Gwen, Usha and Lynn had a sum of money. The amount of money Gwen had was ³₅ of the amount of money Usha had. The ratio of the amount of money Usha had to the total amount of money Lynn and Usha had was 3: 8. After Lynn gave $55 to Usha, she had as much money as Usha. How much more money did Lynn have than Gwen in the end?

Gwen	Usha	Lynn
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	5x5 = 25 u
9 u	15 u	25 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.

	Gwen	Usha	Lynn
Before	9 u	15 u	25 u
Change	No change	+ 55	- 55
After	9 u	15 u + 55	25 u - 55

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

25 u - 55 = 15 u + 55
25 u - 15 u = 55 + 55 
10 u = 110

1 u = 110 ÷ 10 = 11

Amount that Lynn had more than Gwen in the end
= 25 u - 55 - 9 u
= 16 u - 55
= 16 x 11 - 55
= 176 - 55
= $121

Answer(s): $121