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A father is 30 years older than his son. After 12 years. the man will. be as old as his son. find thir present age.

A father is $30$ years older than his son. After $12$ years. the man will. be as old as his son. find thir present age.

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Exponential growth and decay: word problems

Full solution

Q. A father is

30

years older than his son. After

12

years. the man will. be as old as his son. find thir present age.

Denote current ages: Let's denote the son's current age as $s$ years. Therefore, the father's current age will be $s + 30$ years.
Calculate ages in $12$ years: In $12$ years, the son's age will be $s + 12$ years, and the father's age will be $s + 30 + 12 = s + 42$ years.
Set up equation: According to the problem, in $12$ years, the father will be twice as old as the son. So, we set up the equation: $s + 42 = 2(s + 12)$ .
Simplify equation: Simplify the equation: $s + 42 = 2s + 24$ .
Solve for s: Solving for $s$ , we subtract $s$ from both sides: $42 = s + 24$ .

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