The five consecutive integers are -2, -1, 0, 1 and 2.
What are the values of the integers?
Given that;
The sum of five consecutive integers equals 5.5 times the middle integer.
Since the integers are consecutive, let the integer be;
x, x+1, x+2, x+3 and x+4.
Now, sum of the integers equals 5.5 times the middle integer.
Middle integer is x+2.
Hence we have;
x + x+1 + x+2 + x+3 + x+4 = 5.5( x+2 )
x + x+1 + x+2 + x+3 + x+4 = 5.5x + 11
We collect like terms
x + x + x + x + x - 5.5x = 11 - 1 - 2 - 3 - 4
5x - 5.5x = 1
-0.5x = 1
x = -( 1 / 0.5 )
x = -2
Since our integers are; x, x+1, x+2, x+3 and x+4.
We substitute in the value of x
x = -2
x+1 = -2 + 1 = -1
x+2 = -2 + 2 = 0
x+3 = -2 + 3 = 1
x+4 = -2 + 4 = 2
Therefore, the five consecutive integers are -2, -1, 0, 1 and 2.
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