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

2 Answers

Apr 15, 2016

$33, 35, and 37$

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

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

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