The sum of the ages of a father and son is 60 years. Four years ago, the father’s age was three times the age of the son. What are their present ages?
Question
The sum of the ages of a father and son is 60 years. Four years ago, the father’s age was three times the age of the son. What are their present ages?
Solution
Let's denote the father's current age as F and the son's current age as S.
From the problem, we know two things:
- F + S = 60 (The sum of their ages is 60)
- F - 4 = 3 * (S - 4) (Four years ago, the father’s age was three times the age of the son)
We can solve these equations step by step:
Step 1: From equation 1, we can express F as F = 60 - S.
Step 2: Substitute F from step 1 into equation 2, we get 60 - S - 4 = 3 * (S - 4).
Step 3: Simplify the equation, we get 56 - S = 3S - 12.
Step 4: Rearrange the equation, we get 4S = 68.
Step 5: Solve for S, we get S = 68 / 4 = 17. So the son is 17 years old.
Step 6: Substitute S = 17 into equation 1, we get F = 60 - 17 = 43. So the father is 43 years old.
So, the father is 43 years old and the son is 17 years old.
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