When Betty was 43 years old, her son was 3 times her daughter's age. Betty would be twice her son's age when her daughter was 28 years old. How old would Betty be when her daughter was 23 years old?

	Betty	Son	Daughter
Before	43	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	28

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

Difference in Betty's and her son's ages at first
43 - 3 u = 2 p - 1 p
43 - 3 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
3 u - 1 u = 1 p - 28
2 u + 28 = 1 p --- (2)

Make p the same.

(1) = (2)
43 - 3 u = 2 u + 28
2 u + 3 u = 43 - 28
5 u = 15

1 u = 15 ÷ 5 = 3

Age difference between Betty and her daughter
= 43 - 1 u
= 43 - 3
= 40

Betty's age when her daughter was 23 years old
= 40 + 23
= 63

Answer(s): 63