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

Jun 2, 2016

$45 + 47 = 92$

#### Explanation:

$\textcolor{b l u e}{\text{Just using numbers}}$
The next consecutive number is the 2nd number on so it is $\text{mid number } \pm 1$

$\frac{92}{2} \pm 1 = \left(46 - 1\right) \text{ and "(46+1) = 45" and } 47$

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$\textcolor{b l u e}{\text{Using algebra}}$

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 $2 n$
Thus the next number is odd. So $2 n + 1$ is odd

Then as the next number $\left(2 n + 2\right)$ is even the next odd number is $\left(2 n + 3\right)$.

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

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

$\implies n + n + 2 = 92$

$2 n + 2 = 92$

Subtract 2 from both sides

$2 n + 0 = 92 - 2$

$2 n = 90$

Divide both sides by 2

$n = \frac{90}{2} = 45$

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

$45 + 47 = 92$