Elementary 1 Mathematics Binary Equation Application Problems

1.To make a rectangular box with 20 sheets of white cardboard, prepare to divide these white cardboards into two parts, one part for the side and the other part for the bottom. It is known that each white cardboard can be made for 2 sides, or 3 for the bottom surface.

If 1 side and 2 bottom surfaces can be made into a packaging box, then how to divide the method so that the finished side and bottom surface are just matched?

2.The stadium circular track is 400 meters long, and A and B practice long-distance running and cycling at a certain speed. If they go in the opposite direction, they meet every 80 seconds, and if they go in the same direction, B catches up with A every 80 seconds.

3.A class of students went on an outing of 18 kilometers to Beishan. There is only one car, and it needs to be divided into two groups, group A takes the car first, and group B walks.

The car goes to place A, group A gets off and walks, the car returns to pick up group B, and the last two groups arrive at Beishan at the same time. The speed of the car is known to be 60 km h and the walking speed is 4 km hFind the distance from point A to the north mountain.

4.In the 11 rounds of the Dan Cup football tournament (i.e. each team needs to play 11 games), a win is worth 3 points, a draw is worth 1 point, and a loss is worth 0 points. The number of wins of the Guoxing Sangao club team is 4 times the number of losses, and the result is a total of 25 points.

5.It took four hours for a drug boat to go 70 nautical miles away from the water and return to the water by the same route after the mission was completed, to find out the speed of the drug boat in still water and the speed of the current.

6.Someone only has 2 yuan and 5 yuan in currency, he wants to buy a commodity worth 27 yuan, for some reason the merchant does not give him money, he needs to pay exactly 27, and asks how many payment methods there are.

7.The canteen has a batch of grain in stock, and if 140 kilograms are used per day, according to the estimated number of days, there is a shortage of 50 kilograms: if 120 kilograms are used per day, then there will be 70 kilograms left after the expiration, and it is estimated that the existing grain stock is 700 800 kilograms, but ** a week, can you test his estimate by calculation?

8.To manufacture a certain commodity, 1 person uses a machine and 3 people rely on manual work, and 60 pieces can be made every day; 2 people use the machine, 2 people rely on manual work, and 80 pieces can be made per day. May I ask how many pieces can be made per day by 3 people with a machine and one person by hand?

9.There are 83 students in classes A and B, 86 students in classes B and C, and 88 students in classes C and D. Find out how many people are in class A and B.

10.A and B run on the circular road at the same speed, facing each other every two minutes. Traveling in the same direction, meeting every six minutes, A is known to run faster than B. How many laps does A and B run per minute?

1) According to the title, the number of vehicles transporting A navel oranges is x, and the number of vehicles transporting B navel oranges is y, then the number of vehicles transporting C navel oranges is (20-x-y), then there are:

6x 5y 4(20-x-y)=100

2), from (1) know, the number of vehicles transporting a, b, c three kinds of navel oranges are x, -2x 20, x, from the meaning of the title: x 4, and -2x 20 4, the solution: 4 x 8, because x is an integer, so the value of x is , so there are 5 kinds of arrangement schemes.

Scheme 1: Shipment of 4 cars of A navel oranges, 12 cars of B navel oranges, and 4 cars of C navel oranges;

Scheme 2: Shipment of 5 cars of A navel oranges, 10 cars of B navel oranges, and 5 cars of C navel oranges;

Plan 3: Shipment of 6 cars of A navel oranges, 8 cars of B navel oranges, and 6 cars of C navel oranges;

Scheme 4: Shipment of 7 cars of A navel oranges, 6 cars of B navel oranges, and 7 cars of C navel oranges;

Plan 5: Ship 8 cars of A navel oranges, 4 cars of B navel oranges, and 8 cars of C navel oranges;

1. In order to encourage water conservation, a city stipulates that the part of the monthly water consumption of each household that does not exceed the standard water consumption shall be charged at RMB per cubic meter, and the excess part shall be charged at RMB 3 per cubic meter. Xiaohua's family used 9 cubic meters of water in April and paid the water bill.

Find the standard monthly water consumption of each household in the city.

2. The long-distance bus from A to B originally needed to travel 7 hours, but after the opening of the expressway, the distance was shortened by 45km, and the average speed increased by 30km per hour, and the result was that it only needed to travel 4 hours to arrive. Find the length of the highway between A and B.

3. Fill the container with 12 liters of alcohol, pour out a part and fill it with water; The second time I pour out the same amount of mixed liquid as the previous time, and then fill it with water, the water in the container is 3 times that of pure alcohol, and I ask how much alcohol is poured out the first time?

4. For a project, it takes 50 days for A to complete it alone, and it takes 60 days for B to complete it alone, and two people do it together, A takes 1 day off every three days, and B rests 1 day every five days, how many days does it take to complete all the work?

5. Two trains depart from two cities 600 kilometers apart at the same time and meet 3 hours after departure. If the first train departs half an hour before the second train, then meet an hour after the departure of the second train and ask how many kilometers each train travels per hour?

6. The automobile industry is one of the pillar industries of our city, and the output and benefits are increasing year by year According to statistics, in 2008, the annual output of a certain brand of cars in our city was 10,000 units, and by 2010, the annual output of the brand cars reached 100,000 If the average annual growth rate of the annual output of the brand of cars has remained unchanged for five years since 2008, how many units of the annual output of the brand cars in 2011?

7. The extracurricular table tennis team of the first (4) class of junior high school bought two pairs of table tennis boards, if each person pays 9 yuan, then 5 yuan, if each person pays 8 yuan, then there is still a shortage of 2 yuan, please ask questions according to the above scenarios and solve the equation in parallel

8. In the first 11 games of Group A of the National Football League, a team remained unbeaten in a row, accumulating a total of 23 points, according to the rules of the game, a win is worth 3 points, and a draw is worth 1 point, so how many games have the pair won?

