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
2. 1) 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.
Now a commodity is reduced in price 10% for promotion. 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.
3. The sum of the original unit prices of commodities A and B is 100 yuan. Due to market changes, a commodity decreased by 65,438+00%. B After the price adjustment of commodities rose by 5%, the sum of the unit prices of the two commodities rose 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
4. The number of people in Workshop A is 30 less than 4/5 of Workshop B. If 10 people are transferred from Workshop B to Workshop A, then the number of people in Workshop A is 3/4 of 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.
5.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 they start at 8 o'clock in the morning, and they are still 36 kilometers apart at 10 in the morning, and 36 kilometers apart at noon 12. 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.
6 ..A The length of cars A and B is 180m. If two trains travel relatively, it takes * * *12s from the time when the front meets the rear; 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..
7. 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. It is twice as thick as it is thin, and the time of power failure is found.
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.
1. A group plans to make a batch of "Chinese knots". If everyone does five, it will be nine more than planned. If everyone does four, it will be less than planned 15. How many team members are there? How many Chinese knots do they plan to make?
There are x members in the team.
5x=4x+ 15+9
5x-4x= 15+9
8. A middle school organizes a spring outing for junior one students. It was originally planned to rent a number of 45-seat buses, but 15 people had no seats. If you rent the same number of 60-seat buses and have one more, the rest will be just full. We want to ask
(1) What is the number of students in Grade One? How many 45-seat buses were originally planned to be rented?
Solution: Rent 45-seat bus X and 60-seat bus (x- 1).
45x+ 15=60(x- 1)
Solution: x=5 45x+ 15=240 (person)
The number of students in Grade One is 240.
It is planned to rent five 45-seat buses.
9. Input a batch of accounting statements into the computer. It takes 20 hours for Party A to do it alone, and it takes 12h for Party B to do it alone. Now Party A works alone for 4 hours, and the rest is done by both parties. How long will Party A and Party B cooperate?
Solutions; Set to XH
1/5+ 1/20X+ 1/ 12X = 1
8/60X=4/5
X=6
The cooperation time of A and B is 6H.
The sum of 10.A, B and C is 53, so the ratio of A to B is 4: 3, C is 2 less than B, B is () and C is ().
Let a be 4X. Then b is 3X. C is 3X-2.
4X+3X+3X-2=53
10X=53+2
10X=55
X=5.5
3X= 16.5
3X-2= 16.5-2= 14.5
B is 16.5 and c is 14.5.
1 1. The length of the thick candle is the same as that of the thin candle. The thick candle burns for 5 hours and the thin candle burns for 4 hours. After the power failure, two candles are lit at the same time and put out at the same time after a call. It was found that the length of a thick candle was four times that of a thin candle. How long is the power outage?
Set the power outage for x hours. The thick candle burns 1/5 per hour, and the thin candle burns 1/4 per hour.
1- 1/5X = 4( 1- 1/4)
1- 1/5X=4-X
- 1/5+X=4- 1
4/5X=3
X= 15/4
12. For three digits, the number at 100 is larger than the number at 10 by 1 0, and the number at the third digit is 3/2 smaller than the number at 10. If the order of the three digits is reversed, the sum of the three digits and the original three digits is 1 17 1. Find this three-digit number
Let ten digits be x.
Then100× (x+1)+10x+3x-2+100 * (x+1)+/kloc-0+.
simplify
424x= 1272
So: x=3
This three-digit number is 437.
13. Three classes in Grade One of Senior High School donated books to Hope Primary School, and one class collected books 152 volumes. The number of books donated by class two is the average of three classes, and the number of books donated by class three is 40% of the total number of books donated by grade three. How many books did Class Three donate?
Solution: Set up 2 classes to donate X copies.
