Lucy, Nicole and Elyse had a sum of money. The amount of money Lucy had was ³₅ of the amount of money Nicole had. The ratio of the amount of money Nicole had to the total amount of money Elyse and Nicole had was 3: 7. After Elyse gave $10 to Nicole, she had as much money as Nicole. How much more money did Elyse have than Lucy in the end?

Lucy	Nicole	Elyse
3x3 = 9 u	5x3 = 15 u
	3x5 = 15 u	4x5 = 20 u
9 u	15 u	20 u

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

	Lucy	Nicole	Elyse
Before	9 u	15 u	20 u
Change	No change	+ 10	- 10
After	9 u	15 u + 10	20 u - 10

The amount that Elyse and Nicole had in the end is the same.

20 u - 10 = 15 u + 10
20 u - 15 u = 10 + 10 
5 u = 20

1 u = 20 ÷ 5 = 4

Amount that Elyse had more than Lucy in the end
= 20 u - 10 - 9 u
= 11 u - 10
= 11 x 4 - 10
= 44 - 10
= $34

Answer(s): $34