How do you find three consecutive odd integers such that the sum of the first and third equals the sum of the second and 25?

1 Answer
Jun 29, 2016

The three consecutive odd integers are 23, 25, 27.

Explanation:

Let $x$ be the first odd integer
So,
$x + 2$ is the second odd integer
$x + 4$ is the third odd integer

Let's us translate the given expression into algebraic expression:
sum of the first and the third integer equals the sum of the second and 25
that means :
if we add the first and third integer that is :$x + \left(x + 4\right)$
equals to the sum of the second and 25:$= \left(x + 2\right) + 25$

The equation will be stated as:

$x + x + 4 = x + 2 + 25$
$2 x + 4 = x + 27$
Solving the equation we have:
$2 x - x = 27 - 4$
$x = 23$

So the first odd integer is 23
The second integer will be $x + 2 = 25$
The third integer is $x + 4 = 27$

So the three consecutive odd integers are:23 ,25 ,27.