Julie, Sarah and Fiona had a sum of money. The amount of money Julie had was ³₄ of the amount of money Sarah had. The ratio of the amount of money Sarah had to the total amount of money Fiona and Sarah had was 3: 7. After Fiona gave $44 to Sarah, she had as much money as Sarah. How much more money did Fiona have than Julie in the end?

Julie	Sarah	Fiona
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

The amount that Sarah had is the repeated identity. Make the amount that Sarah had the same.  LCM of 4 and 3 is 12.

	Julie	Sarah	Fiona
Before	9 u	12 u	16 u
Change	No change	+ 44	- 44
After	9 u	12 u + 44	16 u - 44

The amount that Fiona and Sarah had in the end is the same.

16 u - 44 = 12 u + 44
16 u - 12 u = 44 + 44 
4 u = 88

1 u = 88 ÷ 4 = 22

Amount that Fiona had more than Julie in the end
= 16 u - 44 - 9 u
= 7 u - 44
= 7 x 22 - 44
= 154 - 44
= $110

Answer(s): $110