The sum of 3 consecutive even numbers is 78. What is the second number in...

Assume that the father is x years old and that the combined ages of the two children is y years.
As per the question,
x=2y.....(1)
After 20 years,
x+20=y+20+20
⇒ x+20=y+40
⇒ x=y+20.....(2)
Equating (1) & (2),
y = 20
Substituting y = 20 in equation (1), we obtain
x = 40
Therefore, the father's age is 40 years.

Given that there is a 2 difference between even numbers,
The sum of three consecutive even numbers can be generalized as follows.
Let the 3 even numbers be : ${\displaystyle n,n+2,n+4}$
${\displaystyle \Rightarrow n+(n+2)+(n+4)=78\leftarrow \text{equation to be solved}}$
${\displaystyle \Rightarrow 3n+6=78}$
Subtract 6 from both sides.
${\displaystyle 3n\cancel{+6}\cancel{-6}=78-6}$
${\displaystyle \Rightarrow 3n=72}$
To solve for n, divide both sides by 3
${\displaystyle \frac{\cancel{3}n}{\cancel{3}}=\frac{72}{3}}$
${\displaystyle \Rightarrow n=24\leftarrow \text{first even number}}$
${\displaystyle n+2=24+2=26\leftarrow \text{second even number}}$
${\displaystyle n+4=24+4=28\leftarrow \text{third even number}}$#
${\displaystyle \text{Check:}24+26+28=78}$