First odd integer: 2k+1 (note: using 2k+1 insures it is an odd integer)
Second odd integer: 2k+3
Third odd integer: 2k+5
First + Second + Third = 117
2k+1 + 2k+3 + 2k+5 = 117 substituted for First, Second, and Third
6k + 9 = 117 added like terms
6k = 108 subtracted 7 from both sides
k = 18
First: 2k + 1 = 2(18) + 1 = 36 + 1 = 37
Second: 2k + 3 = 2(18) + 3 = 36 + 3 = 39
Third: 2k + 5 = 2(18) + 5 = 36 + 5 = 41
Answer: 37, 39, 41
