# How do you find three consecutive odd integers, whose sum is 57?

May 21, 2018

Let the first and the smallest integer be $x - 2$

Then... the second integer will be $x$

Then.... the third integer will be $x + 2$

Now... their sum is $57$

$x \cancel{- 2} + x + x + \cancel{2} = 57$

You get

$3 x = 57$

$x = \frac{57}{3}$

color(red)(x=19( that's the second integer)

First integer
$x - 2 = 19 - 2$

color(red)(x-2=17

Third integer
$x + 2 = 19 + 2$

color(red)(x+2=21

May 21, 2018

Three consecutive odd integers are $17 , 19 , 21$

#### Explanation:

Let the three consecutive odd integers are $2 x - 1 , 2 x + 1 , 2 x + 3$

Then , $2 x - 1 + 2 x + 1 + 2 x + 3 = 57 \mathmr{and} 6 x + 3 = 57$ or

$6 x = 54 \therefore x = 9 , 2 x - 1 = 17 , 2 x + 1 = 19 , 2 x + 3 = 21$

Three consecutive odd integers are $17 , 19 , 21$ [Ans]