Define Variables

Let the number of students in classroom A be $A$ and in classroom B be $B$.

$A, B$

Set up First Condition

If 7 students are shifted from A to B, A becomes $A - 7$ and B becomes $B + 7$. Given that B will have twice the number of students as A: $B + 7 = 2(A - 7)B + 7 = 2A - 14 \implies B - 2A = -21$

$B - 2A = -21$

Set up Second Condition

If 3 students are sent from B to A, A becomes $A + 3$ and B becomes $B - 3$. Both classrooms have the same number of students: $A + 3 = B - 3 \implies B - A = 6$

$B - A = 6$

Solve Simultaneous Equations

From $B - A = 6$, we get $B = A + 6$. Substituting this into the first equation: $(A + 6) - 2A = -21 \implies -A = -27 \implies A = 27$ Then $B = 27 + 6 = 33$.

$A = 27, \quad B = 33$

Calculate Positive Difference

The positive difference between the number of students in the two classrooms is: $B - A = 33 - 27 = 6$

$33 - 27 = 6$