When Zara was 38 years old, her daughter was 3 times her son's age. Zara would be twice her daughter's age when her son was 28 years old. How old would Zara be when her son was 23 years old?

	Zara	Daughter	Son
Before	38	3 u	1 u
Change	+ ?	+ ?	+ ?
After	2 p	1 p	28

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

Difference in Zara's and her daughter's ages at first
38 - 3 u = 2 p - 1 p
38 - 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 - 28
2 u + 28 = 1 p --- (2)

Make p the same.

(1) = (2)
38 - 3 u = 2 u + 28
2 u + 3 u = 38 - 28
5 u = 10

1 u = 10 ÷ 5 = 2

Age difference between Zara and her son
= 38 - 1 u
= 38 - 2
= 36

Zara's age when her son was 23 years old
= 36 + 23
= 59

Answer(s): 59