Santa sent a special group of elves to march in the Disney World Chrisas Day Parade. At the beginning of the ceremony, the elves formed a perfect square; that is, there were the same number of rows and columns. suddenly they changed formation and became a rectangle in which the number of columns of musicians was greater by 5 then it had been in the pprevious formation. how many elves were marching in the parade? plzzzzzzzzzzzzzzzzzzzzz heeeeeeeeeeelpppppppppppp
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Let positive integers x and y be the numbers of columns and rows in the rectangle formation..
In the square formation, the numbers of columns and of rows are each (x - 5)
Thus xy = (x - 5)²
Solving the equation for integers x and y:
y = (x - 5)²/x
y = (x² - 10x + 25)/x
y = x - 10 + 25/x
For y to be an integer, x must be either 5 or 25
For x = 05, y = 5 - 10 + 25/5 = 0, which is not a positive integer
For x = 25, y = 25 - 10 + 25/25 = 16 > 0
The number of elves in the parade is
xy = 25*16 = 400
In the square formation, the numbers of columns and of rows are each (x - 5)
Thus xy = (x - 5)²
Solving the equation for integers x and y:
y = (x - 5)²/x
y = (x² - 10x + 25)/x
y = x - 10 + 25/x
For y to be an integer, x must be either 5 or 25
For x = 05, y = 5 - 10 + 25/5 = 0, which is not a positive integer
For x = 25, y = 25 - 10 + 25/25 = 16 > 0
The number of elves in the parade is
xy = 25*16 = 400