In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and

Question

In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

Accepted Answer

Let the age of the daughter be x.

The father is three times the daughter's age, so the father is 3x.
The brother is seven years older than the sister, so the son is x plus 7.
The son is half the age of the mother, so the mother is 2(x + 7).
The wife is nine years younger than her husband, so the mother is also 3x minus 9.

Setting the two expressions equal: 2(x + 7) = 3x - 9.
Expanding: 2x + 14 = 3x - 9.
Solving: x = 23.

The daughter is 23, the son is 30, the father is 69, and the mother is 60.
Verification: Son (30) is half of mother (60). Father (69) minus mother (60) = 9. Son (30) minus daughter (23) = 7. All conditions are satisfied.

Answer

40 years

Answer

45 years

Answer

50 years

Answer

60 years

In a family, a couple has a son and a daughter. The age of the father is three times that of his daughter and the age of the son is half of his mother. The wife is nine years younger to her husband and the brother is seven years older than his sister. What is the age of the mother?

Explanation

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