Question 387988
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Hi,         
Let x, (x+1) and (x+2) represent the three consecutive integers
question states***
  x  + (x+1) + (x+2)= 417  the equation that will determine the three integers

Solving for x
 3x + 3 = 417
    3x = 414
     x = 138, the first of the three consecutive integers
the three consecutive integers are 138, 139 and 140 

CHECKING our Answer
  138 +  139 + 140 = 417