SOLUTION: my age plus my son age is equal to my fathers age which is 78 years old.when i was my son age he was just a quarter as old as i am now.how old am i?

Let My age = M
Let my son's age = S.  So

M + S = 78

Let that be x years ago, which means 

M - x = S  and my son was S - x

S - x = M

So we have three equations in 3 unknowns:

M + S = 78
M - x = S
S - x = M

Clear the fraction in the third one:

M + S = 78
M - x = S
4S - 4x = M

Line up the letters and symbols:

 M +  S     = 78
 M -  S - x =  0
-M - 4S - 4x = 0 

Solve that system of equations and get

M = 48, S = 30, x = 18

So I am 48.

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Checking:

48+30 = 78 that checks

that is 18 years ago when I was 48-18 or 30. That checks.

18 years ago he was 30-18 or 12, which is just a quarter of 48.
That checks. 

Edwin