Gillian, Kimberly and Fanny had a sum of money. The amount of money Gillian had was ³₄ of the amount of money Kimberly had. The ratio of the amount of money Kimberly had to the total amount of money Fanny and Kimberly had was 2: 7. After Fanny gave $57 to Kimberly, she had as much money as Kimberly. How much more money did Fanny have than Gillian in the end?

Gillian	Kimberly	Fanny
3x1 = 3 u	4x1 = 4 u
	2x2 = 4 u	5x2 = 10 u
3 u	4 u	10 u

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

	Gillian	Kimberly	Fanny
Before	3 u	4 u	10 u
Change	No change	+ 57	- 57
After	3 u	4 u + 57	10 u - 57

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

10 u - 57 = 4 u + 57
10 u - 4 u = 57 + 57 
6 u = 114

1 u = 114 ÷ 6 = 19

Amount that Fanny had more than Gillian in the end
= 10 u - 57 - 3 u
= 7 u - 57
= 7 x 19 - 57
= 133 - 57
= $76

Answer(s): $76