The sum of 3 consecutive odd integers is 105, how do you find the numbers?

2 Answers
Apr 15, 2016

Answer:

#33, 35, and 37#

Explanation:

Let the middle number of the three consecutive odd numbers be #n#.
Therefore the other two numbers will be #n-2# and #n+2#

#color(white)("XXX")n-2#
#color(white)("XXX")n#
#color(white)("X")underline(+color(white)("X") n+2)#
#color(white)("XXX")3ncolor(white)("XXXX")=105#

#rarr n=35#
and the other two numbers are #33# and #37#

Apr 15, 2016

Answer:

33,35,37

Explanation:

First of all lets say the unknown numbers are #x-2, x and x+2#.
We can represent it like this because the question says that they are consecutive odd numbers, and by definition they will differ by 2 each time

By summing these terms together, we can solve for #x#:
#105=x-2+x+x+2#
#105=3x#
#x=35#
Now that we have #x#, we can say the the consecutive odd numbers are #35-2, 35# and #35+2#, which are 33,35,37