The students of a class are made to stand in rows. If 4 students are extra in each row, there would be 2 rows less. If 4 students are less in each row, there would be 4 rows more. How many students are there in the class?
Answers
Answer:
96
Step-by-step explanation:
Let x be a number of students in a row and y be a number of students in a column. Then the amount of kids is xy.
(x+4)(y-2)=(x-4)(y+4)=xy
xy+4y-2x-8=xy-4y+4x-16=xy
4y-2x-8= -4y+4x-16=0 add two first equations.
2x-24=0
x=12
4y-24-8=0
4y=32
y=8
xy=12*8=96
Answer:
96 students
Step-by-step explanation:
let no of rows = x
let no of students in each row = y
total no of students = xy
⇒ If 4 students are extra in each row, there would be 2 rows less
(y + 4) ( x - 2) = xy
xy - 2y + 4x - 8 = xy
4x - 2y - 8 = 0
2(2x - y - 4) = 0
2x - y - 4= 0
y = 2x - 4 ------{i}
⇒ If 4 students are less in each row, there would be 4 more rows.
(y - 4) (x + 4) = xy
xy + 4y - 4x - 16 = xy
-(-4y + 4x + 4) = 0
4(-y + x + 4) = 0
-y + x + 4 = 0 ------{ii}
from {i} and {ii}
-(2x - 4) + x + 4 = 0
-2x + 4 + x + 4 = 0
x - 8 = 0
x = 8
y = 2x - 4
y = 16 - 4
y = 12
total no of students = xy = 8×12 = 96 students