Usha, Winnie and Hazel had a sum of money. The amount of money Usha had was ³₄ of the amount of money Winnie had. The ratio of the amount of money Winnie had to the total amount of money Hazel and Winnie had was 2: 5. After Hazel gave $31 to Winnie, she had as much money as Winnie. How much more money did Hazel have than Usha in the end?

Usha	Winnie	Hazel
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

The amount that Winnie had is the repeated identity. Make the amount that Winnie had the same.  LCM of 4 and 2 is 4.

	Usha	Winnie	Hazel
Before	3 u	4 u	6 u
Change	No change	+ 31	- 31
After	3 u	4 u + 31	6 u - 31

The amount that Hazel and Winnie had in the end is the same.

6 u - 31 = 4 u + 31
6 u - 4 u = 31 + 31 
2 u = 62

1 u = 62 ÷ 2 = 31

Amount that Hazel had more than Usha in the end
= 6 u - 31 - 3 u
= 3 u - 31
= 3 x 31 - 31
= 93 - 31
= $62

Answer(s): $62