Amarching 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?

There are 120 people in the marching band.

Step-by-step explanation:

Let no. of people in the band be x.

In the first rectangular arrangement,

Width of rectangle () = w people.

Length of rectangle () = (w-7) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width length

x =  (equation 1);

In the second rectangular arrangement,

Width of rectangle () = (w-3) people.

Length of rectangle () = (w-5) people

Therefore,

no. of people in the band(x) = Area of the rectangle = Product of width and Length

x = width length

x =  (equation 2);

Therefore, from equation 1 and equation 2 , we get,

Therefore,

w = 15  (equation 3)

From equation 1 and equation 3, we get

x =

x = 120.

Therefore,

no. of people in the marching band = 120 people