The first volume of the seventh grade mathematics application questions and answers: 1- 10 questions.
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 produced for 9 days, and there are still 908 parts to complete the production plan. How many parts 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, A and B, are driving in opposite directions from two places 272 kilometers apart. Three hours later, the distance between the two cars is still 17 km. 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 6 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 jumped rope. The boys are divided into five groups to play football. How many people are there in each group on average?
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 did the canteen deliver?
The canteen brought x kilograms of flour.
3x-30= 150
3x= 180
x=60
The canteen brought 60 kilograms of flour.
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.
The seventh grade mathematics first volume application question and answer: 1 1-20 questions.
1 1, Li Shifu bought 72 meters of cloth and just made 20 adult clothes and 16 children's clothes. Each adult garment uses 2.4 meters, while each child garment uses how many meters of fabric?
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 50 kilometers per hour, B travels 40 kilometers per hour, and 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 respectively at the same time, headed for the other side, and met two hours later. If A and B start from A and go in the same direction at the same time, then A will catch up with B after 4 hours. Given the speed of Party A as 15 km/h, find the speed of Party 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 the original 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 football, 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. White light is low in price, but it consumes a lot of electricity. If the electricity bill is 1 yuan/(kwh), that is, 1 kwh 1 yuan, try to give Xiaoming some suggestions according to what he has learned in the third chapter of the textbook. What is the basis for choosing which lamps to buy?
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 =0.0735 X 24 hours = 1.764 yuan.
Monthly electricity charge = 1.764 X 30 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.
A= 1 163.265 hours
That is to say, when the light bulb can be used for 1 163.265 hours or 48.47 days, the money spent by the 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 Mexican consumers charge an average of 0.5 yuan per kilowatt hour in April, 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. Therefore, the ratio of delivery personnel to sales personnel is 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.
The seventh grade mathematics first volume application question and answer: 2 1-29 questions.
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=2.4
That's a power outage of 2.4 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=2.4
That's a power outage of 2.4 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). It is designed to produce m pieces of clothes and x pieces of clothes.
0.6x+ 1. 1(80-x)？ 70 ①
0.9x+0.4(80-x)？ 52 ②
Solve ①x? 36
②x？ 40 is 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). Option 1: 45? 36+50? 44=3820 (yuan)
Option 2: 45? 37+50? 43=38 15 (yuan)
Option 3: 45? 38+50? 42=38 10 (yuan)
Option 4: 45? 39+50? 4 1=3805 (yuan)
Option 5: 45? 40+50? 40=3800 (yuan)
29 Xiao Wang's home decoration. He went to the store to buy lamps. There are 100 watt incandescent lamps and 40 watt energy-saving lamps at the counter in the store. Their unit prices are two yuan and 32 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
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 chooses energy-saving lamps.