https://file.aiquickdraw.com/mathbot/file/1726680805514rvaz5cvj.jpg

Let's solve this problem step by step.

Let:
- \( A \) be the number of students in Room A.
- \( B \) be the number of students in Room B.

### Condition 1:
- If 10 students are sent from Room A to Room B, the number of students in each room becomes equal.
  \[
  A - 10 = B + 10
  \]
  This simplifies to:
  \[
  A - B = 20 \quad \text{(Equation 1)}
  \]

### Condition 2:
- If 20 students are sent from Room B to Room A, the number of students in Room A becomes double the number of students in Room B.
  \[
  A + 20 = 2 \times (B - 20)
  \]
  Simplifying:
  \[
  A + 20 = 2B - 40
  \]
  \[
  A = 2B - 60 \quad \text{(Equation 2)}
  \]

### Solving the system of equations:
From **Equation 1**: \( A = B + 20 \).

Substitute this into **Equation 2**:
\[
B + 20 = 2B - 60
\]
Simplify:
\[
20 + 60 = B
\]
\[
B = 80
\]

Now, substitute \( B = 80 \) back into **Equation 1**:
\[
A - 80 = 20
\]
\[
A = 100
\]

### Final Answer:
The number of students in Room A is **100**, and the number of students in Room B is **80**.

Thus, the correct option is:
\[
\boxed{2) \ 100, 80}
\]

Would you like further details on the steps? 

Here are 5 related questions:
1. How do we solve simultaneous equations using substitution?
2. What are the different methods to solve a system of linear equations?
3. Can these types of problems be modeled graphically?
4. How can we check if the answer is correct in word problems like these?
5. How do algebraic expressions help in formulating real-life scenarios?

**Tip:** When solving systems of equations, always label your equations and carefully substitute values to avoid errors!

There are some students in two rooms A and B. If 10 students are sent from room A to room B, the number of students in each room becomes equal. While if 20 students are sent from room B to room A, the number of students in room A becomes double the number of students in room B. Find the number of students in room A and room B respectively.

Solve the problem of finding the number of students in two rooms using algebraic simultaneous equations. Learn step-by-step how to use algebraic concepts to form and solve equations. Suitable for students in Grades 7-10.

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