SOLUTION: Students of a class are made to stand in rows. if one student is Extra in each row, there would be 2 rows less in the arrangement. if one student is less in each row,there woul

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Question 1099228: Students of a class are made to stand in rows.
if one student is Extra in each row, there would be 2 rows less in the arrangement.
if one student is less in each row,there would be 3 rows more.
find the number of students in the class
Found 2 solutions by ikleyn, Edwin McCravy:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Exactly this problem with the given data was solved at the lesson
    - Had they sold . . ., Problem 4
in this site.

The answer is:   60 boys;  12  rows and  5  boys in each row.



Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
The original arrangement of the class is S students in each of R rows.
So SR = the number of students in the class.

The first new arrangement of the class is S+1 students in each of R-2 rows.
So (S+1)(R-2) also equals the number of students in the class.

The second new arrangement of the class is S-1 students in each of R+3 rows.
So (S-1)(R+3) also equals the students in the class.

Since the number of students is the same under each of the three
arrangements,

SR = (S+1)(R-2) = (S-1)(R+3)

SR =  SR-2S+R-2 =  SR+3S-R-3

Subtract SR from all three sides:

 0 =    -2S+R-2 =     3S-R-3 
 
So each of those are equal to 0

-2S+R-2 = 0    
 3S-R-3 = 0

Adding the two equations term by term:

  S -5 = 0
     S = 5

Substituting S = 5 in -2S+R-2 = 0 

-2(5)+R-2 = 0
  -10+R-2 = 0
    -12+R = 0
        R = 12

So the number of students is SR = (5)(12) = 60

Checking.

In the original arrangement there were 5 students in each of 12 rows.

In the first new arrangement there were 6 students in each of 10 rows.
That's 1 student more and 2 rows less than in the original arrangement. 

In the second new arrangement there were 4 students in each of 15 rows.
That's 1 student less and 3 rows more than in the original arrangement. 

Edwin