When Emily was 32 years old, her daughter was 3 times her son's age. Emily would be twice her daughter's age when her son was 22 years old. How old would Emily be when her son was 10 years old?

	Emily	Daughter	Son
Before	32	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	22

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

Difference in Emily's and her daughter's ages at first
32 - 3 u = 2 p - 1 p
32 - 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 - 22
2 u + 22 = 1 p --- (2)

Make p the same.

(1) = (2)
32 - 3 u = 2 u + 22
2 u + 3 u = 32 - 22
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Emily and her son
= 32 - 1 u
= 32 - 2
= 30

Emily's age when her son was 10 years old
= 30 + 10
= 40

Answer(s): 40