When Nicole was 47 years old, her daughter was 2 times her son's age. Nicole would be twice her daughter's age when her son was 32 years old. How old would Nicole be when her son was 4 years old?

	Nicole	Daughter	Son
Before	47	2 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	32

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

Difference in Nicole'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 - 32
1 u + 32 = 1 p --- (2)

Make p the same.

(1) = (2)
47 - 2 u = 1 u + 32
1 u + 2 u = 47 - 32
3 u = 15

1 u = 15 ÷ 3 = 5

Age difference between Nicole and her son
= 47 - 1 u
= 47 - 5
= 42

Nicole's age when her son was 4 years old
= 42 + 4
= 46

Answer(s): 46