Mother–daughter equation system – A mother is five times her daughter’s present age. After 5 years she will be three times her daughter’s age. Find the mother’s current age.

Introduction / Context:This is a standard two-equation ages setup with current and future ratios. Solving carefully yields exact present ages without guessing.

Given Data / Assumptions:

• Let daughter = D, mother = M.
• M = 5D (now).
• M + 5 = 3(D + 5) (after 5 years).

Concept / Approach:Substitute M from the first equation into the second and solve for D; then compute M.

Step-by-Step Solution:5D + 5 = 3D + 15.2D = 10 ⇒ D = 5.M = 5D = 25.

Verification / Alternative check:After 5 years: mother 30, daughter 10; 30 = 3 × 10 holds.

Why Other Options Are Wrong:They do not meet both the present 5× and future 3× constraints simultaneously.

Common Pitfalls:Adding 5 to only one side or mixing present and future ages in a single step.

Final Answer:25 years