Question

The sum of three consecutive odd integers is 189, what are the integers?

Answer 1

`61 , 63` and `65`

Explanation:

An odd number take the form: `2k+1`

Hence the next odd numbers must `2k+3` and `2k+5`

Sum means to add together:

`(2k+1) + ( 2k+3 ) + (2k+5) = 189`

Colect like terms:

`=> 6k + 9 = 189`

`=> 6k = 180`

`=> (6k)/6 = 180 / 6`

`=> k = 30`

`=> 2k+1 = (2*30)+1 = 61`

Hence the odd numbers are `61 , 63 , 65`

Answer 2

See explanation below

Explanation:

stablish a first degree equation

"three CONSECUTIVE odd integers"

Let x, the first, x+2 is the next and x+4 is the next (because they are odd, and odd are build up in this way)

`x+x+2+x+4=189`

`3x=189-6=183`

`x=61`, the next is `63` and next is `65`