Two consecutive odd integers have a sum of 48, what are the two odd integers?

1 Answer
Jan 27, 2016

Answer:

23 and 25 together add to 48.

Explanation:

You can think of two consecutive odd integers as being value #x# and #x+2#. #x# is the smaller of the two, and #x+2# is 2 more than it (1 more than it would be even). We can now use that in an algebra equation:

#(x) + (x + 2) = 48#

Consolidate left side:
#2x + 2 = 48#

Subtract 2 from both sides:
#2x = 46#

Divide both sides by 2:
#x = 23#

Now, knowing that the smaller number was #x# and #x = 23#, we can plug #23# into #x+2# and get #25#.

Another way to solve this requires a bit of intuition. If we divide #48# by #2# we get #24#, which is even. But if we subtract #1# from it, and add #1# as well, we can get the two odd numbers that are next to it.