Vanessa, Emma and Usha had a sum of money. The amount of money Vanessa had was ²₃ of the amount of money Emma had. The ratio of the amount of money Emma had to the total amount of money Usha and Emma had was 4: 9. After Usha gave $90 to Emma, she had as much money as Emma. How much more money did Usha have than Vanessa in the end?

Vanessa	Emma	Usha
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

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

	Vanessa	Emma	Usha
Before	8 u	12 u	15 u
Change	No change	+ 90	- 90
After	8 u	12 u + 90	15 u - 90

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

15 u - 90 = 12 u + 90
15 u - 12 u = 90 + 90 
3 u = 180

1 u = 180 ÷ 3 = 60

Amount that Usha had more than Vanessa in the end
= 15 u - 90 - 8 u
= 7 u - 90
= 7 x 60 - 90
= 420 - 90
= $330

Answer(s): $330