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

May 27, 2018

$61 , 63$ and $65$

#### Explanation:

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

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

$\left(2 k + 1\right) + \left(2 k + 3\right) + \left(2 k + 5\right) = 189$

Colect like terms:

$\implies 6 k + 9 = 189$

$\implies 6 k = 180$

$\implies \frac{6 k}{6} = \frac{180}{6}$

$\implies k = 30$

$\implies 2 k + 1 = \left(2 \cdot 30\right) + 1 = 61$

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

May 27, 2018

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)

$x + x + 2 + x + 4 = 189$

$3 x = 189 - 6 = 183$

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