The sum of three consecutive even integers is 12 less than the middle integer. What's the answer?

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Answer 1 · 2018-06-29T04:58:56

$color(crimson)("The three consecutive even numbers are "-8, -6, -4$

Let a, b, c be the three integers.

$a = b -2, c = b + 2$

$a + b + c = 3b = b - 12, " given"$

$3b - b = -12 " or " b = -6$

$:. a = b - 2 = -6 - 2 = -8 " & " c = b + 2 = -6 + 2 = -4$

Answer 2 · 2018-06-29T06:32:34

See explanation.

Any even integer can be expressed as $2n$ for some integer $n$ . Now if the middle integer is $2n$ , then the other are: $2n-2$ and $2n+2$ .

With the given variables the condition can be written as:

$2n-2+2n+2n+2=2n-12$

$6n=2n-12$

$4n=-12$

$n=-3$

Now we have to substitute $-3$ for $n$ in the formulas:

$2n-2=-8$

$2n=-6$

$2n+2=-4$

Answer:

The three integers are: $-8$ , $-6$ and $-4$ .