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If the sum of three consecutive odd integers is 129, what are the integers?

2 Answers

Feb 3, 2016

$41, 43, and 45$

Explanation:

Let the smallest of the three consecutive odd numbers be $n$

Then the three odd numbers will be: $n, n+2, n+4$

We are told
$color(white)("XXX")n+(n+2)+(n+4)=129$

$rarrcolor(white)("XXX")3n+6=129$

$rarrcolor(white)("XXX")3n=123$

$rarrcolor(white)("XXX")n=41$

and the three consecutive odd numbers are $41, (41+2), (41+4)$

$phi$

Feb 3, 2016

Let the first number be $omega$
The difference of consecutive odd numbers is $2$
So,the next two numbers are $omega+2$ , $omega+4$

Then,

$rarr(omega) +(omega+2)+(omega+4)=129$

Remove brackets:

$rarromega +omega+2+omega+4=129$

$rarr3omega+6=129$

$rarr3omega=129-6$

$rarr3omega=123$

$rarromega=123/3=41$

So, $omega+2=41+2=43 , omega+4=41+4=45$

The three integers are $41,43 and 45$

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