The current mean age of a married pair and their daughter is 35 years. Fifteen years ahead, the mother's age will match the combined current ages of the father and daughter. Determine the mother's current age.
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Answer: D. 45 years
Explanation
Setting up simultaneous linear equations for the family ages reflects the current mean of thirty five years. Accounting for the fifteen year future age shift matches the mother's age to the combined current ages. Solving the resulting algebraic system confirms that the mother's current age is forty five years. The sum of ages for a group equals the mean age multiplied by the total number of members. Future age calculations require adding the same number of years to each individual family member. Algebraic word problems translate descriptive statements into solvable systems of linear equations.
Insurance actuaries use demographic age distribution models to calculate life expectancy and policy risks. Genealogy researchers verify historical family records by cross referencing birth dates and relative ages. Estate planners analyze generational age gaps when structuring multi generational trusts and wills. Option a yields an inconsistent age sum when tested against the fifteen year future condition. Option b falls short of satisfying the combined family age equation after the time shift. Option c produces an age value that violates the initial mean age constraint for the family.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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