9. Use white iron sheet to make canned food boxes, each iron sheet can make 15 box bodies, or 42 box bottoms, a box body and two box bottoms are matched into a set of canned food boxes, the existing 108 white iron sheets, how many pieces of box body are used, how many pieces of box bottom, can be just made into a complete set of canned food boxes?

10. Warehouse A stores 35 tons of grain, warehouse B stores 19 tons of grain, and now transfers 15 tons of grain, how many tons should be allocated to each of the two warehouses, so that the amount of grain in warehouse A is twice that of warehouse B?

1, the answer is 6

2. The answer is 375 km, 340 km.

3, the answer is 6

In order to encourage water conservation, a city stipulates that each household.

Let the distance between the two cities be x, and the speed of the aircraft when there is no wind is y, then x y+24=2+5 6

x/y-24=3

The solution is y=840 km.

So the flight distance between the two cities is 3 (840-24) = 2448 km.

The speed of the aircraft when there is no wind x, the distance between the two cities 3 * (x-24) 2 hours 50 minutes = 17 6 hours.

17/6*（x+24)=3*（x-24）

x = 840 kmh.

3*(x-24)=2448km.

Let the purchase price of commodity A be n yuan, and the purchase price of commodity B be m yuan, and the system of equations will be obtained according to the question:

1+10%）n + 1+10%）m =490+ (1+10%）m =399

Solution: n = 209 and 1 11

m = 254 and 6 11

Solution: Let the purchase price of commodity A be x and the purchase price of B be y, and the first equation is x(1+10)+y(1+10)=490;

The second term equation x(1+10) 70 +y(1+10) 90% = 399 The first term, 11x+11y=4900, x = (4900-11y) 11 The second term, 77x+99y=39900

x=(4900-11y) 11 from the first term; Substituting the second equation is simplified to obtain 22y=39900-4900*7=5600, y=2800 11=:

Substituting the y-value into the first equation is calculated.

x=2100/11=

It can't be exhausted.

Let the purchase price of commodity A be X yuan; The purchase price of commodity B is Y yuan.

Let's solve it for ourselves.

Let the distance of A and B be x kilometers, the planned time is y hours, and the column equation is x 50 = y + 24 60 ...1)x/75=y-24/60 ..2) Lianli (1) (2), solution.

x=120 y=2

120 2 = 60 (kmh).

The product of two seemingly unknown numbers in the equation upstairs is not a single equation.

Solution: Let the time for him arrive on time be x minutes, and the speed of arriving on time is y kilometers per hour;

Then the distance he has traveled is xy;

The time it takes to get him late is (x+24) minutes; The known speed is 50km h. Then this distance is (x+24)*50;

The time it takes to get him early is (x-24) minutes; The speed is known to be 70km h. Then this distance is (x-24)*70;

So we get two equations:

x+24）*50=xy；**1 formula(x-24)*70=xy; **2 solves this system of equations to get: x = 120 (minutes).

y=60（km/h）

A: He travels at a speed of 60 kilometers per hour and arrives on time.

Solution: Set A drink to survive x bottles, and B to produce Y bottles.

x+y=100···1

2x+3y=270···2

Transform 1 into x=100-y··· 3

Put 3 generations 22 (100-y) + 3y = 270

The solution is x=30 y=70

A produces 30 bottles of beverages and 70 bottles of beverages B.

Let A produce x bottles and B produce Y bottles, then the equation can be listed from the conditions: x+y=100, equation: 2x+3y=270, multiply the equation by 2, and get the equation :

2x+2y=200, equation - equation y=70, then x=30

Let's say A produces x bottles and B produces Y bottles.

The system of equations is 2*x+3*y=270 x+y=100

This results in x=30 y=70

Set up A beverage to survive x bottles, B beverage to produce Y bottles.

x+y=100···1

2x+3y=270···2

Transform 1 into x=100-y··· 3

Put 3 generations 22 (100-y) + 3y = 270

The solution is x=30 y=70

A: ......

If x sheets are used as the box body and Y sheets are used as the bottom of the box, there are 8x box bodies and 22y box bottoms.

x+y=190

8x=22y/2

The solution is x=110 and y=80

That is, 110 sheets are used for the body of the box, and 80 sheets are used for the bottom of the box.

2.Solution: There are x kilometers of flat roads and y kilometers of slopes.

From the title: x 60 + y 30 =

x/50+y/40=6

Solution: x=150

y=120A: 150 km for flat roads and 120 km for slopes.

3.Put x=1, y=0;x=2,y=3；x=3,y=28 into the system of equations.

a+b+c=0...1) 4a+2b+c=3...2) 9a+3b+c=28...3)

3)-(1)-(2) gives 4a=25+c....4) Simplification (2) yields 4a=3-2b-c

That is, 25+c=3-2b-c

Get c+b=-11

That is, a = 11 substitute a = 11 into (2).

The solution yields b = -30

That is, the function c=19 is explained by .

y=11x squared -30x+19 substitutes x=-1 into y= (1).

x+y+z=6 (2)

3x-y-z=-2 (3)

2) + (3) get:

4x=4x=1

1)-(2) De:

x+2y=5

y=2 is substituted into (2) to get:

The solution of the system of equations z=3 is: x=1;y=2；Z=3 is finished, I wish you a happy study.

If you don't understand, you can ask.

When they meet again, only when B runs one lap more distance than A.

400 (290-250) = 10 minutes.

Solution: Let's say that after X minutes, the two meet again.

290-250）x=400

40x=400

x=10A: The two meet again after 10 minutes.

Set S minutes after the two people meet again, B runs 1 lap more than A, which is the so-called super lap, that is, 250s + 400 = 290s

s=10