Boys of a scout group want to stand in rows.

Question

Boys of a scout group want to stand in rows. If one scout is added in each row then number of rows will be reduced by two, but if one scout is reduced from each row, we will need three more rows. What is the total scout count in the group?

Answer 1

Let's let 

x = # scout in a row

y = # rows

 

The total number of scouts is xy

 

But if we add a scout to each row we reduce the number of rows by 2

(x+1)(y-2)

 

If we reduce the scouts in a row by 1, then we increase the number of rows by 3

(x-1)(y+3)

 

Each of these products should be equal

 

(x+1)(y-2) = xy

(x-1)(y+3) = xy

 

Foil the left side of each equation

 

xy + y - 2x - 2 = xy  

xy - y + 3x - 3 = xy

 

Since there is an xy on each side of the equations,

y - 2x-2 = 0

-y + 3x- 3 = 0

 

We can use the elimination (or addition) method to combine these two equations

 

x-5 = 0

x = 5

 

and since y - 2x - 2 = 0

y - 2(5) - 2 = 0

y-12=0

y = 12

 

xy = 60

 

There are 60 scouts, originally arranged in 12 rows of 5

If we add one scout to each row, we can reduce the number of rows by 2 --> 6(10)= 60

If we remove one scout from each row, we need 3 more rows --> 4(15) = 60