + m = 1/2 y
y + m = x
Solve it and get it.
x = 27
y = 36
A: A is 27 years old and B is 36 years old.
Solution: Suppose B is x years old this year, then A is (63-X) years old this year.
1/2 x-(63-x)= 63-2x
X = 36 is obtained by solving.
So 63-x = 63-36 = 27.
A: A is 27 years old and B is 36 years old.
Student 4: Solution: According to the meaning of the question, the age of getting a B this year is:
63÷ (1/2÷ 2+1/2+1) = 36 (years old)
So A's age this year is 63-36 = 27 (years old).
A: A is 27 years old and B is 36 years old.
3. A national ministry has three organs, A, B and C, and the civil servants of these three organs are 88, 52 and 60 in turn. This year's institutional reform requires the three organs to lay off employees in the same proportion, and there are still 150 civil servants left in the three organs. So how many people are left in the C organ?
Solution1:x+52x/60+88x/60 =150, then x=45.
Solution 2: X+52x/60+88x/60 = (88+52+60)-150 Then x= 15.
4. Make a copy of the material. If you copy 30 words per minute, you can finish it in a few hours. When you copy to 2\5, the work efficiency will be increased by 40% due to changing the method. In this way, you can finish it half an hour in advance. How many words are there in this material?
If this material * * * has an X, then: X/30-30 = (X/30) * (2/5)+(X * 3/5)/(30 *140%).
Solution: x=5250
5. There are 400g of saline water with salt content of 15%. Teacher Zhang requires that the salt water concentration be 12%. A classmate added 1 10g water after calculation. Please verify whether the amount of water added by your classmates is correct by solving the equation.
Suppose x grams of water is needed, then: (400+x) *12% = 400 *15% gives x= 100.
In the pasture, the grass grows evenly every day. If it eats 36 sheep, it will eat grass in 8 days. If it eats 30 sheep, it will eat grass in 10 days. If it eats 6 cows, how many days can it eat grass? (It is known that three sheep eat 1 day of grass just like 1 head cow eats 1 day of grass. )
It is known that three sheep ate 1 day of pasture, which is exactly 1 day for cattle, so we can use conditions instead: 36 sheep ate pasture for 8 days, replaced by 12 cows, and ate pasture for 8 days, because the known conditions tell three sheep that 1 day ate pasture is exactly 6544. So we divide 36 by 3 and get 12. The problem is six cows, which is related to the result we just calculated, so we divide the condition by two at the same time to get six cows and eat the pasture in four days.
Xiao Li goes to school from home. When he walked at a speed of 75M/ min for 3 minutes, he found that walking at this speed would be 2 minutes late, so he changed the speed to 90M/ min and arrived 4 minutes earlier. When does he leave home before class?
Xiao Li goes to school from home. When he walked at a speed of 75M/ min for 3 minutes, he found that walking at this speed would be 2 minutes late, so he changed the speed to 90M/ min and arrived 4 minutes earlier. When does he leave home before class?
Suppose he starts at point X before class, then the distance is 75*(X+2).
75(X+2)=75*3+90*(X-3-4)
X=37
He should start at 37 before class.
A local train leaves from Station A at a speed of 48 kilometers per hour. 45 minutes later, an express train departs from Station A at a speed of 60 kilometers per hour, taking the same route as the local train. How many hours can the express catch up with the local train?
A local train leaves from Station A at a speed of 48 kilometers per hour. 45 minutes later, an express train departs from Station A at a speed of 60 kilometers per hour, taking the same route as the local train. How many hours can the express catch up with the local train?
Suppose you catch up in x hours.
X[60-48]=48*45/60
X=3
That is, catch up in three hours.
For two-digit numbers, the number of the tenth digit is twice that of the fourth digit. If the tenth digit is reversed from the fourth digit, the number obtained is 36 less than the original number. Find the original two digits.
For two-digit numbers, the number of the tenth digit is twice that of the fourth digit. If the tenth digit is reversed from the fourth digit, the number obtained is 36 less than the original number. Find the original two digits.
Let x be in ten positions and y in one position.
X=2Y
( 10X+Y)-36= 10Y+X
Simplified: 9X-9Y=36
X-Y=4