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

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

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Answer 1 · 2016-06-02T21:16:37

$45 + 47 = 92$ $45+47= 92$

Explanation:

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

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

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$Using algebra$ $color(blue)("Using algebra")$

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

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

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

However, you end up doing a conversion at the end as $n$ $n$ 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 $n$ $n$
Then the next odd number is $n + 2$ $n+2$

$\Rightarrow n + n + 2 = 92$ $=>n+n+2=92$

$2 n + 2 = 92$ $2n+2=92$

Subtract 2 from both sides

$2 n + 0 = 92 - 2$ $2n+0=92-2$

$2 n = 90$ $2n=90$

Divide both sides by 2

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

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

$45 + 47 = 92$ $45+47= 92$

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

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