Question

The sum of two consecutive odd integers is 92, what are the numbers?

Answer 1

`45+47= 92`

Explanation:

`color(blue)("Just using numbers")`
The next consecutive number is the 2nd number on so it is `"mid number "+-1`

`92/2+-1= (46-1) " and "(46+1) = 45" and "47`

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
`color(blue)("Using algebra")`

I have done this to start you thinking in a particular way!

You could be very fussy and use:
Let a number be `n`
Then it becomes an even number if you write it as `2n`
Thus the next number is odd. So `2n+1` is odd

Then as the next number `(2n+2)` is even the next odd number is `(2n+3)`.

However, you end up doing a conversion at the end as `n` is not the actual first number.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
This is better. It works just as well so state:

Let the first odd number be `n`
Then the next odd number is `n+2`

`=>n+n+2=92`

`2n+2=92`

Subtract 2 from both sides

`2n+0=92-2`

`2n=90`

Divide both sides by 2

`n=90/2=45`

So the second odd number is `45+2=47`

`45+47= 92`