Question

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?

Answer 1

Answer:

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 ($w_{1}$) = w people.

Length of rectangle ($l_{1}$) = (w-7) people

Therefore,

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

x = width $\times$ length

x = $w\times (w-7)$  (equation 1);

In the second rectangular arrangement,

Width of rectangle ($w_{2}$) = (w-3) people.

Length of rectangle ($l_{2}$) = (w-5) people

Therefore,

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

x = width $\times$ length

x = $(w-3)\times(w-5)$  (equation 2);

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

$w\times(w-7)=(w-3)\times(w-5)$

$w^{2}-7w=w^{2} - 8w + 15$

Therefore,

w = 15  (equation 3)

From equation 1 and equation 3, we get

x = $15\times(15-7)$

x = 120.

Therefore,

no. of people in the marching band = 120 people