Gem, Hilda and Xylia had a sum of money. The amount of money Gem had was ²₃ of the amount of money Hilda had. The ratio of the amount of money Hilda had to the total amount of money Xylia and Hilda had was 4: 9. After Xylia gave $27 to Hilda, she had as much money as Hilda. How much more money did Xylia have than Gem in the end?

Gem	Hilda	Xylia
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

The amount that Hilda had is the repeated identity. Make the amount that Hilda had the same.  LCM of 3 and 4 is 12.

	Gem	Hilda	Xylia
Before	8 u	12 u	15 u
Change	No change	+ 27	- 27
After	8 u	12 u + 27	15 u - 27

The amount that Xylia and Hilda had in the end is the same.

15 u - 27 = 12 u + 27
15 u - 12 u = 27 + 27 
3 u = 54

1 u = 54 ÷ 3 = 18

Amount that Xylia had more than Gem in the end
= 15 u - 27 - 8 u
= 7 u - 27
= 7 x 18 - 27
= 126 - 27
= $99

Answer(s): $99