Vanessa, Sarah and Roshel had a sum of money. The amount of money Vanessa 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 Roshel and Sarah had was 3: 7. After Roshel gave $48 to Sarah, she had as much money as Sarah. How much more money did Roshel have than Vanessa in the end?

Vanessa	Sarah	Roshel
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.

	Vanessa	Sarah	Roshel
Before	9 u	12 u	16 u
Change	No change	+ 48	- 48
After	9 u	12 u + 48	16 u - 48

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

16 u - 48 = 12 u + 48
16 u - 12 u = 48 + 48 
4 u = 96

1 u = 96 ÷ 4 = 24

Amount that Roshel had more than Vanessa in the end
= 16 u - 48 - 9 u
= 7 u - 48
= 7 x 24 - 48
= 168 - 48
= $120

Answer(s): $120