A father is now three times as old as his son, twelve years ago he was six times as old as his son. how old are the son and the father?
now:
son ---- x
father -- 3x
12 years ago:
son = x-12
father = 3x-12
3x-12 = 3(x-12)
solve for x
To solve this problem, we can use a system of equations based on the given information.
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.