The sum of three consecutive even integers is 42, what are the integers?

1 Answer
Oct 16, 2015

Answer:

#12#, #14#, and #16#

Explanation:

You know that thee consecutive even integers add up to give #42#.

If you take #2x# to be the first even number of the series, you can say that

#2x + 2 -># the second number of the series

#(2x + 2) + 2 = 2x + 4 -># the third number of the series

This means that you have

#overbrace(2x)^(color(blue)("first even no.")) + overbrace((2x + 2))^(color(red)("second even no.")) + overbrace((2x + 4))^(color(purple)("third even no.")) = 42#

This is equivalent to

#6x + 6 = 42#

#6x = 36 implies x = 36/6 = 6#

The three consecutive even integers that add up to #42# are

#2 * x = 12#

#2 * x + 2 = 14#

#2 * x + 4 = 16#