Erika, Julie and Nicole had a sum of money. The amount of money Erika had was ²₃ of the amount of money Julie had. The ratio of the amount of money Julie had to the total amount of money Nicole and Julie had was 4: 9. After Nicole gave $45 to Julie, she had as much money as Julie. How much more money did Nicole have than Erika in the end?

Erika	Julie	Nicole
2x4 = 8 u	3x4 = 12 u
	4x3 = 12 u	5x3 = 15 u
8 u	12 u	15 u

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

	Erika	Julie	Nicole
Before	8 u	12 u	15 u
Change	No change	+ 45	- 45
After	8 u	12 u + 45	15 u - 45

The amount that Nicole and Julie had in the end is the same.

15 u - 45 = 12 u + 45
15 u - 12 u = 45 + 45 
3 u = 90

1 u = 90 ÷ 3 = 30

Amount that Nicole had more than Erika in the end
= 15 u - 45 - 8 u
= 7 u - 45
= 7 x 30 - 45
= 210 - 45
= $165

Answer(s): $165