Erika, Raeann and Shannon had a sum of money. The amount of money Erika had was ²₅ of the amount of money Raeann had. The ratio of the amount of money Raeann had to the total amount of money Shannon and Raeann had was 4: 9. After Shannon gave $90 to Raeann, she had as much money as Raeann. How much more money did Shannon have than Erika in the end?

Erika	Raeann	Shannon
2x4 = 8 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
8 u	20 u	25 u

The amount that Raeann had is the repeated identity. Make the amount that Raeann had the same.  LCM of 5 and 4 is 20.

	Erika	Raeann	Shannon
Before	8 u	20 u	25 u
Change	No change	+ 90	- 90
After	8 u	20 u + 90	25 u - 90

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

25 u - 90 = 20 u + 90
25 u - 20 u = 90 + 90 
5 u = 180

1 u = 180 ÷ 5 = 36

Amount that Shannon had more than Erika in the end
= 25 u - 90 - 8 u
= 17 u - 90
= 17 x 36 - 90
= 612 - 90
= $522

Answer(s): $522