When Elyse was 42 years old, her son was 2 times her daughter's age. Elyse would be twice her son's age when her daughter was 27 years old. How old would Elyse be when her daughter was 4 years old?

	Elyse	Son	Daughter
Before	42	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	27

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

Difference in Elyse's and her son's ages at first
42 - 2 u = 2 p - 1 p
42 - 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)
42 - 2 u = 1 u + 27
1 u + 2 u = 42 - 27
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Elyse and her daughter
= 42 - 1 u
= 42 - 5
= 37

Elyse's age when her daughter was 4 years old
= 37 + 4
= 41

Answer(s): 41