SOLUTION: Students of a class are made to stand in rows . If 4 students are extra in a row , there would be two rows less . If 4 students are less in a row , there would be 4 more rows . Fin

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

Hence, the number of students is 96.



Paul.