Final answer:
The problem requires setting up a system of equations to solve for the number of students in two examination rooms, A and B, based on the given conditions. After solving the equations, it is found that room A initially has 35 students and room B has 25 students.
Step-by-step explanation:
We can solve the problem involving the two examination rooms, A and B, using a system of equations. Let's denote the number of students in room A as x and the number of students in room B as y. According to the problem, when 10 candidates are moved from A to B, both rooms have the same number of students. Hence, the first equation is:
x - 10 = y + 10
The second condition states that when 20 candidates are moved from B to A, the number of students in A is double the number of students in B. This leads to the second equation:
x + 20 = 2(y - 20)
Now, let's solve this system of equations:
- Step 1: Simplify both equations to find a relationship between x and y.
- Step 2: Isolate y in the first equation to get y in terms of x.
- Step 3: Substitute the expression for y from the first equation into the second equation.
- Step 4: Solve the resulting single variable equation for x.
- Step 5: Substitute the value of x back into the original equation to find the value of y.
By following these steps, we find the solution to the system, which gives us the number of students in room A and room B before any students were transferred. By solving the equations, we can conclude that the number of students in room A is 35 and the number of students in room B is 25.