A factory has two workshops, A and B, and the ratio of people in the two workshops is 3:2. Later, due to work needs, six people were transferred from workshop A to workshop B. At this time, the ratio of people in workshops A and B was 3:4. How many people are there in Workshop A and Workshop B?

Method 1: As shown in the figure,

Idea: first find out the corresponding points of six people who transferred from workshop A to workshop B, and then answer the questions.

According to the meaning of the question, the original number of people in workshop A accounts for 3/5 of the total number of people, and the original number of people in workshop B accounts for 2/5 of the total number of people.

After transferring 6 people from Workshop A to Workshop B, Workshop A now accounts for 3/7 of the total number of people, and Workshop B now accounts for 4/7 of the total number of people. So the corresponding score of 6 is: 3/5-3/7 or 4/7-2/5, the total number of people in two workshops, that is:

6÷(3/5-3/7)=35 (person),

Or 6÷(4/7-2/5)=35 (person)

So the original number of people in Workshop A: 35x3/5=2 1 (person)

Original number of people in Workshop B: 35X2/5= 14 (person)

A: The original number of workers in Workshop A is 2 1, and that in Workshop B is 14.

Method 2: Solve problems with simple equations. As shown in the figure below:

Let the total number of workers in Workshop A and Workshop B be X, then according to the original number of workers in Workshop A and Workshop B of 3:2, we can know that:

The original number of people in workshop A is 3/5 times, and that in workshop B is 2/5 times.

After transferring 6 people from Workshop A to Workshop B, the existing number of people in Workshop A is 3/7x and that in Workshop B is 4/7x.

According to the meaning of the question, a simple equation can be drawn:

3/5x-3/7x=6，x=35，

Or: 4/7x-2/5x=6, x=35.

So the original number of people in Workshop A is: 3/5x=3/5x35=2 1 (person).

The original number of people in Workshop B is:

2/5x=2/5X35= 14 (person)

A: A little.

Method 3: According to the meaning of the question, the basic properties of proportion are used to transform the proportion into a multiplication equation, and then one of the quantities is solved by equivalent substitution.

Because a: b =3:2, available, 3 b =2 a,

And from (A 1 6): (B 16) = 3: 4.

Available: (B 16) x3 = (A 16) x4.

Namely: 3b1018 = 4a124.

And because 3 B =2 A, then 2a1018 = 4a124,

2 A =42, solution A =2 1 (person).

Then the original number of people in workshop B is: 2 1X2÷3= 14 (people).

A: A little.

Note 1: Yesterday, a sixth-grade student asked me a practical question about comparison. I used three ways of thinking to solve this problem.

Note 2: It may be helpful to share the solution to this problem with you today. You are welcome to leave a message and give your best solution. Thank you!

Note 3: The picture was drawn by myself.