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# Math Help

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A marching band is performing in a rectangular arrangement, with a width of w people. The length consists of seven less people, or w - 7. In the second stage of their performance, the band re-arranged to form a rectangle with a width of w - 3 people, and with a length of w - 5 people. How many people are in the marching band?

Jun 25, 2018

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The number of people  in the first formation  is   w ( w - 7)

The number of people in the second formation is  ( w - 3) ( w  - 5)

Since the number of people in each formation is the same, we can set these equal to solve for w.....

w  ( w  -7)  =  ( w - 3) ( w - 5)

w^2  - 7w  =  w^2  - 8w + 15     subtract w^2 from both sides

-7w  = -8w  + 15       add 8w to both sides

x  = 15

So....using either of the first two expressions....the number of people in the marching band  is

w  ( w  - 7)  =

15  ( 15 - 7)  =

15 * 8  =

120  people

P.S.  - check to see that  ( w - 3) ( w - 5)  gives the same result....

Jun 25, 2018