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

##### 1 Answer

Oct 16, 2015

#### Explanation:

You know that thee *consecutive even* integers add up to give

If you take *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

#2 * x = 12#

#2 * x + 2 = 14#

#2 * x + 4 = 16#