Nicole, Emily and Risa had a sum of money. The amount of money Nicole had was ²₅ of the amount of money Emily had. The ratio of the amount of money Emily had to the total amount of money Risa and Emily had was 4: 9. After Risa gave $30 to Emily, she had as much money as Emily. How much more money did Risa have than Nicole in the end?

Nicole	Emily	Risa
2x4 = 8 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
8 u	20 u	25 u

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

	Nicole	Emily	Risa
Before	8 u	20 u	25 u
Change	No change	+ 30	- 30
After	8 u	20 u + 30	25 u - 30

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

25 u - 30 = 20 u + 30
25 u - 20 u = 30 + 30 
5 u = 60

1 u = 60 ÷ 5 = 12

Amount that Risa had more than Nicole in the end
= 25 u - 30 - 8 u
= 17 u - 30
= 17 x 12 - 30
= 204 - 30
= $174

Answer(s): $174