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

Nov 27, 2016

26

#### Explanation:

Let the three consecutive nos are $\left(x - 1\right)$, $\left(x\right)$ & $\left(x + 1\right)$.

As per question,

$\left(x - 1\right) + \left(x\right) + \left(x + 1\right)$ = 75

$3 x$ = 75

$x = \frac{75}{3} = 25$

Therefore the largest no = $x + 1$ = 25 + 1 = 26

Nov 27, 2016

The largest or greatest number is 27.

The other two numbers are 23 and 25.

#### Explanation:

Let's call the largest odd number $x$ because this is what we are solving for.

If $x$ is the largest odd number and these are consecutive odd numbers we must subtract $2$ and $4$ from $x$ to get all three consecutive odd numbers.

So, the three consecutive odd numbers are: $x - 4$, $x - 2$ and $x$.

We know their sum, or adding them together, is $75$ so we can write and solve for $x$:

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

$x - 4 + x - 2 + x = 75$

$x + x + x - 4 - 2 = 75$

$3 x - 6 = 75$

$3 x - 6 + 6 = 75 + 6$

$3 x = 81$

(3x)/3 = 81/3#

$x = 27$