When Shiyun was 38 years old, her daughter was 2 times her son's age. Shiyun would be twice her daughter's age when her son was 29 years old. How old would Shiyun be when her son was 5 years old?

	Shiyun	Daughter	Son
Before	38	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Shiyun's and her daughter's ages at first
38 - 2 u = 2 p - 1 p
38 - 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 - 29
1 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
38 - 2 u = 1 u + 29
1 u + 2 u = 38 - 29
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Shiyun and her son
= 38 - 1 u
= 38 - 3
= 35

Shiyun's age when her son was 5 years old
= 35 + 5
= 40

Answer(s): 40