When Shannon was 49 years old, her daughter was 3 times her son's age. Shannon would be twice her daughter's age when her son was 39 years old. How old would Shannon be when her son was 4 years old?

	Shannon	Daughter	Son
Before	49	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	39

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

Difference in Shannon's and her daughter's ages at first
49 - 3 u = 2 p - 1 p
49 - 3 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
3 u - 1 u = 1 p - 39
2 u + 39 = 1 p --- (2)

Make p the same.

(1) = (2)
49 - 3 u = 2 u + 39
2 u + 3 u = 49 - 39
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Shannon and her son
= 49 - 1 u
= 49 - 2
= 47

Shannon's age when her son was 4 years old
= 47 + 4
= 51

Answer(s): 51