Gillian, Gem and Fanny had a sum of money. The amount of money Gillian had was ²₅ of the amount of money Gem had. The ratio of the amount of money Gem had to the total amount of money Fanny and Gem had was 2: 5. After Fanny gave $75 to Gem, she had as much money as Gem. How much more money did Fanny have than Gillian in the end?

Gillian	Gem	Fanny
2x2 = 4 u	5x2 = 10 u
	2x5 = 10 u	3x5 = 15 u
4 u	10 u	15 u

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

	Gillian	Gem	Fanny
Before	4 u	10 u	15 u
Change	No change	+ 75	- 75
After	4 u	10 u + 75	15 u - 75

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

15 u - 75 = 10 u + 75
15 u - 10 u = 75 + 75 
5 u = 150

1 u = 150 ÷ 5 = 30

Amount that Fanny had more than Gillian in the end
= 15 u - 75 - 4 u
= 11 u - 75
= 11 x 30 - 75
= 330 - 75
= $255

Answer(s): $255