Question

If the sum of three consecutive odd integers is 129, what are the integers?

Answer 1

`41, 43, and 45`

Explanation:

Let the smallest of the three consecutive odd numbers be `n`

Then the three odd numbers will be: `n, n+2, n+4`

We are told
`color(white)("XXX")n+(n+2)+(n+4)=129`

`rarrcolor(white)("XXX")3n+6=129`

`rarrcolor(white)("XXX")3n=123`

`rarrcolor(white)("XXX")n=41`

and the three consecutive odd numbers are `41, (41+2), (41+4)`

Answer 2

Let the first number be `omega`
The difference of consecutive odd numbers is `2`
So,the next two numbers are `omega+2` , `omega+4`

Then,

`rarr(omega) +(omega+2)+(omega+4)=129`

Remove brackets:

`rarromega +omega+2+omega+4=129`

`rarr3omega+6=129`

`rarr3omega=129-6`

`rarr3omega=123`

`rarromega=123/3=41`

So,`omega+2=41+2=43 , omega+4=41+4=45`

The three integers are `41,43 and 45`