The sum of the present ages of a mother and daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. How much older is the mother than the daughter?

Question: The sum of the present ages of a mother and daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. How much older is the mother than the daughter?

Solution:
Let mother’s age = M, daughter’s age = D.
Given:
⟹ M+D=50 --------------------------(1)
Five years ago:
⟹ M−5=7(D−5)
⟹ M−5=7D−35
⟹ M=7D−30 ---------------------(2)

Substitute Equation 2 into Equation 1:
(7D−30)+D=50
⟹ 8D=80
⟹ D=10 (Daughter's age)

Then,
M=50−10=40. (Mother's age)
Age difference: 40−10=30
Answer: 30