Xuan, Gillian and Emily had a sum of money. The amount of money Xuan had was ³₄ of the amount of money Gillian had. The ratio of the amount of money Gillian had to the total amount of money Emily and Gillian had was 2: 9. After Emily gave $65 to Gillian, she had as much money as Gillian. How much more money did Emily have than Xuan in the end?

Xuan	Gillian	Emily
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	7x2 = 14 u
3 u	4 u	14 u

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

	Xuan	Gillian	Emily
Before	3 u	4 u	14 u
Change	No change	+ 65	- 65
After	3 u	4 u + 65	14 u - 65

The amount that Emily and Gillian had in the end is the same.

14 u - 65 = 4 u + 65
14 u - 4 u = 65 + 65 
10 u = 130

1 u = 130 ÷ 10 = 13

Amount that Emily had more than Xuan in the end
= 14 u - 65 - 3 u
= 11 u - 65
= 11 x 13 - 65
= 143 - 65
= $78

Answer(s): $78