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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.

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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.

Identify Relationship: Identify the relationship between the father's and son's current ages. $\newline$ Let the son's current age be $x$ years. $\newline$ Then, the father's current age is $x + 30$ years.
Set Up Equation: Set up the equation based on the condition given for $12$ years later. $\newline$ In $12$ years, the son will be $x + 12$ years old. $\newline$ The father will be $(x + 30) + 12 = x + 42$ years old. $\newline$ The problem states that the father will be twice as old as his son in $12$ years. $\newline$ So, $x + 42 = 2(x + 12)$
Solve Equation: Solve the equation. $\newline$ $x + 42 = 2(x + 12)$ $\newline$ $x + 42 = 2x + 24$ $\newline$ $42 - 24 = 2x - x$ $\newline$ $18 = x$
Calculate Father's Age: Calculate the father's current age using the value of $x$ . $\newline$ Father's age = $x + 30 = 18 + 30 = 48$ years.

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