Current location - Training Enrollment Network - Mathematics courses - Math problems in the first grade of junior high school
Math problems in the first grade of junior high school
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

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

A lamp in Xiao Ming's house is broken, and now I want to choose one of two kinds of lamps. One is an energy-saving lamp with 1 1 watt (that is, 0.01kw), 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.

In order to save energy, a unit collects electricity charges 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

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.

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 is 5%, the sum of the unit prices of the two commodities will increase 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 10 people are transferred from workshop B to workshop A, then 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.

A rides a bike from place A to place B, and B rides a bike from place B to place A, both of which advance at a constant speed. You should know that they leave at 8: 00 a.m. at the same time, at 10 in the morning, they are still 36 kilometers apart, and at noon 12, they are 36 kilometers apart. How to 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.

1.A and B are both 180m in length. 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. Light two candles at the same time when there is a power failure, and blow them out at the same time when there is a call. Thick is twice as long as thin, and you can 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.

1.A and B are both 180m in length. 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.

2. Two candles of the same length, the thick one can burn for 3 hours, and the thin one can burn for 8/3 hours. Light two candles at the same time when there is a power failure, and blow them out when a phone comes in. It is twice as thick as it is thin, and the time of power failure is found.

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.

1. In another math test, the teacher gave 25 multiple-choice questions, each with four options, and only one option was correct. The teacher's grading standard is: 4 points for answering a question correctly, 1 point for not answering or answering a question incorrectly, and q:

(1) A classmate got 90 points. How many questions did this classmate answer correctly?

(2) A classmate got 60 points. How many questions did this classmate answer correctly?

2. Guangming Middle School organizes a spring outing for seventh-grade teachers and students. If you rent a few 45-seat buses, it is just full; You can rent one less bus for 60 seats, and there are 15 seats.

(1) Total number of teachers and students seeking to participate in spring outing

(2) It is known that the rental of 45-seat buses is 250 yuan per day, and the rental of 60-seat buses is 300 yuan per day.

What kind of bus can I rent to save money?

(3) If two kinds of buses are rented at the same time, how many buses are rented by the two kinds of buses respectively? Write a taxi plan.

The round table consists of a table top and four legs. If it is 1m cubic, you can use wood to make 50 tables of a round table, or 300 legs of a table. The existing 5m cubic timber, please design how much timber is used to make table legs and how many tables are made.

Please think after answering.

(1) What should be grasped in the process of establishing a linear equation model of one variable to solve practical problems?

(2) What are the steps to solve a linear equation with one variable?

4. There is a three-digit number, the sum of its digits is 16, and the decimal number is the sum of one digit and one hundred digits. If the hundred digits and one digit are reversed, the new number is 594 larger than the original number, so find the original number. (one yuan for one answer)

5. Divide 99 into 4 numbers, make the first number add 2, the second number subtract 2, the third number multiply 2, and the fourth number divide 2, and the results are all equal. How to divide it?

Answer:

1.( 1) Solution: Suppose the student answers X questions correctly, and the wrong answer is (25-X) according to the meaning of the questions.

4*X- 1*(25-X)=90

4*X-25+X=90

5*X= 1 15

X=23

(2) Solution: Suppose the student answers the X question correctly, and the wrong answer is (25-X) according to the meaning of the question.

4*X- 1*(25-X)=60

4*X-25+X=60

5*X=85

X= 17

2. According to the meaning of the question, if the 45-seat X bus can be filled, then the 60-seat X- 1 bus needs 15 empty seats.

45*X=60*(X- 1)- 15

45*X=60*X-60- 15

15*X=75

X=5

(1) The total number of participants in the spring outing is 45 *5 vehicles =225.

(2) The daily cost of 45 seats is 250 yuan *5 cars = 1250 yuan, and the daily cost of 60 seats is 300 yuan *(5- 1) cars = 1200 yuan, so it is more economical to rent 60 seats.

(3) It is most cost-effective to rent three cars with 60 seats 1 45 seats, with 3 * 300+1* 250 =1150.

Please adopt it.