Question

The sum of three consecutive odd integers is 195, what are the integers ?

Answer 1

`63,65,67`

Explanation:

Say that there is some odd integer `x`. We don't know the value of it yet, we just know that `x` is some odd integer.

The next consecutive odd integer would be `2` away, or `x+2`. The next would be `2` after that, or `x+4`.

Thus our three consecutive odd integers are `x,x+2` and `x+4`.

Since we know their sum is `195`, we can say that

`x+(x+2)+(x+4)=195`

Combine like terms and solve for `x`.

`3x+6=195`

`3x=189`

`x=63`

Hence the other two odd numbers are `x+2=65` and `x+4=67`.