# The sum of three consecutive odd numbers equal 255. What are those three number?

Jan 25, 2016

The numbers are
$83 , 85 , 87$

#### Explanation:

The three consecutive odd numbers can be denoted as :

color(green)(x, x+2 and color(green)( x+4

$x + x + 2 + x + 4 = 255$

$3 x + 6 = 255$

$3 x = 255 - 6$

$3 x = 249$

$x = \frac{249}{3}$

color(blue)(x = 83

The numbers are

$x = 83$

$x + 2 = 85$ , and

$x + 4 = 87$

Jan 25, 2016

Since the numbers are consecutive odd numbers, the relationship between the smallest number represented by x and the largest number would be x+ 4, since odd numbers each have a distance of 2 on the number line.

#### Explanation:

Assuming x represents the smallest number, x + 2 represents the middle number and x + 4 represents the largest number.

(x) + (x + 2) + (x + 4) = 255

3x + 6 = 255

3x = 249

x = $\frac{249}{3}$

x = 83.

The smallest number is 83. Therefore the numbers are 83, 85 and 87.

Practice exercises:

1. The sum of four consecutive even numbers is 516. Find the 4 numbers.

Hopefully you understand