When Elyse was 39 years old, her daughter was 3 times her son's age. Elyse would be twice her daughter's age when her son was 29 years old. How old would Elyse be when her son was 22 years old?

	Elyse	Daughter	Son
Before	39	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	29

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

Difference in Elyse's and her daughter's ages at first
39 - 3 u = 2 p - 1 p
39 - 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 - 29
2 u + 29 = 1 p --- (2)

Make p the same.

(1) = (2)
39 - 3 u = 2 u + 29
2 u + 3 u = 39 - 29
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Elyse and her son
= 39 - 1 u
= 39 - 2
= 37

Elyse's age when her son was 22 years old
= 37 + 22
= 59

Answer(s): 59