A father's present age is 6 times his son's present age....

A father's present age is 6 times his son's present age. Thirty years hence the father's age will be ten years less than twice the son's age. After how many years will the son's age be half of the father's present age?
(1) 20
(2) 30
(3) 10
(4) 15

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Key Concepts

Variable Assignment

This concept involves representing unknown quantities, such as current ages, with variables. It is a fundamental step in translating word problems into algebraic expressions, allowing one to work systematically towards a solution.

Translating Word Problems to Equations

This concept focuses on converting the relationships and conditions given in a narrative format—such as proportional ages and differences in future ages—into algebraic equations. This process is crucial for setting up a clear mathematical model of the scenario.

Setting Up and Solving Linear Equations

After forming the appropriate equations, the next key concept is to solve these linear equations using algebraic techniques such as substitution or elimination. This step isolates the variables and determines their numerical values.

Analyzing Future and Present Relationships

Age problems often involve understanding the relationship between current and future ages. This concept deals with adjusting variables by a time factor (e.g., adding years) and forming new equations based on these shifted values, which is essential in solving such problems.

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