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

Mar 5, 2016

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

#### Explanation:

Three consecutive odd integers can be denoted as:
$\left(x\right) , \left(x + 2\right)$ and$\left(x + 4\right)$

The sum $= 231$

So,

$x + x + 2 + x + 4 = 231$

$3 x + 6 = 231$

$3 x = 231 - 6$

$3 x = 225$

$x = \frac{225}{3}$

color(blue)(x=75

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

x+2; color(blue)(77 and

x+4;color(blue)( 79

Mar 5, 2016

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

#### Explanation:

Let the three odd numbers be $2 x - 1$, $2 x + 1$ and $2 x + 3$. (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 $231$

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

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

Hence $6 x = 228$ or $x = \frac{228}{6} = 38$ and numbers are

$2 \times 38 - 1$, $2 \times 38 + 1$ and $2 \times 38 + 3$

or $75$, $77$ and $79$.