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

1 Answer
Jun 2, 2016

Answer:

#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#