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Let
𝑤
w represent the woman’s age and
𝑑
d represent the daughter’s age.
From the problem statement, we have two pieces of information:
The average age of the woman and her daughter is 16 years.
The ratio of their ages is 7 : 1.
Firstly, we set up the equations based on the information given:
𝑤
+
𝑑
2
=
16
2
w+d
=16
Multiply both sides by 2 to eliminate the fraction:
𝑤
+
𝑑
=
32
w+d=32
Daughter’s age = x years
Woman’s age = 7x years
Therefore, 7x + x = 2 × 16 = 32
=> 8x = 32
=> x = 4
Therefore, Woman’s age
= 7x = 7 × 4 = 28 years
Answer: The woman’s age is 28 years.