When Min was 44 years old, her daughter was 4 times her son's age. Min would be twice her daughter's age when her son was 30 years old. How old would Min be when her son was 16 years old?

	Min	Daughter	Son
Before	44	4 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	30

The difference in the ages between Min and her daughter remains unchanged.

Difference in Min's and her daughter's ages at first
44 - 4 u = 2 p - 1 p
44 - 4 u = 1 p --- (1)

The difference in the ages between her daughter and her son remains unchanged.

Difference in her daughter's and her son's ages at first
4 u - 1 u = 1 p - 30
3 u + 30 = 1 p --- (2)

Make p the same.

(1) = (2)
44 - 4 u = 3 u + 30
3 u + 4 u = 44 - 30
7 u = 14

1 u = 14 ÷ 7 = 2

Age difference between Min and her son
= 44 - 1 u
= 44 - 2
= 42

Min's age when her son was 16 years old
= 42 + 16
= 58

Answer(s): 58