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