3x= 152+x+3xX40%
3x= 152+x+6/5x
3x-x-6/5x= 152
4/5x= 152
X = 190...(2) Class
190X3=570 (Ben)
14. The distance between a and b is 3 1 km. An hour later, A rode a bicycle from A to B, and B rode a motorcycle from A to B. It was known that A was driving at a speed of 12 km, and B was driving at a speed of 28 km. How many hours will it take to catch up with A after B leaves?
Let b catch up with equations a and b x hours after departure.
12 (x+ 1) = 28 x = 0.75 hours, or 45 minutes.
15. A cargo ship has a deadweight of 400 tons and a volume of 860m^3. Now it has to carry two kinds of goods, pig iron and cotton. The volume per ton of pig iron is 0.3m^3, and the volume per ton of cotton is 4 cubic meters. How many tons of pig iron and cotton can be loaded to make full use of the load and volume of this ship?
X tons of iron and 400-X tons of cotton.
0.3x+4*(400-x)=860
X = 200t tons
The answer is 200 tons of iron and 200 tons of cotton each.
16. A computer company sells two brands of computers, A and B, and sold 2,200 computers the year before last. Last year, the number of computers sold by A increased by 6% compared with the previous year, and the number of computers sold by B decreased by 5% compared with the previous year. The total sales of the two computers increased by 1 10. How many computers did A and B sell the year before last?
Suppose that computer A sold X units and computer B sold 2200-X units the year before last.
Last year, computer A was 1.06x, and computer B was 0.95 (2200-x).
1.06 x+0.95 *(2200-x)= 2200+ 1 10
x=2000
Then there are 2000 computers A and 200 computers B.
17. The area above the earth is about 7 1 times of the land area, and the surface area of the earth is about 5 1 100 million square kilometers. How big is the land area on the earth? (accurate to 0. 1 100 million square kilometers)
Let the area of the land be x.
X+7 1/29X=5. 1
X= 1.479
That is, the land area is:1.500 million square kilometers.
18. Pour a long cylindrical glass (filled with water) with an internal diameter of 90 mm into a rectangular iron box with a ground diameter of 13 1 * 1 mm and an internal height of 81mm. When the iron box is filled with water, how much does the water level in the glass drop?
Let the descending height be x.
The volume of falling water is equal to the volume of water in the iron box.
3. 14 * 45 * 45 * X = 13 1 * 13 1 * 8 1
X=2 18.6
The water level dropped by 2 18.6 mm.
19. A cylindrical glass with an inner diameter of 120mm and a cylindrical glass plate with an inner diameter of 300mm and an inner height of 32mm can hold the same amount of water. What is the internal height of the glass?
A cylindrical glass with an inner diameter of 120mm and a cylindrical glass plate with an inner diameter of 300mm and an inner height of 32mm can hold the same amount of water.
So the volumes of the two containers are equal.
The volume of a cylindrical glass disk with an inner diameter of 300mm and an inner height of 32mm.
V=π(300/2)^2*32=720000π
Let the internal height of the glass be x.
therefore
X*π( 120/2)^2=720000π
X = 200mm mm
20. Pour the full bucket of water in a cylindrical bucket with an inner diameter of 200mm into a rectangular iron box with internal length, width and height of 300mm, 300mm and 80mm respectively, and just fill it up. Find the water height of cylindrical bucket? (accurate to the millimeter. Dispatch 3. 14)
Let the height of the barrel be x.
3. 14 * 100 * 100 * X = 300 * 300 * 80
X=229
That is, the height of the bucket is 229 mm
2 1. It takes 12 days for a single construction team to lay an underground pipeline, and 18 days for a single construction team to maintain it. How many days will it take for the two engineering teams to construct from both ends at the same time?
Solution: suppose it can be laid in x days.
1/ 18X+ 1/ 12X = 1
2/36X+3/36X= 1
5/36X= 1
X= 1 divided by 5/36
X= 1 times 36/5.
X=36/5
That is 36/5 days.
1. To transport 29.5 tons of coal, transport it three times by a truck with a load of 4 tons, and transport the rest by a truck with a load of 2.5 tons. How many times will it take to complete?
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
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