Question

The sum of 3 consecutive odd integers is 105, how do you find the numbers?

Answer 1

`33, 35, and 37`

Explanation:

Let the middle number of the three consecutive odd numbers be `n`.
Therefore the other two numbers will be `n-2` and `n+2`

`color(white)("XXX")n-2`
`color(white)("XXX")n`
`color(white)("X")underline(+color(white)("X") n+2)`
`color(white)("XXX")3ncolor(white)("XXXX")=105`

`rarr n=35`
and the other two numbers are `33` and `37`

Answer 2

33,35,37

Explanation:

First of all lets say the unknown numbers are `x-2, x and x+2`.
We can represent it like this because the question says that they are consecutive odd numbers, and by definition they will differ by 2 each time

By summing these terms together, we can solve for `x`:
`105=x-2+x+x+2`
`105=3x`
`x=35`
Now that we have `x`, we can say the the consecutive odd numbers are `35-2, 35` and `35+2`, which are 33,35,37