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

Question 199205: Students of a class are made to stand in rows.If four students are extra in a row there would be two rows less.If four students are less in a row there would be four more rows.Find the number of students in the class?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Students of a class are made to stand in rows. If four students are extra in a
row there would be two rows less. If four students are less in a row there
would be four more rows. Find the number of students in the class?
:
let s = number students in a row
let r = number of rows
then
No of students = rs
;
"If four students are extra in a row there would be two rows less."
(r-2)(s+4) = rs
FOIL
rs + 4r - 2s - 8 = rs
rs - rs + 4r - 2s - 8 = 0
4r - 2s = 8
2r - s = 4; simplified, divided by 2
:
"If four students are less in a row there would be four more rows."
(r+4)(s-4) = rs
rs - 4r + 4s - 16 = rs
rs - rs - 4r + 4s = 16
-4r + 4s = 16
-r + s = 4; simplified, divided by 4
:
Adding these two equations eliminates s
2r - s = 4
-r + s = 4
-------------
r = 8 rows
:
find s:
-8 + s = 4
s = 4 + 8
s = 12 students in a row
:
Find the number of students in the class?
8 * 12 = 96 students
:
:
See if that's true
"If four students are extra in a row there would be two rows less."
(12+4)*(8-2) =
16 * 6 = 96
and
"If four students are less in a row there would be four more rows."
(12-4)*(8+4) =
8 * 12 = 96
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