Question 32117
<pre><b>Let the number of students in each row be x, and the number of rows be y.
xy = (x + 4)(y – 2) 
xy = (x – 4)(y + 4)
From xy = (x + 4)(y – 2):
xy = xy – 2x + 4y – 8
xy – xy = xy – 2x + 4y – 8 – xy
0 = -2x + 4y – 8
0 = x – 2y + 4
x – 2y + 4 – 4 = 0 – 4
x – 2y = -4
From xy = (x – 4)(y + 4):
xy = xy + 4x – 4y – 16
xy – xy = xy + 4x – 4y – 16 – xy
0 = 4x – 4y – 16
0 = x – y – 4
x – y – 4 + y + 4 = 0 + y + 4
x = y + 4
Substitute x = y + 4 into x – 2y = -4:
y + 4 – 2y = -4
-y + 4 = -4
-y + 4 – 4 = -4 – 4
-y = -8
y = 8
Substitute y = 8 into x = y + 4:
x = 8 + 4
x = 12
xy = (12)(8) = 96
<font color = green>Hence, the number of students is 96.</font>

Paul.