Gem, Raeann and Xylia had a sum of money. The amount of money Gem had was ⁴₅ of the amount of money Raeann had. The ratio of the amount of money Raeann had to the total amount of money Xylia and Raeann had was 2: 7. After Xylia gave $30 to Raeann, she had as much money as Raeann. How much more money did Xylia have than Gem in the end?

Gem	Raeann	Xylia
4x2 = 8 u	5x2 = 10 u
	2x5 = 10 u	5x5 = 25 u
8 u	10 u	25 u

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

	Gem	Raeann	Xylia
Before	8 u	10 u	25 u
Change	No change	+ 30	- 30
After	8 u	10 u + 30	25 u - 30

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

25 u - 30 = 10 u + 30
25 u - 10 u = 30 + 30 
15 u = 60

1 u = 60 ÷ 15 = 4

Amount that Xylia had more than Gem in the end
= 25 u - 30 - 8 u
= 17 u - 30
= 17 x 4 - 30
= 68 - 30
= $38

Answer(s): $38