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Answer 1 · 2016-11-30T13:43:16

The three consecutive even numbers adding to 78 are: 24, 26 and 28

Let's call the first number we are looking for #x#.

Then because these are consecutive even numbers we need to add #2# and #4# to #x# to get the second and third even numbers or #x + 2# and #x + 4#.

We know these three numbers when added equal 78 so we can write and solve for #x#:

#x + (x + 2) + (x + 4) = 78#

#x + x + 2 + x + 4 = 78#

#x + x + x + 2 + 4 = 78#

#3x + 6 = 78#

#3x + 6 - 6 = 78 - 6#

#3x + 0 = 72#

#3x = 72#

#(3x)/3 = 72/3#

#(cancel(3)x)/cancel(3) = 24#

#x = 24#

Then adding #2# and #4# to this gives:

24, 26 and 28