Nicole, Julie and Opal had a sum of money. The amount of money Nicole 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 Opal and Julie had was 2: 5. After Opal gave $78 to Julie, she had as much money as Julie. How much more money did Opal have than Nicole in the end?

Nicole	Julie	Opal
2x2 = 4 u	3x2 = 6 u
	2x3 = 6 u	3x3 = 9 u
4 u	6 u	9 u

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

	Nicole	Julie	Opal
Before	4 u	6 u	9 u
Change	No change	+ 78	- 78
After	4 u	6 u + 78	9 u - 78

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

9 u - 78 = 6 u + 78
9 u - 6 u = 78 + 78 
3 u = 156

1 u = 156 ÷ 3 = 52

Amount that Opal had more than Nicole in the end
= 9 u - 78 - 4 u
= 5 u - 78
= 5 x 52 - 78
= 260 - 78
= $182

Answer(s): $182