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

Algebra.Com
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)   (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)   (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
RELATED QUESTIONS

Students of a class are made to stand in rows. if one student is Extra in each row,... (answered by ikleyn)
Students of the class are made to stand in rows if one student is extra in a row , there... (answered by ikleyn)
Students of a class are made to stand in rows . If 4 students are extra in a row , there... (answered by Paul)
a student of class 1 meditate stand in rows 4 students are less in each row there would... (answered by ikleyn)
Students of a class are made to stand in rows.If four students are extra in a row there... (answered by ankor@dixie-net.com)
A man is setting out 180 plants in rows, each row having the same number of plants in it. (answered by ptaylor)
Boys of a scout group want to stand in rows. If one scout is added in each row then... (answered by ikleyn)
at a school choir concert 256 students are standing in rows. if the number of students... (answered by Alan3354)
how many students are there in a class if 2 students remain after 4 equal rows of seats... (answered by stanbon)