Fanny, Roshel and Erika had a sum of money. The amount of money Fanny had was ³₄ of the amount of money Roshel had. The ratio of the amount of money Roshel had to the total amount of money Erika and Roshel had was 2: 5. After Erika gave $55 to Roshel, she had as much money as Roshel. How much more money did Erika have than Fanny in the end?

Fanny	Roshel	Erika
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	3x2 = 6 u
3 u	4 u	6 u

The amount that Roshel had is the repeated identity. Make the amount that Roshel had the same.  LCM of 4 and 2 is 4.

	Fanny	Roshel	Erika
Before	3 u	4 u	6 u
Change	No change	+ 55	- 55
After	3 u	4 u + 55	6 u - 55

The amount that Erika and Roshel had in the end is the same.

6 u - 55 = 4 u + 55
6 u - 4 u = 55 + 55 
2 u = 110

1 u = 110 ÷ 2 = 55

Amount that Erika had more than Fanny in the end
= 6 u - 55 - 3 u
= 3 u - 55
= 3 x 55 - 55
= 165 - 55
= $110

Answer(s): $110