<h3>
Answers: 33, 35, 37</h3>
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Explanation:
Consecutive integers are integers like 1,2,3,... or 6,7,8... so they are integers that follow one after another.
Consecutive odd integers are sequences like 3,5,7,... or 21,23,35... meaning they are odd integers following one after another as close as possible.
If x is some integer, then 2x is always even and 2x+1 is always odd
let 2x+1 be that first odd integer
adding on 2 leads to the next odd integer: (2x+1)+2 = 2x+3
adding on another 2 leads to the next one: (2x+3)+2 = 2x+5
The three expressions
2x+1
2x+3
2x+5
represents three consecutive odd integers. They must add to 105
(2x+1)+(2x+3)+(2x+5) = 105
(2x+2x+2x)+(1+3+5) = 105
6x+9 = 105
6x = 105-9
6x = 96
x = 96/6
x = 16
Meaning that
2x+1 = 2(16)+1 = 33 = first odd integer
2x+3 = 2(16)+3 = 35 = second odd integer
2x+5 = 2(16)+5 = 37 = third odd integer
As a check
33+35+37 = 105
which confirms the answer
