# 3 odd consecutive numbers have a sum of 75. What is the greatest number?

Mar 19, 2018

The greatest number would be $27$.

#### Explanation:

Let's put $x$ as the smallest odd number, $x + 2$ can be the second odd number, and $x + 4$ can be the third largest number.

(We found $x + 2$ and $x + 4$ because we are skipping the even numbers.)

So our equation would be:

$x + \left(x + 2\right) + \left(x + 4\right) = 75$

We can simplify that to

$3 x + 6 = 75$

Subtract $6$ from both sides...

$3 x = 69$

Divide both sides by three...

$x = 23$

Now we solve for $x + 2$ and $x + 4$

$2 + x = 23 + 2 = 25$

$4 + x = 23 + 4 = 27$

$27$ is the greatest number.

(To check, you can add all three numbers together... $23 + 25 + 27 = 75$)