When Min was 46 years old, her son was 2 times her daughter's age. Min would be twice her son's age when her daughter was 34 years old. How old would Min be when her daughter was 19 years old?

	Min	Son	Daughter
Before	46	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	34

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

Difference in Min's and her son's ages at first
46 - 2 u = 2 p - 1 p
46 - 2 u = 1 p --- (1)

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

Difference in her son's and her daughter's ages at first
2 u - 1 u = 1 p - 34
1 u + 34 = 1 p --- (2)

Make p the same.

(1) = (2)
46 - 2 u = 1 u + 34
1 u + 2 u = 46 - 34
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Min and her daughter
= 46 - 1 u
= 46 - 4
= 42

Min's age when her daughter was 19 years old
= 42 + 19
= 61

Answer(s): 61