Nicole, Lucy and Fanny had a sum of money. The amount of money Nicole had was ²₅ of the amount of money Lucy had. The ratio of the amount of money Lucy had to the total amount of money Fanny and Lucy had was 2: 5. After Fanny gave $70 to Lucy, she had as much money as Lucy. How much more money did Fanny have than Nicole in the end?

Nicole	Lucy	Fanny
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
4 u	10 u	15 u

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

	Nicole	Lucy	Fanny
Before	4 u	10 u	15 u
Change	No change	+ 70	- 70
After	4 u	10 u + 70	15 u - 70

The amount that Fanny and Lucy had in the end is the same.

15 u - 70 = 10 u + 70
15 u - 10 u = 70 + 70 
5 u = 140

1 u = 140 ÷ 5 = 28

Amount that Fanny had more than Nicole in the end
= 15 u - 70 - 4 u
= 11 u - 70
= 11 x 28 - 70
= 308 - 70
= $238

Answer(s): $238