Kylie, Xuan and Gwen had a sum of money. The amount of money Kylie had was ³₅ of the amount of money Xuan had. The ratio of the amount of money Xuan had to the total amount of money Gwen and Xuan had was 2: 9. After Gwen gave $75 to Xuan, she had as much money as Xuan. How much more money did Gwen have than Kylie in the end?

Kylie	Xuan	Gwen
3x2 = 6 u	5x2 = 10 u
	2x5 = 10 u	7x5 = 35 u
6 u	10 u	35 u

The amount that Xuan had is the repeated identity. Make the amount that Xuan had the same.  LCM of 5 and 2 is 10.

	Kylie	Xuan	Gwen
Before	6 u	10 u	35 u
Change	No change	+ 75	- 75
After	6 u	10 u + 75	35 u - 75

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

35 u - 75 = 10 u + 75
35 u - 10 u = 75 + 75 
25 u = 150

1 u = 150 ÷ 25 = 6

Amount that Gwen had more than Kylie in the end
= 35 u - 75 - 6 u
= 29 u - 75
= 29 x 6 - 75
= 174 - 75
= $99

Answer(s): $99