Betty, Erika and Ivory had a sum of money. The amount of money Betty had was ²₃ of the amount of money Erika had. The ratio of the amount of money Erika had to the total amount of money Ivory and Erika had was 2: 7. After Ivory gave $36 to Erika, she had as much money as Erika. How much more money did Ivory have than Betty in the end?

Betty	Erika	Ivory
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	5x3 = 15 u
4 u	6 u	15 u

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

	Betty	Erika	Ivory
Before	4 u	6 u	15 u
Change	No change	+ 36	- 36
After	4 u	6 u + 36	15 u - 36

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

15 u - 36 = 6 u + 36
15 u - 6 u = 36 + 36 
9 u = 72

1 u = 72 ÷ 9 = 8

Amount that Ivory had more than Betty in the end
= 15 u - 36 - 4 u
= 11 u - 36
= 11 x 8 - 36
= 88 - 36
= $52

Answer(s): $52