Question

The sum of three consecutive odd integers is 231, how do you find the integers?

Answer 1

The integers are `75, 77` and `79`

Explanation:

Three consecutive odd integers can be denoted as:
`(x) , (x+2)` and`(x+4)`

The sum `=231`

So,

`x + x+2 + x+4 = 231`

`3x+6 = 231`

`3x = 231-6`

`3x = 225`

`x=225/3`

`color(blue)(x=75`

The integers are as follows:
`x; color(blue)(75`

`x+2; color(blue)(77` and

`x+4;color(blue)( 79`

Answer 2

Numbers are `75`, `77` and `79`.

Explanation:

Let the three odd numbers be `2x-1`, `2x+1` and `2x+3`. (These numbers have been chosen as these will always be three consecutive odd number for any natural number `x`).

As sum of these numbers is `231`

`2x-1+2x+1+2x+3=231` or

`6x+3=231` or `6x=231-3=228`

Hence `6x=228` or `x=228/6=38` and numbers are

`2xx38-1`, `2xx38+1` and `2xx38+3`

or `75`, `77` and `79`.