When Emma was 47 years old, her daughter was 2 times her son's age. Emma would be twice her daughter's age when her son was 38 years old. How old would Emma be when her son was 19 years old?

	Emma	Daughter	Son
Before	47	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	38

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

Difference in Emma'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 - 38
1 u + 38 = 1 p --- (2)

Make p the same.

(1) = (2)
47 - 2 u = 1 u + 38
1 u + 2 u = 47 - 38
3 u = 9

1 u = 9 ÷ 3 = 3

Age difference between Emma and her son
= 47 - 1 u
= 47 - 3
= 44

Emma's age when her son was 19 years old
= 44 + 19
= 63

Answer(s): 63