Question

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

Answer 1

26

Explanation:

Let the three consecutive nos are `(x-1)`, `(x)` & `(x+1)`.

As per question,

`(x-1) + (x) + (x+1)` = 75

`3x` = 75

`x = 75/3 = 25`

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

Answer 2

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`:

`(x - 4) + (x - 2) + x = 75`

`x - 4 + x - 2 + x = 75`

`x + x + x - 4 - 2 = 75`

`3x - 6 = 75`

`3x - 6 + 6 = 75 + 6`

`3x = 81`

(3x)/3 = 81/3#

`x = 27`