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

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Answer 1 · 2018-05-27T17:12:01

$61, 63$ $61 , 63$ and $65$ $65$

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

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

Sum means to add together:

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

Colect like terms:

$\Rightarrow 6 k + 9 = 189$ $=> 6k + 9 = 189$

$\Rightarrow 6 k = 180$ $=> 6k = 180$

$\Rightarrow \frac{6 k}{6} = \frac{180}{6}$ $=> (6k)/6 = 180 / 6$

$\Rightarrow k = 30$ $=> k = 30$

$\Rightarrow 2 k + 1 = (2 \cdot 30) + 1 = 61$ $=> 2k+1 = (2*30)+1 = 61$

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

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)

$x + x + 2 + x + 4 = 189$ $x+x+2+x+4=189$

$3 x = 189 - 6 = 183$ $3x=189-6=183$

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