Daughter’s present age from two conditions: Five years ago a mother was three times her daughter’s age. Five years from now the mother will be twice her daughter’s age. How old is the daughter today?

Introduction / Context:
Two time-shifted multiplicative relationships determine present ages uniquely. We solve a pair of linear equations derived from the English statements.

Given Data / Assumptions:

• M = mother's present age; D = daughter's present age.
• Five years ago: M − 5 = 3(D − 5).
• Five years from now: M + 5 = 2(D + 5).

Concept / Approach:
Convert each to an equation in M and D, then eliminate M.

Step-by-Step Solution:
1) From the first: M = 3D − 10.2) From the second: M = 2D + 5.3) Equate: 3D − 10 = 2D + 5 ⇒ D = 15.

Verification / Alternative check:
Then M = 2D + 5 = 35. Check: Five years ago 30 vs 10 (3×); in five years 40 vs 20 (2×). Both hold.

Why Other Options Are Wrong:
Other values fail one of the two conditions when verified.

Common Pitfalls:
Arithmetic slips when moving constants: note −5 and +5 belong to both ages at the respective times.

Final Answer:
15 years