Lucy, Usha and Ivory had a sum of money. The amount of money Lucy had was ³₄ of the amount of money Usha had. The ratio of the amount of money Usha had to the total amount of money Ivory and Usha had was 3: 7. After Ivory gave $4 to Usha, she had as much money as Usha. How much more money did Ivory have than Lucy in the end?

Lucy	Usha	Ivory
3x3 = 9 u	4x3 = 12 u
	3x4 = 12 u	4x4 = 16 u
9 u	12 u	16 u

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

	Lucy	Usha	Ivory
Before	9 u	12 u	16 u
Change	No change	+ 4	- 4
After	9 u	12 u + 4	16 u - 4

The amount that Ivory and Usha had in the end is the same.

16 u - 4 = 12 u + 4
16 u - 12 u = 4 + 4 
4 u = 8

1 u = 8 ÷ 4 = 2

Amount that Ivory had more than Lucy in the end
= 16 u - 4 - 9 u
= 7 u - 4
= 7 x 2 - 4
= 14 - 4
= $10

Answer(s): $10