Sarah, Ivory and Betty had a sum of money. The amount of money Sarah had was ²₃ of the amount of money Ivory had. The ratio of the amount of money Ivory had to the total amount of money Betty and Ivory had was 2: 5. After Betty gave $96 to Ivory, she had as much money as Ivory. How much more money did Betty have than Sarah in the end?

Sarah	Ivory	Betty
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	3x3 = 9 u
4 u	6 u	9 u

The amount that Ivory had is the repeated identity. Make the amount that Ivory had the same.  LCM of 3 and 2 is 6.

	Sarah	Ivory	Betty
Before	4 u	6 u	9 u
Change	No change	+ 96	- 96
After	4 u	6 u + 96	9 u - 96

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

9 u - 96 = 6 u + 96
9 u - 6 u = 96 + 96 
3 u = 192

1 u = 192 ÷ 3 = 64

Amount that Betty had more than Sarah in the end
= 9 u - 96 - 4 u
= 5 u - 96
= 5 x 64 - 96
= 320 - 96
= $224

Answer(s): $224