Vanessa, Cathy and Lucy had a sum of money. The amount of money Vanessa had was ³₅ of the amount of money Cathy had. The ratio of the amount of money Cathy had to the total amount of money Lucy and Cathy had was 3: 7. After Lucy gave $25 to Cathy, she had as much money as Cathy. How much more money did Lucy have than Vanessa in the end?

Vanessa	Cathy	Lucy
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
9 u	15 u	20 u

The amount that Cathy had is the repeated identity. Make the amount that Cathy had the same.  LCM of 5 and 3 is 15.

	Vanessa	Cathy	Lucy
Before	9 u	15 u	20 u
Change	No change	+ 25	- 25
After	9 u	15 u + 25	20 u - 25

The amount that Lucy and Cathy had in the end is the same.

20 u - 25 = 15 u + 25
20 u - 15 u = 25 + 25 
5 u = 50

1 u = 50 ÷ 5 = 10

Amount that Lucy had more than Vanessa in the end
= 20 u - 25 - 9 u
= 11 u - 25
= 11 x 10 - 25
= 110 - 25
= $85

Answer(s): $85