When Sarah was 49 years old, her daughter was 2 times her son's age. Sarah would be twice her daughter's age when her son was 37 years old. How old would Sarah be when her son was 11 years old?

	Sarah	Daughter	Son
Before	49	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	37

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

Difference in Sarah's and her daughter's ages at first
49 - 2 u = 2 p - 1 p
49 - 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 - 37
1 u + 37 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 2 u = 1 u + 37
1 u + 2 u = 49 - 37
3 u = 12

1 u = 12 ÷ 3 = 4

Age difference between Sarah and her son
= 49 - 1 u
= 49 - 4
= 45

Sarah's age when her son was 11 years old
= 45 + 11
= 56

Answer(s): 56