Given information:
- Each person in a group of teachers and students is given the same number of chocolates as the number of students.
- If 4 more students are added, then in order to have the same number of chocolates per person as earlier, 28 more chocolates are needed.

Let's solve this problem step by step.

Let's assume the initial number of students in the group is 'x'.
So, initially, the number of chocolates distributed would also be 'x' because each person is given the same number of chocolates as the number of students.

The total number of chocolates initially = Number of students × Number of chocolates per student = x × x = x^2

If 4 more students are added, the new total number of students in the group would be 'x + 4'.

According to the given condition, in order to have the same number of chocolates per person as earlier, 28 more chocolates are needed.

So, the new total number of chocolates = Total number of students × Number of chocolates per student

New total number of chocolates = (x + 4) × (x + 4) = (x + 4)^2

According to the given condition, the new total number of chocolates is 28 more than the initial total number of chocolates.

So, we can write the equation as:

(x + 4)^2 = x^2 + 28

Expanding the equation:

x^2 + 8x + 16 = x^2 + 28

Subtracting x^2 from both sides:

8x + 16 = 28

Subtracting 16 from both sides:

8x = 12

Dividing both sides by 8:

x = 12/8

x = 3/2

Since the number of students cannot be a fraction, we can conclude that our assumption is incorrect.

Let's assume the initial number of students in the group is 'y'.

So, initially, the number of chocolates distributed would also be 'y' because each person is given the same number of chocolates as the number of students.

The total number of chocolates initially = Number of students × Number of chocolates per student = y × y = y^2

If 4 more students are added, the new total number of students in the group would be 'y + 4'.

According to the given condition, in order to have the same number of chocolates per person as earlier, 28 more chocolates are needed.

So, the new total number of chocolates = Total number of students × Number of chocolates per student

New total number of chocolates = (y + 4) × (y + 4) = (y + 4)^2

According to the given condition, the new total number of chocolates is 28 more than the initial total number of chocolates.

So, we can write the equation as:

(y + 4)^2 = y^2 + 28

Expanding the equation:

y^2 + 8y + 16 = y^2 + 28

Subtracting y^2 from both sides:

8y + 16 = 28

Subtracting 16 from both sides:

8y = 12

Dividing both sides by 8:

y = 12/8

y = 3/2

Since the number of students cannot be a fraction, we can conclude that our assumption is incorrect.

Therefore,