now:
son ---- x
father -- 3x
12 years ago:
son = x-12
father = 3x-12
3x-12 = 3(x-12)
solve for x
son ---- x
father -- 3x
12 years ago:
son = x-12
father = 3x-12
3x-12 = 3(x-12)
solve for x
Let's assume the current age of the son is S, and the current age of the father is F.
According to the problem:
1) "A father is now three times as old as his son" implies:
F = 3S
2) "Twelve years ago he was six times as old as his son" implies:
(F - 12) = 6(S - 12)
Now we can solve this system of equations to find the ages of the son and the father.
Substitute the value of F from equation 1 into equation 2:
(3S - 12) = 6(S - 12)
Now, distribute the 6 on the right side:
3S - 12 = 6S - 72
Rearrange the equation by moving the variables to one side and constants to the other side:
6S - 3S = 72 - 12
Combine like terms:
3S = 60
Divide both sides by 3:
S = 20
Now, substitute this value of S back into equation 1 to find F:
F = 3S
F = 3(20)
F = 60
Therefore, the son is 20 years old and the father is 60 years old.