Hazel, Usha and Gwen had a sum of money. The amount of money Hazel had was ⁴₅ of the amount of money Usha had. The ratio of the amount of money Usha had to the total amount of money Gwen and Usha had was 3: 7. After Gwen gave $80 to Usha, she had as much money as Usha. How much more money did Gwen have than Hazel in the end?

Hazel	Usha	Gwen
4x3 = 12 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
12 u	15 u	20 u

The amount that Usha had is the repeated identity. Make the amount that Usha had the same.  LCM of 5 and 3 is 15.

	Hazel	Usha	Gwen
Before	12 u	15 u	20 u
Change	No change	+ 80	- 80
After	12 u	15 u + 80	20 u - 80

The amount that Gwen and Usha had in the end is the same.

20 u - 80 = 15 u + 80
20 u - 15 u = 80 + 80 
5 u = 160

1 u = 160 ÷ 5 = 32

Amount that Gwen had more than Hazel in the end
= 20 u - 80 - 12 u
= 8 u - 80
= 8 x 32 - 80
= 256 - 80
= $176

Answer(s): $176