Question

Find all sets of three consecutive integers whose sums are greater than 102 and less than 109

Answer 1

Let x be the number.

Then:
(x)+(x+1)+(x+2)>102
(x)+(x+1)+(x+2)<109

x+x+1+x+2
3x+3>102
3x>102-3
3x>99
x>22

3x+3<109
3x<109-3
3x<106
x<35.33

Therefore, the number can be bigger than 22 but less than 35.333 to meet the requirements.

Hope I helped :)