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