When Shiyun was 36 years old, her son was 2 times her daughter's age. Shiyun would be twice her son's age when her daughter was 27 years old. How old would Shiyun be when her daughter was 18 years old?

	Shiyun	Son	Daughter
Before	36	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Shiyun's and her son's ages at first
36 - 2 u = 2 p - 1 p
36 - 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 - 27
1 u + 27 = 1 p --- (2)

Make p the same.

(1) = (2)
36 - 2 u = 1 u + 27
1 u + 2 u = 36 - 27
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Shiyun and her daughter
= 36 - 1 u
= 36 - 3
= 33

Shiyun's age when her daughter was 18 years old
= 33 + 18
= 51

Answer(s): 51