Question

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

Answer 1

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

Explanation:

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

See explanation.

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`.