The sum of three consecutive odd integers is 189, what are the integers?

Question

16456 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-05-27T17:12:01

#61 , 63 # and #65 #

An odd number take the form: # 2k+1 #

Hence the next odd numbers must #2k+3 # and #2k+5 #

Sum means to add together:

#(2k+1) + ( 2k+3 ) + (2k+5) = 189 #

Colect like terms:

#=> 6k + 9 = 189 #

#=> 6k = 180 #

# => (6k)/6 = 180 / 6 #

#=> k = 30 #

#=> 2k+1 = (2*30)+1 = 61 #

Hence the odd numbers are #61 , 63 , 65 #

Answer 2 · 2018-05-27T17:22:27

See explanation below

stablish a first degree equation

"three CONSECUTIVE odd integers"

Let x, the first, x+2 is the next and x+4 is the next (because they are odd, and odd are build up in this way)

#x+x+2+x+4=189#

#3x=189-6=183#

#x=61#, the next is #63# and next is #65#