Elementary school math problems, equation solving, junior high school math problems, equation solvin

1): If they stand at opposite ends of the 100-meter runway and walk towards each other at the same time, ask how many seconds will they meet?

Let x seconds meet.

4x+6x=100

x 10 seconds.

2): If Xiao Ming is at the beginning of the 100-meter runway, and Xiao Gang is 10 meters ahead of him, ask when Xiao Ming can catch up with Xiao Gang?

Let X seconds Xiao Ming catch up with Xiao Gang.

4x+10＝6x

x 5 seconds.

Solution: (1) Set x seconds after meeting.

4x+6x=100

The solution is x=10

A: The two met 10 seconds later.

2) After setting x seconds, Xiao Ming can catch up with Xiao Gang.

4x+10=6x

Solve x=5 Answer: After 5 seconds, Xiao Ming can catch up with Xiao Gang.

Solution: (1) Let x seconds meet.

4＋6）x=100

10x=100

Solution, we get x=10

So, 10 seconds meet.

2) Set x seconds to catch up.

6－4）x=10

2x=10 to get x=5

So, catch up 5 seconds after the start.

1. Solution: Let the two meet after x seconds.

4+6）x=100

x=100/（4+6）

x=100/10

x=10A: After 10 seconds, the two meet.

2. Solution: Let Xiao Ming catch up with Xiao Gang after x seconds.

6-4）x=10

x=10/2

x=5A: After 5 seconds, Xiao Ming caught up with Xiao Gang.

Answer: After 5 seconds, Xiao Ming can catch up with Xiao Gang.

Met 10 seconds later.

Catch up after 5 seconds

Let's set the class size to x

There is the equation x 3+2=(x-9) 2

Solving x=39 also gives us that there are 15 books.

Binary equations: Let the number of students in the class be x, and the number of books in the batch be y, and list the binary equations.

y-2=x/3;(x-9)*2=y is solved to obtain x=12;y=6

That is, the number of students in this class is 12, and the number of books in this batch is 6.

The number of books x, the number of people y, two equations: y 3 + 2 = x, y 2-9 = x. The solution is x=75 and y=42

Let the last two digits be x, then hail will go.

2 (100+x)-7=10x+1

The solution is x=24

So this three-digit number is 124

If you don't understand, ask me again.

In general, in this case, it is necessary to consider that one of the numbers may be 0

If x=0, y is equal to 83.

As a result, you just count the numbers, and you find that you can't.

So it's time to consider negative numbers.

If x=-1

As soon as y is found, it = -84

It was established. So the answer is -85 or 83.

**Hello classmates:

2xy＋x＋y＝83

Multiply both sides of the equation by 2 to get: 2x(2xy x y) 2x834xy 2x 2y 166

4xy＋2x＋2y＋1＝167

2x＋1)(2y＋1)＝167

When x and y are integers, 167 is prime and can only be 1 167 or (1) (167).

When x 0, y 83, so x y 83

At x 1, y 84, so x y 85.

So x,y are integers, satisfying the equation 2xy+x+y=83, and the value of x+y is 83 or 85.

When x and y are rational numbers, consider it yourself by referring to the above process.

If the average weight of girls is x and the number of girls is y, then the average weight of boys is 5y 6, and the average weight of the class = the total weight of the class The number of students in the class = the average weight of boys + the average weight of girls and the number of girls Number of boys + number of girls = xy + xy 11 6y = 48, x=44

So the average weight of boys is 44kg

Here's the answer:

If the average weight of the girls in the class is x, then the boys are;

If the number of boys in the class is y, then the number of girls is;

Then, (average weight of boys * number of boys + average weight of girls * number of girls) (number of boys + number of girls), substitution can be done,; Eliminate y, i.e., ,; So the average weight of girls is 44kg, and the average weight of boys is: 44*.

Details can be added, and the famous teacher will explain it to you.

The number of boys in the class is x

80%x+x=48

Solve the following equations (write process, process!!

