When Min was 47 years old, her daughter was 2 times her son's age. Min would be twice her daughter's age when her son was 23 years old. How old would Min be when her son was 6 years old?

	Min	Daughter	Son
Before	47	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	23

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

Difference in Min's and her daughter's ages at first
47 - 2 u = 2 p - 1 p
47 - 2 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
2 u - 1 u = 1 p - 23
1 u + 23 = 1 p --- (2)

Make p the same.

(1) = (2)
47 - 2 u = 1 u + 23
1 u + 2 u = 47 - 23
3 u = 24

1 u = 24 ÷ 3 = 8

Age difference between Min and her son
= 47 - 1 u
= 47 - 8
= 39

Min's age when her son was 6 years old
= 39 + 6
= 45

Answer(s): 45