Vanessa, Jean and Shannon had a sum of money. The amount of money Vanessa had was ²₃ of the amount of money Jean had. The ratio of the amount of money Jean had to the total amount of money Shannon and Jean had was 4: 9. After Shannon gave $33 to Jean, she had as much money as Jean. How much more money did Shannon have than Vanessa in the end?

Vanessa	Jean	Shannon
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

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

	Vanessa	Jean	Shannon
Before	8 u	12 u	15 u
Change	No change	+ 33	- 33
After	8 u	12 u + 33	15 u - 33

The amount that Shannon and Jean had in the end is the same.

15 u - 33 = 12 u + 33
15 u - 12 u = 33 + 33 
3 u = 66

1 u = 66 ÷ 3 = 22

Amount that Shannon had more than Vanessa in the end
= 15 u - 33 - 8 u
= 7 u - 33
= 7 x 22 - 33
= 154 - 33
= $121

Answer(s): $121