A math problem with two unknowns

1. Chickens and rabbits are in the same cage, with a total of 45 heads and 146 feet, how many chickens and rabbits are in the cage?

2. A factory bought a total of 56 tons of materials A and B, and used 9,860 yuan. If material A is 190 yuan per ton and material B is 160 yuan per ton, how many tons of each of the two materials are bought?

3. First-level students go to the canteen for a meeting, if every 4 people sit on a bench, there are 28 people who have no place to sit, and if 6 people sit on a bench, find the number of junior students and the number of benches

4. A factory bought a total of 56 tons of materials A and B, and used 9,860 yuan. If material A is 190 yuan per ton and material B is 160 yuan per ton, how many tons of each of the two materials are bought?

5. Two people in a unit A and B received a total of 9,000 yuan in cash last year and 12,700 yuan in cash this yearIt is known that the amount of cash received this year will increase by 50 for A and 30 for BHow much cash did the two of them get this year?

1) There are 3 times more male students than female students in the school's science and technology group, how many male students are there? How many male and female students are there? How many more male students than female students?

2) The number of students in the fourth grade of Yumin Primary School is double that of the fifth grade, how many students are there in the fourth grade? How many people are in the 4th and 5th grades?

A, B, and C solved a total of 100 math problems, each of whom solved 60 of them, and only one of them solved the problem as a problem, and the problem solved by all 3 people was called an easy problem. How many questions are (more than less)?

Solution: If the B railway is x kilometers long, then the C railway is (x+8) kilometers long, and the Jiahe railway is (2x-189) kilometers long.

2x-189+x+8+x=1191

x=3432x-189=497

A: The length of the first railway is 497 kilometers.

3x+y=16 This is called an indefinite equation, there is no unique solution, there are infinite solutions must be given an x, y equation can be calculated, such as 4x+2y=20 or the problem limits x, y are integers (positive integers), then take one by one. x=1, y=13, x=2, y=10, x=3, y=7, etc., and then select one group that meets the conditions of the question, which may be one group, or many groups.

This kind of problem should be 2 equations, then convert y to x, and then substitute another equation.

She Wang Gang ran for x minutes at a speed of 6m Cong Yuans, 6 60 x (10 x) 4 60 3000, and returned.

Solution: x 5, then the distance s s 6 60 5 1800 meters.

He ran x seconds when he was 6 seconds and a meter.

x+（3000-6x）/4=10*60

A: Each root is long and can be sawn into: 4 (sections), need to cut 3 times, 24 sections need steel bars: 24 4 6 (roots), each cut 3 times, need to cut: 3 6 18 (times).

B: Each one is 2 meters long, can be sawn into: 2 sections), need to cut 4 times, 25 sections need steel bars: 25 5 5 (roots), each cut 4 times, need to cut: 4 5 20 (times).

C: Each root is long and can be sawn into: 3 (segments), need to cut 2 times, 27 sections need steel bars: 27 3 9 (roots), each cut 2 times, need to cut: 2 9 18 (times).

In the same time, B can cut 20 times, and the other two people can cut 18 times each, so B is the fastest.

A24 (saw.)

B25 (2 saws.)

C-27 (saw.)

So B saws the steel bar the fastest.

A: 3 times each 4 stages 24 sections 6 roots 18 times B: 4 times each 5 stages 25 stages 5 roots 20 times C:

2 times per root, 3 stages, 27 stages, 9 roots, 18 times, so it can be seen that B is fast.

Set the unknown number according to your method.

At the same time, A, B and C sawed 24 sections, 25 sections, and 27 sections respectively x y z times.

The following equation is established from the number of roots of A, B, C, and saws.

24/4=x/3

25/5=y/4

27/3=z/2

x=18=zy=20, so B saw the fastest.

Because A, B, and C start and end at the same time. So:

Solution: It took X minutes for A, B and C to run out of sawing.

Then the velocity of A is: 24 (times) 18 x = 18 x

B speed: 20 x. C speed: 18 x.

Then the specific velocity: 18 x : 20 x : 18 x = 18 : 20 : 18

Known 20>18>18.

So B is the fastest!

Ask for adoption! (In order to solve the unknown number, I have been thinking about it for a long time!) ）

The sum of the speeds of two people is always equal.

The sum of the velocities of A and B = 400 24 = 50 3 (m s) The original velocity of A.

22/3（m/s）

Set the original velocity of the armor to x

then (x+2) 24=400

x=400÷24-2=44/3

A: The speed is 44 3m s

The sum of the speeds of two people is always equal.

Set the original velocity of the armor to x

x+(x+2)=400/24

x =22/3

A: The speed is 22 3m s

We use the hypothetical approach.

If the speed of A and B remains the same after the encounter, then after 24 seconds, A will be 24*2=48 meters away from the origin, and B will exceed the origin by 24*2=48 meters.

At this time, it happened that the two of them ran 2 laps, but B traveled 96 meters more than A, that is, the time of 2 laps was 24 seconds * 2 laps = 48 seconds and 96 meters more.

So the difference between the speed of A and B is 96 48 = 2 meters and seconds.

Look at the sum of speeds 400 24 = 50 3

According to the sum difference formula, the first velocity is (50 3-2) 2=22 3 meters and seconds, and if the equation is not used, the first velocity is x

x+(x+2)=400/24

x =22/3