Question

a faather is four times older than his son. however, 20 years later he will be only twice as old as the son. what's the father's present age?

Answer 1

Son = S
Father = F
F = 4S this is the 1st condition.
F + 20 = 2*(S + 20) This is the second Remove the brackets.
F + 20 = 2s + 40 Substitute the the 1st equation into the second
4S + 20 = 2S + 40 Subtract 2S from both sides.
4S - 2S + 20 = 40
2S + 20 = 40 Subtract 20 from both sides.
2S = 40 - 20
2S = 20 Divide by 2
S = 10

The father's current age = 4*10 = 40 <<<< answer.

Answer 2

Let f and s represent the present ages of father and son.
.. f = 4s . . . . the age of the father is 4 times the age of the son
.. (f +20) = 2*(s +20) . . . . in 20 years, the father will only be 2 times the age of the son.

Substituting for f in the second equation, we have
.. 4s +20 = 2(s +20)
.. 2s = 20 . . . . . . . . . . add -20-2s
.. 4s = f = 40 . . . . . . . The father's current age is 40.