Question

There are some students in group A and group B. If one student goes from group A to group B, then the number of students in both groups is the same. But one student goes from group B to group A, then the number of students in group A becomes twice of group B. Find the number of students in each group.

Answer 1

Let the number of students in Group A be x and in Group B be y.

If 1 student moves from A to B, both groups have the same number of students:

x − 1 = y + 1

x − y = 2    ...(1)

If 1 student moves from B to A, Group A becomes twice as large as Group B:

x + 1 = 2(y − 1)

x + 1 = 2y − 2

x − 2y = −3    ...(2)

Subtract Equation 2 from Equation 1 to eliminate x:

(x − y) − (x − 2y) = 2 − (−3)

x − y − x + 2y = 2 + 3

y = 5

Substitute y = 5 back into Equation 1:

x − 5 = 2

x = 7

7 students in Group A and 5 students in Group B.