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At the beginning of a program, the 105 members of a marching band stand in a rectangular formation named Formation A. All of the band members then move into Formation B, which is a different rectangular formation with six more rows, but with two fewer band members per row. How many rows are in Formation A?

 Jul 6, 2018
 #1
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OK, this is what I think:

Since 105 =3 x 5 x 7 =15 x 7.

So, you would have 15 rows of 7 kids per row in Formation A.

In Formation B, you would have =15 + 6 = 21 rows with 5 kids per row. So that:

15 x 7 = 21 x 5

 Jul 7, 2018
edited by Guest  Jul 7, 2018
 #2
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Let  the  number of rows of the original formation  =  R

And let the  number of columns  =  C

 

So   R * C  = 105   ⇒    C  = 105/R       (1)    

 

Now...in the new formation.....the  number of rows  is  ( R + 6)  and the number of columns = (C - 2)

So we have that   

(R + 6) (C - 2)  = 105  ....  expand...   

R*C + 6C - 2R - 12  = 105   

105 + 6C - 2R  - 12 = 105     ...simplify...

6C - 2R =  12      sub  (1)  into this

 

6(105/R) - 2R  = 12       multiply through  by R

630  -  2R^2  = 12R     rearrange

2R^2  + 12R  - 630 = 0      divide through  y  2

 

R^2  + 6R  - 315   = 0   factor

(R + 21) ( R - 15)  = 0 

 

Set  both factors to 0  and solve for R

R  = -21   reject

R  = 15   accept

 

So....there were 15  rows  in Formation A

 

 

 

cool cool cool

 Jul 7, 2018

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