How do you find three consecutive odd integers with the sum of 273?

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Answer 1 · 2017-01-16T12:41:34

See entire solution process below.

First, let's name the three consecutive odd integers.

We can call the first integer #i#.

Then, because they are "consecutive odd integers" we need to add #2# and #4# to the first integer.

Therefore, the 3 consecutive odd integers are: #i#, #i + 2# and #i + 4#.

There three sum to 273 so we can write and solve for #i#:

#i + i + 2 + i + 4 = 273#

#i + i + i + 2 + 4 = 273#

#3i + 6 = 273#

#3i + 6 - color(red)(6) = 273 - color(red)(6)#

#3i + 0 = 267#

#3i = 267#

#(3i)/color(red)(3) = 267/color(red)(3)#

#(color(red)(cancel(color(black)(3)))i)/cancel(color(red)(3)) = 89#

#i = 89#

and

#i + 2 = 91#

and

#i + 4 = 93#

The three consecutive odd integers are:

89 + 91 + 93 = 273