Fanny, Diana and Nicole had a sum of money. The amount of money Fanny had was ²₅ of the amount of money Diana had. The ratio of the amount of money Diana had to the total amount of money Nicole and Diana had was 4: 9. After Nicole gave $20 to Diana, she had as much money as Diana. How much more money did Nicole have than Fanny in the end?

Fanny	Diana	Nicole
2x4 = 8 u	5x4 = 20 u
	4x5 = 20 u	5x5 = 25 u
8 u	20 u	25 u

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

	Fanny	Diana	Nicole
Before	8 u	20 u	25 u
Change	No change	+ 20	- 20
After	8 u	20 u + 20	25 u - 20

The amount that Nicole and Diana had in the end is the same.

25 u - 20 = 20 u + 20
25 u - 20 u = 20 + 20 
5 u = 40

1 u = 40 ÷ 5 = 8

Amount that Nicole had more than Fanny in the end
= 25 u - 20 - 8 u
= 17 u - 20
= 17 x 8 - 20
= 136 - 20
= $116

Answer(s): $116