Hazel, Xandra and Zoe had a sum of money. The amount of money Hazel had was ⁴₅ of the amount of money Xandra had. The ratio of the amount of money Xandra had to the total amount of money Zoe and Xandra had was 4: 9. After Zoe gave $10 to Xandra, she had as much money as Xandra. How much more money did Zoe have than Hazel in the end?

Hazel	Xandra	Zoe
4x4 = 16 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
16 u	20 u	25 u

The amount that Xandra had is the repeated identity. Make the amount that Xandra had the same.  LCM of 5 and 4 is 20.

	Hazel	Xandra	Zoe
Before	16 u	20 u	25 u
Change	No change	+ 10	- 10
After	16 u	20 u + 10	25 u - 10

The amount that Zoe and Xandra had in the end is the same.

25 u - 10 = 20 u + 10
25 u - 20 u = 10 + 10 
5 u = 20

1 u = 20 ÷ 5 = 4

Amount that Zoe had more than Hazel in the end
= 25 u - 10 - 16 u
= 9 u - 10
= 9 x 4 - 10
= 36 - 10
= $26

Answer(s): $26