4 years ago the father was 7 times older than his son. After 4 years he will be 3 times older than his son. How old is the son, how old is t

Father's age = f, son's age = s

f - 4 = 7(s - 4)    Four years ago   (1)

f + 4 = 3(s + 4) Four years hence   (2)

From (1) we have  f - 4 = 7s - 28  or  f = 7s - 24  (3)

From (2) we have f + 4 = 3s + 12 or f = 3s + 8   (4)

From (3) and (4):   7s - 24 = 3s + 8  or  4s = 32 so s = 8

Put this back into (4) to get f = 3*8 + 8  or  f = 32

Father's age now is 32

Son's age now is 8

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We can also do this with one variable.

Let x be the son's age 4 years ago,

Then his father's age 4 years ago  = 7x

And years later, - 4 years from now -  the father will be 3 times older than his son. So we have.....

3(x + 8)  = 7x + 8    simplify

3x+ 24  = 7x + 8

4x = 16

So the son's age 4 years ago was 4

And his father was 7(4)  = 28

And 4 yeara later the son is 8 and the father is 32.