1）6x+1=-4

6x=-4-1

6x=-5x=-5/6

2）2x+3=x-1

2x-x=-1-3

x=-43）-3x+5=2x-1

3x-2x=-1-5

5x=-6x=6/5

4）3x-7+4x=6x-2

7x-7=6x-2

7x-6x=7-2

x=5（5）-1/3+x=2x

2x-x=-1/3

x=-1/3

6）7x+6=16-3x

7x+3x=16-6

10x=10

x=1（7）-3/4x+2=13-1/4x-3/4x+1/4x=13-2

1/2x=11

x=-228）5-3x=8x+1

8x+3x=5-1

11x=4x=4/11

9）x-1/3=8x+1

x-8x=1+1/3

7x=4/3

x=-4/21

10）-x=-2/5x+1

x+2/5x=1

3/5x=1

x=-5/3

11）3x-5=7+2x

3x-2x=7+5

x=12

Answer: (1) 6x+1=-4

Shift: 6x=-4-1

Merge: 6x=-5

So: x=-5 6

2）2x+3=x-1

Shift: 2x-x=-1-3

Merge: x=-4

3）-3x+5=2x-1

Shift: -3x-2x=-1-5

Merge: -5x=-6

So: x=6 5

4）3x-7+4x=6x-2

Shift: 3x+4x-6x=-2+7

Merge: x=5

5）-1/3+x=2x

Shift: -1 3=2x-x

Merge: x=-1 3

6）7x+6=16-3x

Shift: 7x+3x=16-6

Merge: 10x=10

So: x=1

7）-3/4x+2=13-1/4x

Shift: (-3 4) x + (1 4) x = 13 - 2 Merge: (-2 4) x = 9

So: x=-18

8）5-3x=8x+1

Shift: -3x-8x=1-5

Merge: -11x=-4

So: x=4 11

9）x-1/3=8x+1

Shift: x-8x=1+1 3

Merge: -7x=4 3

So: x=-4 21

10）-x=-2/5x+1

Shift: -x+(2 5)x=1

Merge: -(3 5)x=1

So: x=-5 3

11）3x-5=7+2x

Shift: 3x-2x=7+5

Merge: x=12

If you should be transferred to Team A x people, then you should be transferred to Team B 42 - x people (68 + x) 3 4 = 44 + 42 - x3(68 + x) = 4 (86 - x) 204 + 3x = 344 - 4x

3x + 4x = 344 - 204

7x = 140

x = 140÷7

x = 20

A = x = 20

B = 42 - x = 22

A: 20 people should be transferred to Team A and 22 people should be transferred to Team B.

Team A should be transferred x people.

3（68+x）/4=44+42-x

Solution x=20

42-20=22 people.

Answer: 20 people should be transferred to team A and 22 people should be transferred to team B.

It should be transferred to Team A x people.

3/4*(68+x)=44+(42-x)

x=20 42-20=22

20 people should be transferred to team A and 22 people from team B.

If you buy x pens, you buy 22-x ballpoint pens, and you can get x 102 23 from the solution

So you can buy 4 pens, 18 ballpoint pens: 3 pens, 19 ballpoint pens: 2 pens, 20 ballpoint pens: 1 fountain pen, 21 ballpoint pens.

Solution: If you buy a ballpoint pen x pieces, then buy a fountain pen (22-x) 2x * 90% + (22-x) * 8 * 80% 602x *

Negative sign change sign change ).

x 18 (calculate the infinite decimal why not take 17 is not the reason for rounding here to consider the practical problem can be checked When x takes 17, the calculated cost is yuan More than the maximum cost of 60 yuan so do not take) Scheme The number of ballpoint pens: x=18 then Fountain pen: 22-x=4 (Inspection:

18 * 2 + 4 * 8 = 36 + 32 = 68 yuan But because the ballpoint pen is nine percent off, the fountain pen is eight percent off, so 18 * 2 * yuan) is so detailed Not to adopt it is not very good

Let the ballpoint pen be x and the fountain pen y

5x+6y=120 solves the equation system to get x=12, y=10, so x=22-y (small one) and because 5* is less than or equal to 100, it is less than or equal to 100 (small two) and puts the younger generation into the smaller two to less than or equal to 100, so y is less than or equal to 3

In the same way, x is greater than or equal to 19, and in summary, x=19, y=3

Solution: Yuan Yuan.

Suppose you buy all ballpoint pens, yuan, but you need to buy a certain number of pens, so you can choose to buy one pen and 21 ballpoint pens.

In the case of the meta-column equation, if the purchase of fountain pens is x, then the ballpoint pen is 22-x x x and the integer starts from 1, x=1 satisfies.

x=2 satisfies.

x=3 satisfied.

x=4 satisfied.

x=5 is not satisfied.

7 for A and 5 for B.

Let A x B y.

Equations; x+1=(y-2)2

x-1=y+1

It should be solved!