The present age of a father is three years more than three times the age of his son. Three years hence the father's age will be $10$ years more than twice the age of the son. Determine their present a

Question

The present age of a father is three years more than three times the age of his son. Three years hence the father's age will be $10$ years more than twice the age of the son. Determine their present ages.

Accepted Answer

Step 1: Let the present age of son be $x$ years. Father's present age $= (3x + 3)$ years.
Step 2: After $3$ years: Son's age $= (x + 3)$, Father's age $= (3x + 6)$.
Step 3: Given: $3x + 6 = 2(x + 3) + 10$
Step 4: $3x + 6 = 2x + 6 + 10 \Rightarrow x = 10$
Step 5: Son's age $= 10$ years
Step 6: Father's age $= 3(10) + 3 = 33$ years

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