Kathy, Cathy and Raeann had a sum of money. The amount of money Kathy had was ²₅ of the amount of money Cathy had. The ratio of the amount of money Cathy had to the total amount of money Raeann and Cathy had was 2: 5. After Raeann gave $30 to Cathy, she had as much money as Cathy. How much more money did Raeann have than Kathy in the end?

Kathy	Cathy	Raeann
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
4 u	10 u	15 u

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

	Kathy	Cathy	Raeann
Before	4 u	10 u	15 u
Change	No change	+ 30	- 30
After	4 u	10 u + 30	15 u - 30

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

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

1 u = 60 ÷ 5 = 12

Amount that Raeann had more than Kathy in the end
= 15 u - 30 - 4 u
= 11 u - 30
= 11 x 12 - 30
= 132 - 30
= $102

Answer(s): $102