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#.